| 1 | MODULE chem_gasphase_mod |
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| 2 | !------------------------------------------------------------------------------! |
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| 3 | ! |
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| 4 | ! ******Module chem_gasphase_mod is automatically generated by kpp4palm ****** |
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| 5 | ! |
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| 6 | ! *********Please do NOT change this Code ********* |
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| 7 | ! |
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| 8 | !------------------------------------------------------------------------------! |
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| 9 | ! This file is part of the PALM model system. |
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| 10 | ! |
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| 11 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 12 | ! terms of the GNU General Public License as published by the Free Software |
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| 13 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 14 | ! version. |
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| 15 | ! |
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| 16 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 17 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 18 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 19 | ! |
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| 20 | ! You should have received a copy of the GNU General Public License along with |
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| 21 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 22 | ! |
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| 23 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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| 24 | !--------------------------------------------------------------------------------! |
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| 25 | ! |
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| 26 | ! Current revisions: |
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| 27 | ! ------------------ |
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| 28 | ! |
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| 29 | ! |
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| 30 | ! Former revisions: |
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| 31 | ! ----------------- |
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| 32 | ! $Id: module_header 2460 2017-09-13 14:47:48Z forkel $ |
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| 33 | ! Removed preprocessor directive __chem |
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| 34 | ! |
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| 35 | ! 2460 2017-09-13 14:47:48Z forkel |
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| 36 | ! |
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| 37 | ! |
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| 38 | ! Variables for photolyis added |
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| 39 | ! |
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| 40 | ! |
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| 41 | ! |
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| 42 | ! |
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| 43 | ! |
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| 44 | ! Nov. 2016: Intial version (Klaus Ketelsen) |
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| 45 | ! |
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| 46 | !------------------------------------------------------------------------------! |
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| 47 | ! |
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| 48 | |
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| 49 | |
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| 50 | ! Set kpp Double Precision to PALM Default Precision |
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| 51 | |
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| 52 | USE kinds, ONLY: dp=>wp |
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| 53 | |
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| 54 | USE pegrid, ONLY: myid,threads_per_task |
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| 55 | |
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| 56 | IMPLICIT NONE |
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| 57 | PRIVATE |
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| 58 | !SAVE ! NOTE: OCCURS AGAIN IN AUTOMATICALLY GENERATED CODE ... |
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| 59 | |
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| 60 | ! PUBLIC :: IERR_NAMES |
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| 61 | |
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| 62 | ! PUBLIC :: SPC_NAMES,EQN_NAMES,EQN_TAGS,REQ_HET,REQ_AEROSOL,REQ_PHOTRAT & |
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| 63 | ! ,REQ_MCFCT,IP_MAX,jname |
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| 64 | |
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| 65 | PUBLIC :: eqn_names, phot_names,spc_names |
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| 66 | PUBLIC :: nmaxfixsteps |
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| 67 | PUBLIC :: atol,rtol |
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| 68 | PUBLIC :: nspec,nreact |
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| 69 | PUBLIC :: temp |
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| 70 | PUBLIC :: phot |
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| 71 | PUBLIC :: rconst |
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| 72 | PUBLIC :: nvar |
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| 73 | PUBLIC :: nphot |
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| 74 | |
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| 75 | PUBLIC :: initialize,integrate,update_rconst |
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| 76 | PUBLIC :: chem_gasphase_integrate |
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| 77 | PUBLIC :: initialize_kpp_ctrl |
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| 78 | |
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| 79 | ! END OF MODULE HEADER TEMPLATE |
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| 80 | |
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| 81 | ! Variables used for vector mode |
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| 82 | |
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| 83 | LOGICAL, PARAMETER :: l_vector = .FALSE. |
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| 84 | INTEGER, PARAMETER :: i_lu_di = 0 |
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| 85 | INTEGER, PARAMETER :: vl_dim = 1 |
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| 86 | INTEGER :: vl |
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| 87 | |
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| 88 | INTEGER :: vl_glo |
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| 89 | INTEGER :: is,ie |
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| 90 | |
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| 91 | INTEGER, DIMENSION(vl_dim) :: kacc,krej |
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| 92 | INTEGER, DIMENSION(vl_dim) :: ierrv |
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| 93 | LOGICAL :: data_loaded = .false. |
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| 94 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 95 | ! |
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| 96 | ! Parameter Module File |
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| 97 | ! |
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| 98 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 99 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 100 | ! KPP is distributed under GPL,the general public licence |
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| 101 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 102 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 103 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 104 | ! With important contributions from: |
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| 105 | ! M. Damian,Villanova University,USA |
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| 106 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 107 | ! |
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| 108 | ! File : chem_gasphase_mod_Parameters.f90 |
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| 109 | ! Time : Fri Dec 8 11:54:15 2017 |
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| 110 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
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| 111 | ! Equation file : chem_gasphase_mod.kpp |
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| 112 | ! Output root filename : chem_gasphase_mod |
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| 113 | ! |
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| 114 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 115 | |
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| 116 | |
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| 117 | |
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| 118 | |
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| 119 | |
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| 120 | |
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| 121 | ! NSPEC - Number of chemical species |
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| 122 | INTEGER,PARAMETER :: nspec = 2 |
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| 123 | ! NVAR - Number of Variable species |
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| 124 | INTEGER,PARAMETER :: nvar = 2 |
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| 125 | ! NVARACT - Number of Active species |
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| 126 | INTEGER,PARAMETER :: nvaract = 2 |
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| 127 | ! NFIX - Number of Fixed species |
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| 128 | INTEGER,PARAMETER :: nfix = 1 |
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| 129 | ! NREACT - Number of reactions |
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| 130 | INTEGER,PARAMETER :: nreact = 2 |
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| 131 | ! NVARST - Starting of variables in conc. vect. |
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| 132 | INTEGER,PARAMETER :: nvarst = 1 |
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| 133 | ! NFIXST - Starting of fixed in conc. vect. |
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| 134 | INTEGER,PARAMETER :: nfixst = 3 |
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| 135 | ! NONZERO - Number of nonzero entries in Jacobian |
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| 136 | INTEGER,PARAMETER :: nonzero = 2 |
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| 137 | ! LU_NONZERO - Number of nonzero entries in LU factoriz. of Jacobian |
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| 138 | INTEGER,PARAMETER :: lu_nonzero = 2 |
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| 139 | ! CNVAR - (NVAR+1) Number of elements in compressed row format |
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| 140 | INTEGER,PARAMETER :: cnvar = 3 |
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| 141 | ! CNEQN - (NREACT+1) Number stoicm elements in compressed col format |
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| 142 | INTEGER,PARAMETER :: cneqn = 3 |
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| 143 | ! NHESS - Length of Sparse Hessian |
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| 144 | INTEGER,PARAMETER :: nhess = 1 |
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| 145 | ! NLOOKAT - Number of species to look at |
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| 146 | INTEGER,PARAMETER :: nlookat = 0 |
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| 147 | ! NMONITOR - Number of species to monitor |
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| 148 | INTEGER,PARAMETER :: nmonitor = 0 |
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| 149 | ! NMASS - Number of atoms to check mass balance |
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| 150 | INTEGER,PARAMETER :: nmass = 1 |
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| 151 | |
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| 152 | ! Index declaration for variable species in C and VAR |
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| 153 | ! VAR(ind_spc) = C(ind_spc) |
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| 154 | |
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| 155 | INTEGER,PARAMETER,PUBLIC :: ind_pm10 = 1 |
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| 156 | INTEGER,PARAMETER,PUBLIC :: ind_pm25 = 2 |
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| 157 | |
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| 158 | ! Index declaration for fixed species in C |
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| 159 | ! C(ind_spc) |
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| 160 | |
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| 161 | |
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| 162 | ! Index declaration for fixed species in FIX |
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| 163 | ! FIX(indf_spc) = C(ind_spc) = C(NVAR+indf_spc) |
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| 164 | |
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| 165 | |
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| 166 | ! NJVRP - Length of sparse Jacobian JVRP |
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| 167 | INTEGER,PARAMETER :: njvrp = 2 |
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| 168 | |
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| 169 | ! NSTOICM - Length of Sparse Stoichiometric Matrix |
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| 170 | INTEGER,PARAMETER :: nstoicm = 1 |
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| 171 | |
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| 172 | |
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| 173 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 174 | ! |
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| 175 | ! Global Data Module File |
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| 176 | ! |
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| 177 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 178 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 179 | ! KPP is distributed under GPL,the general public licence |
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| 180 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 181 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 182 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 183 | ! With important contributions from: |
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| 184 | ! M. Damian,Villanova University,USA |
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| 185 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 186 | ! |
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| 187 | ! File : chem_gasphase_mod_Global.f90 |
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| 188 | ! Time : Fri Dec 8 11:54:15 2017 |
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| 189 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
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| 190 | ! Equation file : chem_gasphase_mod.kpp |
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| 191 | ! Output root filename : chem_gasphase_mod |
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| 192 | ! |
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| 193 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 194 | |
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| 195 | |
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| 196 | |
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| 197 | |
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| 198 | |
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| 199 | |
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| 200 | ! Declaration of global variables |
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| 201 | |
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| 202 | ! C - Concentration of all species |
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| 203 | REAL(kind=dp):: c(nspec) |
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| 204 | ! VAR - Concentrations of variable species (global) |
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| 205 | REAL(kind=dp):: var(nvar) |
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| 206 | ! FIX - Concentrations of fixed species (global) |
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| 207 | REAL(kind=dp):: fix(nfix) |
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| 208 | ! VAR,FIX are chunks of array C |
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| 209 | equivalence( c(1),var(1)) |
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| 210 | ! RCONST - Rate constants (global) |
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| 211 | REAL(kind=dp):: rconst(nreact) |
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| 212 | ! TIME - Current integration time |
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| 213 | REAL(kind=dp):: time |
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| 214 | ! SUN - Sunlight intensity between [0,1] |
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| 215 | REAL(kind=dp):: sun |
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| 216 | ! TEMP - Temperature |
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| 217 | REAL(dp),dimension(:),allocatable :: temp |
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| 218 | ! RTOLS - (scalar) Relative tolerance |
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| 219 | REAL(kind=dp):: rtols |
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| 220 | ! TSTART - Integration start time |
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| 221 | REAL(kind=dp):: tstart |
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| 222 | ! TEND - Integration end time |
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| 223 | REAL(kind=dp):: tend |
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| 224 | ! DT - Integration step |
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| 225 | REAL(kind=dp):: dt |
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| 226 | ! ATOL - Absolute tolerance |
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| 227 | REAL(kind=dp):: atol(nvar) |
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| 228 | ! RTOL - Relative tolerance |
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| 229 | REAL(kind=dp):: rtol(nvar) |
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| 230 | ! STEPMIN - Lower bound for integration step |
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| 231 | REAL(kind=dp):: stepmin |
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| 232 | ! STEPMAX - Upper bound for integration step |
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| 233 | REAL(kind=dp):: stepmax |
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| 234 | ! CFACTOR - Conversion factor for concentration units |
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| 235 | REAL(kind=dp):: cfactor |
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| 236 | ! DDMTYPE - DDM sensitivity w.r.t.: 0=init.val.,1=params |
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| 237 | INTEGER :: ddmtype |
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| 238 | |
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| 239 | ! INLINED global variable declarations |
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| 240 | |
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| 241 | ! declaration of global variable declarations for photolysis will come from |
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| 242 | |
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| 243 | ! INLINED global variable declarations |
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| 244 | |
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| 245 | |
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| 246 | |
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| 247 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 248 | ! |
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| 249 | ! Sparse Jacobian Data Structures File |
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| 250 | ! |
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| 251 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 252 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 253 | ! KPP is distributed under GPL,the general public licence |
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| 254 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 255 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 256 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 257 | ! With important contributions from: |
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| 258 | ! M. Damian,Villanova University,USA |
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| 259 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 260 | ! |
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| 261 | ! File : chem_gasphase_mod_JacobianSP.f90 |
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| 262 | ! Time : Fri Dec 8 11:54:15 2017 |
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| 263 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
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| 264 | ! Equation file : chem_gasphase_mod.kpp |
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| 265 | ! Output root filename : chem_gasphase_mod |
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| 266 | ! |
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| 267 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 268 | |
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| 269 | |
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| 270 | |
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| 271 | |
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| 272 | |
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| 273 | |
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| 274 | ! Sparse Jacobian Data |
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| 275 | |
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| 276 | |
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| 277 | INTEGER,PARAMETER,DIMENSION(2):: lu_irow = (/ & |
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| 278 | 1, 2 /) |
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| 279 | |
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| 280 | INTEGER,PARAMETER,DIMENSION(2):: lu_icol = (/ & |
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| 281 | 1, 2 /) |
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| 282 | |
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| 283 | INTEGER,PARAMETER,DIMENSION(3):: lu_crow = (/ & |
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| 284 | 1, 2, 3 /) |
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| 285 | |
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| 286 | INTEGER,PARAMETER,DIMENSION(3):: lu_diag = (/ & |
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| 287 | 1, 2, 3 /) |
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| 288 | |
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| 289 | |
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| 290 | |
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| 291 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 292 | ! |
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| 293 | ! Utility Data Module File |
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| 294 | ! |
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| 295 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 296 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 297 | ! KPP is distributed under GPL,the general public licence |
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| 298 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 299 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 300 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 301 | ! With important contributions from: |
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| 302 | ! M. Damian,Villanova University,USA |
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| 303 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 304 | ! |
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| 305 | ! File : chem_gasphase_mod_Monitor.f90 |
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| 306 | ! Time : Fri Dec 8 11:54:15 2017 |
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| 307 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
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| 308 | ! Equation file : chem_gasphase_mod.kpp |
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| 309 | ! Output root filename : chem_gasphase_mod |
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| 310 | ! |
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| 311 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 312 | |
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| 313 | |
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| 314 | |
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| 315 | |
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| 316 | |
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| 317 | CHARACTER(len=15),PARAMETER,DIMENSION(2):: spc_names = (/ & |
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| 318 | 'PM10 ','PM25 ' /) |
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| 319 | |
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| 320 | INTEGER,DIMENSION(1):: lookat |
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| 321 | INTEGER,DIMENSION(1):: monitor |
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| 322 | CHARACTER(len=15),DIMENSION(1):: smass |
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| 323 | CHARACTER(len=100),PARAMETER,DIMENSION(2):: eqn_names = (/ & |
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| 324 | 'PM10 --> PM10 ',& |
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| 325 | 'PM25 --> PM25 ' /) |
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| 326 | |
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| 327 | ! INLINED global variables |
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| 328 | |
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| 329 | ! inline f90_data: declaration of global variables for photolysis |
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| 330 | ! REAL(kind=dp):: phot(nphot)must eventually be moved to global later for |
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| 331 | INTEGER,PARAMETER :: nphot = 1 |
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| 332 | ! phot photolysis frequencies |
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| 333 | REAL(kind=dp):: phot(nphot) |
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| 334 | |
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| 335 | INTEGER,PARAMETER,PUBLIC :: j_no2 = 1 |
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| 336 | |
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| 337 | CHARACTER(len=15),PARAMETER,DIMENSION(nphot):: phot_names = (/ & |
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| 338 | 'J_NO2 '/) |
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| 339 | |
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| 340 | ! End INLINED global variables |
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| 341 | |
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| 342 | |
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| 343 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 344 | |
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| 345 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 346 | |
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| 347 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 348 | |
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| 349 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 350 | |
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| 351 | |
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| 352 | ! variable definations from individual module headers |
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| 353 | |
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| 354 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 355 | ! |
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| 356 | ! Initialization File |
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| 357 | ! |
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| 358 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 359 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 360 | ! KPP is distributed under GPL,the general public licence |
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| 361 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 362 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 363 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 364 | ! With important contributions from: |
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| 365 | ! M. Damian,Villanova University,USA |
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| 366 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 367 | ! |
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| 368 | ! File : chem_gasphase_mod_Initialize.f90 |
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| 369 | ! Time : Fri Dec 8 11:54:15 2017 |
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| 370 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
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| 371 | ! Equation file : chem_gasphase_mod.kpp |
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| 372 | ! Output root filename : chem_gasphase_mod |
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| 373 | ! |
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| 374 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 375 | |
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| 376 | |
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| 377 | |
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| 378 | |
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| 379 | |
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| 380 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 381 | ! |
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| 382 | ! Numerical Integrator (Time-Stepping) File |
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| 383 | ! |
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| 384 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 385 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 386 | ! KPP is distributed under GPL,the general public licence |
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| 387 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 388 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 389 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 390 | ! With important contributions from: |
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| 391 | ! M. Damian,Villanova University,USA |
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| 392 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 393 | ! |
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| 394 | ! File : chem_gasphase_mod_Integrator.f90 |
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| 395 | ! Time : Fri Dec 8 11:54:15 2017 |
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| 396 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
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| 397 | ! Equation file : chem_gasphase_mod.kpp |
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| 398 | ! Output root filename : chem_gasphase_mod |
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| 399 | ! |
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| 400 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 401 | |
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| 402 | |
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| 403 | |
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| 404 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 405 | ! |
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| 406 | ! INTEGRATE - Integrator routine |
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| 407 | ! Arguments : |
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| 408 | ! TIN - Start Time for Integration |
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| 409 | ! TOUT - End Time for Integration |
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| 410 | ! |
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| 411 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 412 | |
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| 413 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 414 | ! Rosenbrock - Implementation of several Rosenbrock methods: ! |
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| 415 | ! *Ros2 ! |
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| 416 | ! *Ros3 ! |
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| 417 | ! *Ros4 ! |
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| 418 | ! *Rodas3 ! |
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| 419 | ! *Rodas4 ! |
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| 420 | ! By default the code employs the KPP sparse linear algebra routines ! |
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| 421 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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| 422 | ! ! |
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| 423 | ! (C) Adrian Sandu,August 2004 ! |
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| 424 | ! Virginia Polytechnic Institute and State University ! |
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| 425 | ! Contact: sandu@cs.vt.edu ! |
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| 426 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 ! ! |
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| 427 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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| 428 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 429 | |
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| 430 | |
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| 431 | SAVE |
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| 432 | |
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| 433 | !~~~> statistics on the work performed by the rosenbrock method |
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| 434 | INTEGER,PARAMETER :: nfun=1,njac=2,nstp=3,nacc=4,& |
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| 435 | nrej=5,ndec=6,nsol=7,nsng=8,& |
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| 436 | ntexit=1,nhexit=2,nhnew = 3 |
|---|
| 437 | |
|---|
| 438 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 439 | ! |
|---|
| 440 | ! Linear Algebra Data and Routines File |
|---|
| 441 | ! |
|---|
| 442 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 443 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 444 | ! KPP is distributed under GPL,the general public licence |
|---|
| 445 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 446 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 447 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 448 | ! With important contributions from: |
|---|
| 449 | ! M. Damian,Villanova University,USA |
|---|
| 450 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 451 | ! |
|---|
| 452 | ! File : chem_gasphase_mod_LinearAlgebra.f90 |
|---|
| 453 | ! Time : Fri Dec 8 11:54:15 2017 |
|---|
| 454 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
|---|
| 455 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 456 | ! Output root filename : chem_gasphase_mod |
|---|
| 457 | ! |
|---|
| 458 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 459 | |
|---|
| 460 | |
|---|
| 461 | |
|---|
| 462 | |
|---|
| 463 | |
|---|
| 464 | |
|---|
| 465 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 466 | ! |
|---|
| 467 | ! The ODE Jacobian of Chemical Model File |
|---|
| 468 | ! |
|---|
| 469 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 470 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 471 | ! KPP is distributed under GPL,the general public licence |
|---|
| 472 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 473 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 474 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 475 | ! With important contributions from: |
|---|
| 476 | ! M. Damian,Villanova University,USA |
|---|
| 477 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 478 | ! |
|---|
| 479 | ! File : chem_gasphase_mod_Jacobian.f90 |
|---|
| 480 | ! Time : Fri Dec 8 11:54:15 2017 |
|---|
| 481 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
|---|
| 482 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 483 | ! Output root filename : chem_gasphase_mod |
|---|
| 484 | ! |
|---|
| 485 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 486 | |
|---|
| 487 | |
|---|
| 488 | |
|---|
| 489 | |
|---|
| 490 | |
|---|
| 491 | |
|---|
| 492 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 493 | ! |
|---|
| 494 | ! The ODE Function of Chemical Model File |
|---|
| 495 | ! |
|---|
| 496 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 497 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 498 | ! KPP is distributed under GPL,the general public licence |
|---|
| 499 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 500 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 501 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 502 | ! With important contributions from: |
|---|
| 503 | ! M. Damian,Villanova University,USA |
|---|
| 504 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 505 | ! |
|---|
| 506 | ! File : chem_gasphase_mod_Function.f90 |
|---|
| 507 | ! Time : Fri Dec 8 11:54:15 2017 |
|---|
| 508 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
|---|
| 509 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 510 | ! Output root filename : chem_gasphase_mod |
|---|
| 511 | ! |
|---|
| 512 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 513 | |
|---|
| 514 | |
|---|
| 515 | |
|---|
| 516 | |
|---|
| 517 | |
|---|
| 518 | ! A - Rate for each equation |
|---|
| 519 | REAL(kind=dp):: a(nreact) |
|---|
| 520 | |
|---|
| 521 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 522 | ! |
|---|
| 523 | ! The Reaction Rates File |
|---|
| 524 | ! |
|---|
| 525 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 526 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 527 | ! KPP is distributed under GPL,the general public licence |
|---|
| 528 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 529 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 530 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 531 | ! With important contributions from: |
|---|
| 532 | ! M. Damian,Villanova University,USA |
|---|
| 533 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 534 | ! |
|---|
| 535 | ! File : chem_gasphase_mod_Rates.f90 |
|---|
| 536 | ! Time : Fri Dec 8 11:54:15 2017 |
|---|
| 537 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
|---|
| 538 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 539 | ! Output root filename : chem_gasphase_mod |
|---|
| 540 | ! |
|---|
| 541 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 542 | |
|---|
| 543 | |
|---|
| 544 | |
|---|
| 545 | |
|---|
| 546 | |
|---|
| 547 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 548 | ! |
|---|
| 549 | ! Auxiliary Routines File |
|---|
| 550 | ! |
|---|
| 551 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 552 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 553 | ! KPP is distributed under GPL,the general public licence |
|---|
| 554 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 555 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 556 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 557 | ! With important contributions from: |
|---|
| 558 | ! M. Damian,Villanova University,USA |
|---|
| 559 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 560 | ! |
|---|
| 561 | ! File : chem_gasphase_mod_Util.f90 |
|---|
| 562 | ! Time : Fri Dec 8 11:54:15 2017 |
|---|
| 563 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20171117/GASPHASE_PREPROC/tmp_kpp4palm |
|---|
| 564 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 565 | ! Output root filename : chem_gasphase_mod |
|---|
| 566 | ! |
|---|
| 567 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 568 | |
|---|
| 569 | |
|---|
| 570 | |
|---|
| 571 | |
|---|
| 572 | |
|---|
| 573 | |
|---|
| 574 | ! header MODULE initialize_kpp_ctrl_template |
|---|
| 575 | |
|---|
| 576 | ! notes: |
|---|
| 577 | ! - l_vector is automatically defined by kp4 |
|---|
| 578 | ! - vl_dim is automatically defined by kp4 |
|---|
| 579 | ! - i_lu_di is automatically defined by kp4 |
|---|
| 580 | ! - wanted is automatically defined by xmecca |
|---|
| 581 | ! - icntrl rcntrl are automatically defined by kpp |
|---|
| 582 | ! - "USE messy_main_tools" is in MODULE_header of messy_mecca_kpp.f90 |
|---|
| 583 | ! - SAVE will be automatically added by kp4 |
|---|
| 584 | |
|---|
| 585 | !SAVE |
|---|
| 586 | |
|---|
| 587 | ! for fixed time step control |
|---|
| 588 | ! ... max. number of fixed time steps (sum must be 1) |
|---|
| 589 | INTEGER,PARAMETER :: nmaxfixsteps = 50 |
|---|
| 590 | ! ... switch for fixed time stepping |
|---|
| 591 | LOGICAL,PUBLIC :: l_fixed_step = .false. |
|---|
| 592 | INTEGER,PUBLIC :: nfsteps = 1 |
|---|
| 593 | ! ... number of kpp control PARAMETERs |
|---|
| 594 | INTEGER,PARAMETER,PUBLIC :: nkppctrl = 20 |
|---|
| 595 | ! |
|---|
| 596 | INTEGER, DIMENSION(nkppctrl),PUBLIC :: icntrl = 0 |
|---|
| 597 | REAL(dp),DIMENSION(nkppctrl),PUBLIC :: rcntrl = 0.0_dp |
|---|
| 598 | REAL(dp),DIMENSION(nmaxfixsteps),PUBLIC :: t_steps = 0.0_dp |
|---|
| 599 | |
|---|
| 600 | ! END header MODULE initialize_kpp_ctrl_template |
|---|
| 601 | |
|---|
| 602 | |
|---|
| 603 | ! Interface Block |
|---|
| 604 | |
|---|
| 605 | INTERFACE initialize |
|---|
| 606 | MODULE PROCEDURE initialize |
|---|
| 607 | END INTERFACE initialize |
|---|
| 608 | |
|---|
| 609 | INTERFACE integrate |
|---|
| 610 | MODULE PROCEDURE integrate |
|---|
| 611 | END INTERFACE integrate |
|---|
| 612 | |
|---|
| 613 | INTERFACE fun |
|---|
| 614 | MODULE PROCEDURE fun |
|---|
| 615 | END INTERFACE fun |
|---|
| 616 | |
|---|
| 617 | INTERFACE kppsolve |
|---|
| 618 | MODULE PROCEDURE kppsolve |
|---|
| 619 | END INTERFACE kppsolve |
|---|
| 620 | |
|---|
| 621 | INTERFACE kppdecomp |
|---|
| 622 | MODULE PROCEDURE kppdecomp |
|---|
| 623 | END INTERFACE kppdecomp |
|---|
| 624 | |
|---|
| 625 | INTERFACE wlamch |
|---|
| 626 | MODULE PROCEDURE wlamch |
|---|
| 627 | END INTERFACE wlamch |
|---|
| 628 | |
|---|
| 629 | INTERFACE wlamch_add |
|---|
| 630 | MODULE PROCEDURE wlamch_add |
|---|
| 631 | END INTERFACE wlamch_add |
|---|
| 632 | |
|---|
| 633 | INTERFACE jac_sp |
|---|
| 634 | MODULE PROCEDURE jac_sp |
|---|
| 635 | END INTERFACE jac_sp |
|---|
| 636 | |
|---|
| 637 | INTERFACE k_arr |
|---|
| 638 | MODULE PROCEDURE k_arr |
|---|
| 639 | END INTERFACE k_arr |
|---|
| 640 | |
|---|
| 641 | INTERFACE update_rconst |
|---|
| 642 | MODULE PROCEDURE update_rconst |
|---|
| 643 | END INTERFACE update_rconst |
|---|
| 644 | |
|---|
| 645 | INTERFACE arr2 |
|---|
| 646 | MODULE PROCEDURE arr2 |
|---|
| 647 | END INTERFACE arr2 |
|---|
| 648 | |
|---|
| 649 | INTERFACE initialize_kpp_ctrl |
|---|
| 650 | MODULE PROCEDURE initialize_kpp_ctrl |
|---|
| 651 | END INTERFACE initialize_kpp_ctrl |
|---|
| 652 | |
|---|
| 653 | INTERFACE error_output |
|---|
| 654 | MODULE PROCEDURE error_output |
|---|
| 655 | END INTERFACE error_output |
|---|
| 656 | |
|---|
| 657 | !interface not working INTERFACE wcopy |
|---|
| 658 | !interface not working MODULE PROCEDURE wcopy |
|---|
| 659 | !interface not working END INTERFACE wcopy |
|---|
| 660 | |
|---|
| 661 | INTERFACE wscal |
|---|
| 662 | MODULE PROCEDURE wscal |
|---|
| 663 | END INTERFACE wscal |
|---|
| 664 | |
|---|
| 665 | !interface not working INTERFACE waxpy |
|---|
| 666 | !interface not working MODULE PROCEDURE waxpy |
|---|
| 667 | !interface not working END INTERFACE waxpy |
|---|
| 668 | |
|---|
| 669 | INTERFACE rosenbrock |
|---|
| 670 | MODULE PROCEDURE rosenbrock |
|---|
| 671 | END INTERFACE rosenbrock |
|---|
| 672 | |
|---|
| 673 | INTERFACE funtemplate |
|---|
| 674 | MODULE PROCEDURE funtemplate |
|---|
| 675 | END INTERFACE funtemplate |
|---|
| 676 | |
|---|
| 677 | INTERFACE jactemplate |
|---|
| 678 | MODULE PROCEDURE jactemplate |
|---|
| 679 | END INTERFACE jactemplate |
|---|
| 680 | |
|---|
| 681 | INTERFACE chem_gasphase_integrate |
|---|
| 682 | MODULE PROCEDURE chem_gasphase_integrate |
|---|
| 683 | END INTERFACE chem_gasphase_integrate |
|---|
| 684 | |
|---|
| 685 | INTERFACE fill_temp |
|---|
| 686 | MODULE PROCEDURE fill_temp |
|---|
| 687 | END INTERFACE fill_temp |
|---|
| 688 | PUBLIC fill_temp |
|---|
| 689 | |
|---|
| 690 | |
|---|
| 691 | CONTAINS |
|---|
| 692 | |
|---|
| 693 | SUBROUTINE initialize() |
|---|
| 694 | |
|---|
| 695 | |
|---|
| 696 | |
|---|
| 697 | INTEGER :: i |
|---|
| 698 | REAL(kind=dp):: x |
|---|
| 699 | |
|---|
| 700 | cfactor = 1.000000e+00_dp |
|---|
| 701 | |
|---|
| 702 | x = (0.)*cfactor |
|---|
| 703 | DO i = 1,nvar |
|---|
| 704 | var(i) = x |
|---|
| 705 | ENDDO |
|---|
| 706 | |
|---|
| 707 | x = (0.)*cfactor |
|---|
| 708 | DO i = 1,nfix |
|---|
| 709 | fix(i) = x |
|---|
| 710 | ENDDO |
|---|
| 711 | |
|---|
| 712 | ! constant rate coefficients |
|---|
| 713 | ! END constant rate coefficients |
|---|
| 714 | |
|---|
| 715 | ! INLINED initializations |
|---|
| 716 | |
|---|
| 717 | ! End INLINED initializations |
|---|
| 718 | |
|---|
| 719 | |
|---|
| 720 | END SUBROUTINE initialize |
|---|
| 721 | |
|---|
| 722 | SUBROUTINE integrate( tin,tout,& |
|---|
| 723 | icntrl_u,rcntrl_u,istatus_u,rstatus_u,ierr_u) |
|---|
| 724 | |
|---|
| 725 | |
|---|
| 726 | REAL(kind=dp),INTENT(in):: tin ! start time |
|---|
| 727 | REAL(kind=dp),INTENT(in):: tout ! END time |
|---|
| 728 | ! OPTIONAL input PARAMETERs and statistics |
|---|
| 729 | INTEGER, INTENT(in), OPTIONAL :: icntrl_u(20) |
|---|
| 730 | REAL(kind=dp),INTENT(in), OPTIONAL :: rcntrl_u(20) |
|---|
| 731 | INTEGER, INTENT(out),OPTIONAL :: istatus_u(20) |
|---|
| 732 | REAL(kind=dp),INTENT(out),OPTIONAL :: rstatus_u(20) |
|---|
| 733 | INTEGER, INTENT(out),OPTIONAL :: ierr_u |
|---|
| 734 | |
|---|
| 735 | REAL(kind=dp):: rcntrl(20),rstatus(20) |
|---|
| 736 | INTEGER :: icntrl(20),istatus(20),ierr |
|---|
| 737 | |
|---|
| 738 | INTEGER,SAVE :: ntotal = 0 |
|---|
| 739 | |
|---|
| 740 | icntrl(:) = 0 |
|---|
| 741 | rcntrl(:) = 0.0_dp |
|---|
| 742 | istatus(:) = 0 |
|---|
| 743 | rstatus(:) = 0.0_dp |
|---|
| 744 | |
|---|
| 745 | !~~~> fine-tune the integrator: |
|---|
| 746 | icntrl(1) = 0 ! 0 - non- autonomous,1 - autonomous |
|---|
| 747 | icntrl(2) = 0 ! 0 - vector tolerances,1 - scalars |
|---|
| 748 | |
|---|
| 749 | ! IF OPTIONAL PARAMETERs are given,and IF they are >0, |
|---|
| 750 | ! THEN they overwrite default settings. |
|---|
| 751 | IF (present(icntrl_u))THEN |
|---|
| 752 | where(icntrl_u(:)> 0)icntrl(:) = icntrl_u(:) |
|---|
| 753 | ENDIF |
|---|
| 754 | IF (present(rcntrl_u))THEN |
|---|
| 755 | where(rcntrl_u(:)> 0)rcntrl(:) = rcntrl_u(:) |
|---|
| 756 | ENDIF |
|---|
| 757 | |
|---|
| 758 | |
|---|
| 759 | CALL rosenbrock(nvar,var,tin,tout, & |
|---|
| 760 | atol,rtol, & |
|---|
| 761 | rcntrl,icntrl,rstatus,istatus,ierr) |
|---|
| 762 | |
|---|
| 763 | !~~~> debug option: show no of steps |
|---|
| 764 | ! ntotal = ntotal + istatus(nstp) |
|---|
| 765 | ! PRINT*,'NSTEPS=',ISTATUS(Nstp),' (',Ntotal,')',' O3=',VAR(ind_O3) |
|---|
| 766 | |
|---|
| 767 | stepmin = rstatus(nhexit) |
|---|
| 768 | ! IF OPTIONAL PARAMETERs are given for output they |
|---|
| 769 | ! are updated with the RETURN information |
|---|
| 770 | IF (present(istatus_u))istatus_u(:) = istatus(:) |
|---|
| 771 | IF (present(rstatus_u))rstatus_u(:) = rstatus(:) |
|---|
| 772 | IF (present(ierr_u)) ierr_u = ierr |
|---|
| 773 | |
|---|
| 774 | END SUBROUTINE integrate |
|---|
| 775 | |
|---|
| 776 | SUBROUTINE fun(v,f,rct,vdot) |
|---|
| 777 | |
|---|
| 778 | ! V - Concentrations of variable species (local) |
|---|
| 779 | REAL(kind=dp):: v(nvar) |
|---|
| 780 | ! F - Concentrations of fixed species (local) |
|---|
| 781 | REAL(kind=dp):: f(nfix) |
|---|
| 782 | ! RCT - Rate constants (local) |
|---|
| 783 | REAL(kind=dp):: rct(nreact) |
|---|
| 784 | ! Vdot - Time derivative of variable species concentrations |
|---|
| 785 | REAL(kind=dp):: vdot(nvar) |
|---|
| 786 | |
|---|
| 787 | |
|---|
| 788 | ! Computation of equation rates |
|---|
| 789 | |
|---|
| 790 | ! Aggregate function |
|---|
| 791 | vdot(1) = 0 |
|---|
| 792 | vdot(2) = 0 |
|---|
| 793 | |
|---|
| 794 | END SUBROUTINE fun |
|---|
| 795 | |
|---|
| 796 | SUBROUTINE kppsolve(jvs,x) |
|---|
| 797 | |
|---|
| 798 | ! JVS - sparse Jacobian of variables |
|---|
| 799 | REAL(kind=dp):: jvs(lu_nonzero) |
|---|
| 800 | ! X - Vector for variables |
|---|
| 801 | REAL(kind=dp):: x(nvar) |
|---|
| 802 | |
|---|
| 803 | x(2) = x(2)/ jvs(2) |
|---|
| 804 | x(1) = x(1)/ jvs(1) |
|---|
| 805 | |
|---|
| 806 | END SUBROUTINE kppsolve |
|---|
| 807 | |
|---|
| 808 | SUBROUTINE kppdecomp( jvs,ier) |
|---|
| 809 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 810 | ! Sparse LU factorization |
|---|
| 811 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 812 | |
|---|
| 813 | |
|---|
| 814 | INTEGER :: ier |
|---|
| 815 | REAL(kind=dp):: jvs(lu_nonzero),w(nvar),a |
|---|
| 816 | INTEGER :: k,kk,j,jj |
|---|
| 817 | |
|---|
| 818 | a = 0. ! mz_rs_20050606 |
|---|
| 819 | ier = 0 |
|---|
| 820 | DO k=1,nvar |
|---|
| 821 | ! mz_rs_20050606: don't check if real value == 0 |
|---|
| 822 | ! IF(jvs( lu_diag(k)).eq. 0.)THEN |
|---|
| 823 | IF(abs(jvs(lu_diag(k)))< tiny(a))THEN |
|---|
| 824 | ier = k |
|---|
| 825 | RETURN |
|---|
| 826 | ENDIF |
|---|
| 827 | DO kk = lu_crow(k),lu_crow(k+ 1)- 1 |
|---|
| 828 | w( lu_icol(kk)) = jvs(kk) |
|---|
| 829 | ENDDO |
|---|
| 830 | DO kk = lu_crow(k),lu_diag(k)- 1 |
|---|
| 831 | j = lu_icol(kk) |
|---|
| 832 | a = - w(j)/ jvs( lu_diag(j)) |
|---|
| 833 | w(j) = - a |
|---|
| 834 | DO jj = lu_diag(j)+ 1,lu_crow(j+ 1)- 1 |
|---|
| 835 | w( lu_icol(jj)) = w( lu_icol(jj))+ a*jvs(jj) |
|---|
| 836 | ENDDO |
|---|
| 837 | ENDDO |
|---|
| 838 | DO kk = lu_crow(k),lu_crow(k+ 1)- 1 |
|---|
| 839 | jvs(kk) = w( lu_icol(kk)) |
|---|
| 840 | ENDDO |
|---|
| 841 | ENDDO |
|---|
| 842 | |
|---|
| 843 | END SUBROUTINE kppdecomp |
|---|
| 844 | |
|---|
| 845 | REAL(kind=dp)FUNCTION wlamch( c) |
|---|
| 846 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 847 | ! returns epsilon machine |
|---|
| 848 | ! after LAPACK |
|---|
| 849 | ! replace this by the function from the optimized LAPACK implementation: |
|---|
| 850 | ! CALL SLAMCH('E') or CALL DLAMCH('E') |
|---|
| 851 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 852 | ! USE chem_gasphase_mod_Precision |
|---|
| 853 | |
|---|
| 854 | CHARACTER :: c |
|---|
| 855 | INTEGER :: i |
|---|
| 856 | REAL(kind=dp),SAVE :: eps |
|---|
| 857 | REAL(kind=dp) :: suma |
|---|
| 858 | REAL(kind=dp),PARAMETER :: one=1.0_dp, half=0.5_dp |
|---|
| 859 | LOGICAL,SAVE :: first=.true. |
|---|
| 860 | |
|---|
| 861 | IF (first)THEN |
|---|
| 862 | first = .false. |
|---|
| 863 | eps = half**(16) |
|---|
| 864 | DO i = 17,80 |
|---|
| 865 | eps = eps*half |
|---|
| 866 | CALL wlamch_add(one,eps,suma) |
|---|
| 867 | IF (suma.le.one)goto 10 |
|---|
| 868 | ENDDO |
|---|
| 869 | PRINT*,'ERROR IN WLAMCH. EPS < ',Eps |
|---|
| 870 | RETURN |
|---|
| 871 | 10 eps = eps*2 |
|---|
| 872 | i = i- 1 |
|---|
| 873 | ENDIF |
|---|
| 874 | |
|---|
| 875 | wlamch = eps |
|---|
| 876 | |
|---|
| 877 | END FUNCTION wlamch |
|---|
| 878 | |
|---|
| 879 | SUBROUTINE wlamch_add( a,b,suma) |
|---|
| 880 | ! USE chem_gasphase_mod_Precision |
|---|
| 881 | |
|---|
| 882 | REAL(kind=dp)a,b,suma |
|---|
| 883 | suma = a + b |
|---|
| 884 | |
|---|
| 885 | END SUBROUTINE wlamch_add |
|---|
| 886 | |
|---|
| 887 | SUBROUTINE jac_sp(v,f,rct,jvs) |
|---|
| 888 | |
|---|
| 889 | ! V - Concentrations of variable species (local) |
|---|
| 890 | REAL(kind=dp):: v(nvar) |
|---|
| 891 | ! F - Concentrations of fixed species (local) |
|---|
| 892 | REAL(kind=dp):: f(nfix) |
|---|
| 893 | ! RCT - Rate constants (local) |
|---|
| 894 | REAL(kind=dp):: rct(nreact) |
|---|
| 895 | ! JVS - sparse Jacobian of variables |
|---|
| 896 | REAL(kind=dp):: jvs(lu_nonzero) |
|---|
| 897 | |
|---|
| 898 | |
|---|
| 899 | ! Local variables |
|---|
| 900 | ! B - Temporary array |
|---|
| 901 | REAL(kind=dp):: b(2) |
|---|
| 902 | |
|---|
| 903 | ! B(1) = dA(1)/dV(1) |
|---|
| 904 | b(1) = rct(1) |
|---|
| 905 | ! B(2) = dA(2)/dV(2) |
|---|
| 906 | b(2) = rct(2) |
|---|
| 907 | |
|---|
| 908 | ! Construct the Jacobian terms from B's |
|---|
| 909 | ! JVS(1) = Jac_FULL(1,1) |
|---|
| 910 | jvs(1) = 0 |
|---|
| 911 | ! JVS(2) = Jac_FULL(2,2) |
|---|
| 912 | jvs(2) = 0 |
|---|
| 913 | |
|---|
| 914 | END SUBROUTINE jac_sp |
|---|
| 915 | |
|---|
| 916 | elemental REAL(kind=dp)FUNCTION k_arr (k_298,tdep,temp) |
|---|
| 917 | ! arrhenius FUNCTION |
|---|
| 918 | |
|---|
| 919 | REAL, INTENT(in):: k_298 ! k at t = 298.15k |
|---|
| 920 | REAL, INTENT(in):: tdep ! temperature dependence |
|---|
| 921 | REAL(kind=dp),INTENT(in):: temp ! temperature |
|---|
| 922 | |
|---|
| 923 | intrinsic exp |
|---|
| 924 | |
|---|
| 925 | k_arr = k_298 *exp(tdep*(1._dp/temp- 3.3540e-3_dp))! 1/298.15=3.3540e-3 |
|---|
| 926 | |
|---|
| 927 | END FUNCTION k_arr |
|---|
| 928 | |
|---|
| 929 | SUBROUTINE update_rconst() |
|---|
| 930 | INTEGER :: j,k |
|---|
| 931 | |
|---|
| 932 | k = is |
|---|
| 933 | |
|---|
| 934 | ! Begin INLINED RCONST |
|---|
| 935 | |
|---|
| 936 | |
|---|
| 937 | ! End INLINED RCONST |
|---|
| 938 | |
|---|
| 939 | rconst(1) = (1.0_dp) |
|---|
| 940 | rconst(2) = (1.0_dp) |
|---|
| 941 | |
|---|
| 942 | END SUBROUTINE update_rconst |
|---|
| 943 | |
|---|
| 944 | REAL(kind=dp)FUNCTION arr2( a0,b0,temp) |
|---|
| 945 | REAL(kind=dp):: temp |
|---|
| 946 | REAL(kind=dp):: a0,b0 |
|---|
| 947 | arr2 = a0 *exp( - b0 / temp) |
|---|
| 948 | END FUNCTION arr2 |
|---|
| 949 | |
|---|
| 950 | SUBROUTINE initialize_kpp_ctrl(status,iou,modstr) |
|---|
| 951 | |
|---|
| 952 | |
|---|
| 953 | ! i/o |
|---|
| 954 | INTEGER, INTENT(out):: status |
|---|
| 955 | INTEGER, INTENT(in) :: iou ! LOGICAL i/o unit |
|---|
| 956 | CHARACTER(len=*),INTENT(in) :: modstr ! read <modstr>.nml |
|---|
| 957 | |
|---|
| 958 | ! local |
|---|
| 959 | REAL(dp):: tsum |
|---|
| 960 | INTEGER :: i |
|---|
| 961 | |
|---|
| 962 | ! check fixed time steps |
|---|
| 963 | tsum = 0.0_dp |
|---|
| 964 | DO i=1,nmaxfixsteps |
|---|
| 965 | IF (t_steps(i)< tiny(0.0_dp))exit |
|---|
| 966 | tsum = tsum + t_steps(i) |
|---|
| 967 | ENDDO |
|---|
| 968 | |
|---|
| 969 | nfsteps = i- 1 |
|---|
| 970 | |
|---|
| 971 | l_fixed_step = (nfsteps > 0).and.((tsum - 1.0)< tiny(0.0_dp)) |
|---|
| 972 | |
|---|
| 973 | IF (l_vector)THEN |
|---|
| 974 | WRITE(*,*) ' MODE : VECTOR (LENGTH=',VL_DIM,')' |
|---|
| 975 | ELSE |
|---|
| 976 | WRITE(*,*) ' MODE : SCALAR' |
|---|
| 977 | ENDIF |
|---|
| 978 | ! |
|---|
| 979 | WRITE(*,*) ' DE-INDEXING MODE :',I_LU_DI |
|---|
| 980 | ! |
|---|
| 981 | WRITE(*,*) ' ICNTRL : ',icntrl |
|---|
| 982 | WRITE(*,*) ' RCNTRL : ',rcntrl |
|---|
| 983 | ! |
|---|
| 984 | ! note: this is only meaningful for vectorized (kp4)rosenbrock- methods |
|---|
| 985 | IF (l_vector)THEN |
|---|
| 986 | IF (l_fixed_step)THEN |
|---|
| 987 | WRITE(*,*) ' TIME STEPS : FIXED (',t_steps(1:nfsteps),')' |
|---|
| 988 | ELSE |
|---|
| 989 | WRITE(*,*) ' TIME STEPS : AUTOMATIC' |
|---|
| 990 | ENDIF |
|---|
| 991 | ELSE |
|---|
| 992 | WRITE(*,*) ' TIME STEPS : AUTOMATIC '//& |
|---|
| 993 | &'(t_steps (CTRL_KPP) ignored in SCALAR MODE)' |
|---|
| 994 | ENDIF |
|---|
| 995 | ! mz_pj_20070531- |
|---|
| 996 | |
|---|
| 997 | status = 0 |
|---|
| 998 | |
|---|
| 999 | |
|---|
| 1000 | END SUBROUTINE initialize_kpp_ctrl |
|---|
| 1001 | |
|---|
| 1002 | SUBROUTINE error_output(c,ierr,pe) |
|---|
| 1003 | |
|---|
| 1004 | |
|---|
| 1005 | INTEGER,INTENT(in):: ierr |
|---|
| 1006 | INTEGER,INTENT(in):: pe |
|---|
| 1007 | REAL(dp),DIMENSION(:),INTENT(in):: c |
|---|
| 1008 | |
|---|
| 1009 | write(6,*) 'ERROR in chem_gasphase_mod ',ierr,C(1) |
|---|
| 1010 | |
|---|
| 1011 | |
|---|
| 1012 | END SUBROUTINE error_output |
|---|
| 1013 | |
|---|
| 1014 | SUBROUTINE wcopy(n,x,incx,y,incy) |
|---|
| 1015 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1016 | ! copies a vector,x,to a vector,y: y <- x |
|---|
| 1017 | ! only for incX=incY=1 |
|---|
| 1018 | ! after BLAS |
|---|
| 1019 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 1020 | ! CALL SCOPY(N,X,1,Y,1) or CALL DCOPY(N,X,1,Y,1) |
|---|
| 1021 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1022 | ! USE chem_gasphase_mod_Precision |
|---|
| 1023 | |
|---|
| 1024 | INTEGER :: i,incx,incy,m,mp1,n |
|---|
| 1025 | REAL(kind=dp):: x(n),y(n) |
|---|
| 1026 | |
|---|
| 1027 | IF (n.le.0)RETURN |
|---|
| 1028 | |
|---|
| 1029 | m = mod(n,8) |
|---|
| 1030 | IF( m .ne. 0)THEN |
|---|
| 1031 | DO i = 1,m |
|---|
| 1032 | y(i) = x(i) |
|---|
| 1033 | ENDDO |
|---|
| 1034 | IF( n .lt. 8)RETURN |
|---|
| 1035 | ENDIF |
|---|
| 1036 | mp1 = m+ 1 |
|---|
| 1037 | DO i = mp1,n,8 |
|---|
| 1038 | y(i) = x(i) |
|---|
| 1039 | y(i + 1) = x(i + 1) |
|---|
| 1040 | y(i + 2) = x(i + 2) |
|---|
| 1041 | y(i + 3) = x(i + 3) |
|---|
| 1042 | y(i + 4) = x(i + 4) |
|---|
| 1043 | y(i + 5) = x(i + 5) |
|---|
| 1044 | y(i + 6) = x(i + 6) |
|---|
| 1045 | y(i + 7) = x(i + 7) |
|---|
| 1046 | ENDDO |
|---|
| 1047 | |
|---|
| 1048 | END SUBROUTINE wcopy |
|---|
| 1049 | |
|---|
| 1050 | SUBROUTINE wscal(n,alpha,x,incx) |
|---|
| 1051 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1052 | ! constant times a vector: x(1:N) <- Alpha*x(1:N) |
|---|
| 1053 | ! only for incX=incY=1 |
|---|
| 1054 | ! after BLAS |
|---|
| 1055 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 1056 | ! CALL SSCAL(N,Alpha,X,1) or CALL DSCAL(N,Alpha,X,1) |
|---|
| 1057 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1058 | |
|---|
| 1059 | INTEGER :: i,incx,m,mp1,n |
|---|
| 1060 | REAL(kind=dp) :: x(n),alpha |
|---|
| 1061 | REAL(kind=dp),PARAMETER :: zero=0.0_dp, one=1.0_dp |
|---|
| 1062 | |
|---|
| 1063 | IF (alpha .eq. one)RETURN |
|---|
| 1064 | IF (n .le. 0)RETURN |
|---|
| 1065 | |
|---|
| 1066 | m = mod(n,5) |
|---|
| 1067 | IF( m .ne. 0)THEN |
|---|
| 1068 | IF (alpha .eq. (- one))THEN |
|---|
| 1069 | DO i = 1,m |
|---|
| 1070 | x(i) = - x(i) |
|---|
| 1071 | ENDDO |
|---|
| 1072 | ELSEIF (alpha .eq. zero)THEN |
|---|
| 1073 | DO i = 1,m |
|---|
| 1074 | x(i) = zero |
|---|
| 1075 | ENDDO |
|---|
| 1076 | ELSE |
|---|
| 1077 | DO i = 1,m |
|---|
| 1078 | x(i) = alpha*x(i) |
|---|
| 1079 | ENDDO |
|---|
| 1080 | ENDIF |
|---|
| 1081 | IF( n .lt. 5)RETURN |
|---|
| 1082 | ENDIF |
|---|
| 1083 | mp1 = m + 1 |
|---|
| 1084 | IF (alpha .eq. (- one))THEN |
|---|
| 1085 | DO i = mp1,n,5 |
|---|
| 1086 | x(i) = - x(i) |
|---|
| 1087 | x(i + 1) = - x(i + 1) |
|---|
| 1088 | x(i + 2) = - x(i + 2) |
|---|
| 1089 | x(i + 3) = - x(i + 3) |
|---|
| 1090 | x(i + 4) = - x(i + 4) |
|---|
| 1091 | ENDDO |
|---|
| 1092 | ELSEIF (alpha .eq. zero)THEN |
|---|
| 1093 | DO i = mp1,n,5 |
|---|
| 1094 | x(i) = zero |
|---|
| 1095 | x(i + 1) = zero |
|---|
| 1096 | x(i + 2) = zero |
|---|
| 1097 | x(i + 3) = zero |
|---|
| 1098 | x(i + 4) = zero |
|---|
| 1099 | ENDDO |
|---|
| 1100 | ELSE |
|---|
| 1101 | DO i = mp1,n,5 |
|---|
| 1102 | x(i) = alpha*x(i) |
|---|
| 1103 | x(i + 1) = alpha*x(i + 1) |
|---|
| 1104 | x(i + 2) = alpha*x(i + 2) |
|---|
| 1105 | x(i + 3) = alpha*x(i + 3) |
|---|
| 1106 | x(i + 4) = alpha*x(i + 4) |
|---|
| 1107 | ENDDO |
|---|
| 1108 | ENDIF |
|---|
| 1109 | |
|---|
| 1110 | END SUBROUTINE wscal |
|---|
| 1111 | |
|---|
| 1112 | SUBROUTINE waxpy(n,alpha,x,incx,y,incy) |
|---|
| 1113 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1114 | ! constant times a vector plus a vector: y <- y + Alpha*x |
|---|
| 1115 | ! only for incX=incY=1 |
|---|
| 1116 | ! after BLAS |
|---|
| 1117 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 1118 | ! CALL SAXPY(N,Alpha,X,1,Y,1) or CALL DAXPY(N,Alpha,X,1,Y,1) |
|---|
| 1119 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1120 | |
|---|
| 1121 | INTEGER :: i,incx,incy,m,mp1,n |
|---|
| 1122 | REAL(kind=dp):: x(n),y(n),alpha |
|---|
| 1123 | REAL(kind=dp),PARAMETER :: zero = 0.0_dp |
|---|
| 1124 | |
|---|
| 1125 | IF (alpha .eq. zero)RETURN |
|---|
| 1126 | IF (n .le. 0)RETURN |
|---|
| 1127 | |
|---|
| 1128 | m = mod(n,4) |
|---|
| 1129 | IF( m .ne. 0)THEN |
|---|
| 1130 | DO i = 1,m |
|---|
| 1131 | y(i) = y(i)+ alpha*x(i) |
|---|
| 1132 | ENDDO |
|---|
| 1133 | IF( n .lt. 4)RETURN |
|---|
| 1134 | ENDIF |
|---|
| 1135 | mp1 = m + 1 |
|---|
| 1136 | DO i = mp1,n,4 |
|---|
| 1137 | y(i) = y(i)+ alpha*x(i) |
|---|
| 1138 | y(i + 1) = y(i + 1)+ alpha*x(i + 1) |
|---|
| 1139 | y(i + 2) = y(i + 2)+ alpha*x(i + 2) |
|---|
| 1140 | y(i + 3) = y(i + 3)+ alpha*x(i + 3) |
|---|
| 1141 | ENDDO |
|---|
| 1142 | |
|---|
| 1143 | END SUBROUTINE waxpy |
|---|
| 1144 | |
|---|
| 1145 | SUBROUTINE rosenbrock(n,y,tstart,tend,& |
|---|
| 1146 | abstol,reltol, & |
|---|
| 1147 | rcntrl,icntrl,rstatus,istatus,ierr) |
|---|
| 1148 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1149 | ! |
|---|
| 1150 | ! Solves the system y'=F(t,y) using a Rosenbrock method defined by: |
|---|
| 1151 | ! |
|---|
| 1152 | ! G = 1/(H*gamma(1)) - Jac(t0,Y0) |
|---|
| 1153 | ! T_i = t0 + Alpha(i)*H |
|---|
| 1154 | ! Y_i = Y0 + \sum_{j=1}^{i-1} A(i,j)*K_j |
|---|
| 1155 | ! G *K_i = Fun( T_i,Y_i)+ \sum_{j=1}^S C(i,j)/H *K_j + |
|---|
| 1156 | ! gamma(i)*dF/dT(t0,Y0) |
|---|
| 1157 | ! Y1 = Y0 + \sum_{j=1}^S M(j)*K_j |
|---|
| 1158 | ! |
|---|
| 1159 | ! For details on Rosenbrock methods and their implementation consult: |
|---|
| 1160 | ! E. Hairer and G. Wanner |
|---|
| 1161 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
|---|
| 1162 | ! Springer series in computational mathematics,Springer-Verlag,1996. |
|---|
| 1163 | ! The codes contained in the book inspired this implementation. |
|---|
| 1164 | ! |
|---|
| 1165 | ! (C) Adrian Sandu,August 2004 |
|---|
| 1166 | ! Virginia Polytechnic Institute and State University |
|---|
| 1167 | ! Contact: sandu@cs.vt.edu |
|---|
| 1168 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 |
|---|
| 1169 | ! This implementation is part of KPP - the Kinetic PreProcessor |
|---|
| 1170 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1171 | ! |
|---|
| 1172 | !~~~> input arguments: |
|---|
| 1173 | ! |
|---|
| 1174 | !- y(n) = vector of initial conditions (at t=tstart) |
|---|
| 1175 | !- [tstart,tend] = time range of integration |
|---|
| 1176 | ! (if Tstart>Tend the integration is performed backwards in time) |
|---|
| 1177 | !- reltol,abstol = user precribed accuracy |
|---|
| 1178 | !- SUBROUTINE fun( t,y,ydot) = ode FUNCTION, |
|---|
| 1179 | ! returns Ydot = Y' = F(T,Y) |
|---|
| 1180 | !- SUBROUTINE jac( t,y,jcb) = jacobian of the ode FUNCTION, |
|---|
| 1181 | ! returns Jcb = dFun/dY |
|---|
| 1182 | !- icntrl(1:20) = INTEGER inputs PARAMETERs |
|---|
| 1183 | !- rcntrl(1:20) = REAL inputs PARAMETERs |
|---|
| 1184 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1185 | ! |
|---|
| 1186 | !~~~> output arguments: |
|---|
| 1187 | ! |
|---|
| 1188 | !- y(n) - > vector of final states (at t- >tEND) |
|---|
| 1189 | !- istatus(1:20) - > INTEGER output PARAMETERs |
|---|
| 1190 | !- rstatus(1:20) - > REAL output PARAMETERs |
|---|
| 1191 | !- ierr - > job status upon RETURN |
|---|
| 1192 | ! success (positive value) or |
|---|
| 1193 | ! failure (negative value) |
|---|
| 1194 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1195 | ! |
|---|
| 1196 | !~~~> input PARAMETERs: |
|---|
| 1197 | ! |
|---|
| 1198 | ! Note: For input parameters equal to zero the default values of the |
|---|
| 1199 | ! corresponding variables are used. |
|---|
| 1200 | ! |
|---|
| 1201 | ! ICNTRL(1) = 1: F = F(y) Independent of T (AUTONOMOUS) |
|---|
| 1202 | ! = 0: F = F(t,y) Depends on T (NON-AUTONOMOUS) |
|---|
| 1203 | ! |
|---|
| 1204 | ! ICNTRL(2) = 0: AbsTol,RelTol are N-dimensional vectors |
|---|
| 1205 | ! = 1: AbsTol,RelTol are scalars |
|---|
| 1206 | ! |
|---|
| 1207 | ! ICNTRL(3) -> selection of a particular Rosenbrock method |
|---|
| 1208 | ! = 0 : Rodas3 (default) |
|---|
| 1209 | ! = 1 : Ros2 |
|---|
| 1210 | ! = 2 : Ros3 |
|---|
| 1211 | ! = 3 : Ros4 |
|---|
| 1212 | ! = 4 : Rodas3 |
|---|
| 1213 | ! = 5 : Rodas4 |
|---|
| 1214 | ! |
|---|
| 1215 | ! ICNTRL(4) -> maximum number of integration steps |
|---|
| 1216 | ! For ICNTRL(4) =0) the default value of 100000 is used |
|---|
| 1217 | ! |
|---|
| 1218 | ! RCNTRL(1) -> Hmin,lower bound for the integration step size |
|---|
| 1219 | ! It is strongly recommended to keep Hmin = ZERO |
|---|
| 1220 | ! RCNTRL(2) -> Hmax,upper bound for the integration step size |
|---|
| 1221 | ! RCNTRL(3) -> Hstart,starting value for the integration step size |
|---|
| 1222 | ! |
|---|
| 1223 | ! RCNTRL(4) -> FacMin,lower bound on step decrease factor (default=0.2) |
|---|
| 1224 | ! RCNTRL(5) -> FacMax,upper bound on step increase factor (default=6) |
|---|
| 1225 | ! RCNTRL(6) -> FacRej,step decrease factor after multiple rejections |
|---|
| 1226 | ! (default=0.1) |
|---|
| 1227 | ! RCNTRL(7) -> FacSafe,by which the new step is slightly smaller |
|---|
| 1228 | ! than the predicted value (default=0.9) |
|---|
| 1229 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1230 | ! |
|---|
| 1231 | ! |
|---|
| 1232 | ! OUTPUT ARGUMENTS: |
|---|
| 1233 | ! ----------------- |
|---|
| 1234 | ! |
|---|
| 1235 | ! T -> T value for which the solution has been computed |
|---|
| 1236 | ! (after successful return T=Tend). |
|---|
| 1237 | ! |
|---|
| 1238 | ! Y(N) -> Numerical solution at T |
|---|
| 1239 | ! |
|---|
| 1240 | ! IDID -> Reports on successfulness upon return: |
|---|
| 1241 | ! = 1 for success |
|---|
| 1242 | ! < 0 for error (value equals error code) |
|---|
| 1243 | ! |
|---|
| 1244 | ! ISTATUS(1) -> No. of function calls |
|---|
| 1245 | ! ISTATUS(2) -> No. of jacobian calls |
|---|
| 1246 | ! ISTATUS(3) -> No. of steps |
|---|
| 1247 | ! ISTATUS(4) -> No. of accepted steps |
|---|
| 1248 | ! ISTATUS(5) -> No. of rejected steps (except at very beginning) |
|---|
| 1249 | ! ISTATUS(6) -> No. of LU decompositions |
|---|
| 1250 | ! ISTATUS(7) -> No. of forward/backward substitutions |
|---|
| 1251 | ! ISTATUS(8) -> No. of singular matrix decompositions |
|---|
| 1252 | ! |
|---|
| 1253 | ! RSTATUS(1) -> Texit,the time corresponding to the |
|---|
| 1254 | ! computed Y upon return |
|---|
| 1255 | ! RSTATUS(2) -> Hexit,last accepted step before exit |
|---|
| 1256 | ! RSTATUS(3) -> Hnew,last predicted step (not yet taken) |
|---|
| 1257 | ! For multiple restarts,use Hnew as Hstart |
|---|
| 1258 | ! in the subsequent run |
|---|
| 1259 | ! |
|---|
| 1260 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1261 | |
|---|
| 1262 | |
|---|
| 1263 | !~~~> arguments |
|---|
| 1264 | INTEGER, INTENT(in) :: n |
|---|
| 1265 | REAL(kind=dp),INTENT(inout):: y(n) |
|---|
| 1266 | REAL(kind=dp),INTENT(in) :: tstart,tend |
|---|
| 1267 | REAL(kind=dp),INTENT(in) :: abstol(n),reltol(n) |
|---|
| 1268 | INTEGER, INTENT(in) :: icntrl(20) |
|---|
| 1269 | REAL(kind=dp),INTENT(in) :: rcntrl(20) |
|---|
| 1270 | INTEGER, INTENT(inout):: istatus(20) |
|---|
| 1271 | REAL(kind=dp),INTENT(inout):: rstatus(20) |
|---|
| 1272 | INTEGER,INTENT(out) :: ierr |
|---|
| 1273 | !~~~> PARAMETERs of the rosenbrock method,up to 6 stages |
|---|
| 1274 | INTEGER :: ros_s,rosmethod |
|---|
| 1275 | INTEGER,PARAMETER :: rs2=1,rs3=2,rs4=3,rd3=4,rd4=5,rg3=6 |
|---|
| 1276 | REAL(kind=dp):: ros_a(15),ros_c(15),ros_m(6),ros_e(6),& |
|---|
| 1277 | ros_alpha(6),ros_gamma(6),ros_elo |
|---|
| 1278 | LOGICAL :: ros_newf(6) |
|---|
| 1279 | CHARACTER(len=12):: ros_name |
|---|
| 1280 | !~~~> local variables |
|---|
| 1281 | REAL(kind=dp):: roundoff,facmin,facmax,facrej,facsafe |
|---|
| 1282 | REAL(kind=dp):: hmin,hmax,hstart |
|---|
| 1283 | REAL(kind=dp):: texit |
|---|
| 1284 | INTEGER :: i,uplimtol,max_no_steps |
|---|
| 1285 | LOGICAL :: autonomous,vectortol |
|---|
| 1286 | !~~~> PARAMETERs |
|---|
| 1287 | REAL(kind=dp),PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
|---|
| 1288 | REAL(kind=dp),PARAMETER :: deltamin = 1.0e-5_dp |
|---|
| 1289 | |
|---|
| 1290 | !~~~> initialize statistics |
|---|
| 1291 | istatus(1:8) = 0 |
|---|
| 1292 | rstatus(1:3) = zero |
|---|
| 1293 | |
|---|
| 1294 | !~~~> autonomous or time dependent ode. default is time dependent. |
|---|
| 1295 | autonomous = .not.(icntrl(1) == 0) |
|---|
| 1296 | |
|---|
| 1297 | !~~~> for scalar tolerances (icntrl(2).ne.0) the code uses abstol(1)and reltol(1) |
|---|
| 1298 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:N) and RelTol(1:N) |
|---|
| 1299 | IF (icntrl(2) == 0)THEN |
|---|
| 1300 | vectortol = .true. |
|---|
| 1301 | uplimtol = n |
|---|
| 1302 | ELSE |
|---|
| 1303 | vectortol = .false. |
|---|
| 1304 | uplimtol = 1 |
|---|
| 1305 | ENDIF |
|---|
| 1306 | |
|---|
| 1307 | !~~~> initialize the particular rosenbrock method selected |
|---|
| 1308 | select CASE (icntrl(3)) |
|---|
| 1309 | CASE (1) |
|---|
| 1310 | CALL ros2 |
|---|
| 1311 | CASE (2) |
|---|
| 1312 | CALL ros3 |
|---|
| 1313 | CASE (3) |
|---|
| 1314 | CALL ros4 |
|---|
| 1315 | CASE (0,4) |
|---|
| 1316 | CALL rodas3 |
|---|
| 1317 | CASE (5) |
|---|
| 1318 | CALL rodas4 |
|---|
| 1319 | CASE (6) |
|---|
| 1320 | CALL rang3 |
|---|
| 1321 | CASE default |
|---|
| 1322 | PRINT *,'Unknown Rosenbrock method: ICNTRL(3) =',ICNTRL(3) |
|---|
| 1323 | CALL ros_errormsg(- 2,tstart,zero,ierr) |
|---|
| 1324 | RETURN |
|---|
| 1325 | END select |
|---|
| 1326 | |
|---|
| 1327 | !~~~> the maximum number of steps admitted |
|---|
| 1328 | IF (icntrl(4) == 0)THEN |
|---|
| 1329 | max_no_steps = 200000 |
|---|
| 1330 | ELSEIF (icntrl(4)> 0)THEN |
|---|
| 1331 | max_no_steps=icntrl(4) |
|---|
| 1332 | ELSE |
|---|
| 1333 | PRINT *,'User-selected max no. of steps: ICNTRL(4) =',ICNTRL(4) |
|---|
| 1334 | CALL ros_errormsg(- 1,tstart,zero,ierr) |
|---|
| 1335 | RETURN |
|---|
| 1336 | ENDIF |
|---|
| 1337 | |
|---|
| 1338 | !~~~> unit roundoff (1+ roundoff>1) |
|---|
| 1339 | Roundoff = WLAMCH('E') |
|---|
| 1340 | |
|---|
| 1341 | !~~~> lower bound on the step size: (positive value) |
|---|
| 1342 | IF (rcntrl(1) == zero)THEN |
|---|
| 1343 | hmin = zero |
|---|
| 1344 | ELSEIF (rcntrl(1)> zero)THEN |
|---|
| 1345 | hmin = rcntrl(1) |
|---|
| 1346 | ELSE |
|---|
| 1347 | PRINT *,'User-selected Hmin: RCNTRL(1) =',RCNTRL(1) |
|---|
| 1348 | CALL ros_errormsg(- 3,tstart,zero,ierr) |
|---|
| 1349 | RETURN |
|---|
| 1350 | ENDIF |
|---|
| 1351 | !~~~> upper bound on the step size: (positive value) |
|---|
| 1352 | IF (rcntrl(2) == zero)THEN |
|---|
| 1353 | hmax = abs(tend-tstart) |
|---|
| 1354 | ELSEIF (rcntrl(2)> zero)THEN |
|---|
| 1355 | hmax = min(abs(rcntrl(2)),abs(tend-tstart)) |
|---|
| 1356 | ELSE |
|---|
| 1357 | PRINT *,'User-selected Hmax: RCNTRL(2) =',RCNTRL(2) |
|---|
| 1358 | CALL ros_errormsg(- 3,tstart,zero,ierr) |
|---|
| 1359 | RETURN |
|---|
| 1360 | ENDIF |
|---|
| 1361 | !~~~> starting step size: (positive value) |
|---|
| 1362 | IF (rcntrl(3) == zero)THEN |
|---|
| 1363 | hstart = max(hmin,deltamin) |
|---|
| 1364 | ELSEIF (rcntrl(3)> zero)THEN |
|---|
| 1365 | hstart = min(abs(rcntrl(3)),abs(tend-tstart)) |
|---|
| 1366 | ELSE |
|---|
| 1367 | PRINT *,'User-selected Hstart: RCNTRL(3) =',RCNTRL(3) |
|---|
| 1368 | CALL ros_errormsg(- 3,tstart,zero,ierr) |
|---|
| 1369 | RETURN |
|---|
| 1370 | ENDIF |
|---|
| 1371 | !~~~> step size can be changed s.t. facmin < hnew/hold < facmax |
|---|
| 1372 | IF (rcntrl(4) == zero)THEN |
|---|
| 1373 | facmin = 0.2_dp |
|---|
| 1374 | ELSEIF (rcntrl(4)> zero)THEN |
|---|
| 1375 | facmin = rcntrl(4) |
|---|
| 1376 | ELSE |
|---|
| 1377 | PRINT *,'User-selected FacMin: RCNTRL(4) =',RCNTRL(4) |
|---|
| 1378 | CALL ros_errormsg(- 4,tstart,zero,ierr) |
|---|
| 1379 | RETURN |
|---|
| 1380 | ENDIF |
|---|
| 1381 | IF (rcntrl(5) == zero)THEN |
|---|
| 1382 | facmax = 6.0_dp |
|---|
| 1383 | ELSEIF (rcntrl(5)> zero)THEN |
|---|
| 1384 | facmax = rcntrl(5) |
|---|
| 1385 | ELSE |
|---|
| 1386 | PRINT *,'User-selected FacMax: RCNTRL(5) =',RCNTRL(5) |
|---|
| 1387 | CALL ros_errormsg(- 4,tstart,zero,ierr) |
|---|
| 1388 | RETURN |
|---|
| 1389 | ENDIF |
|---|
| 1390 | !~~~> facrej: factor to decrease step after 2 succesive rejections |
|---|
| 1391 | IF (rcntrl(6) == zero)THEN |
|---|
| 1392 | facrej = 0.1_dp |
|---|
| 1393 | ELSEIF (rcntrl(6)> zero)THEN |
|---|
| 1394 | facrej = rcntrl(6) |
|---|
| 1395 | ELSE |
|---|
| 1396 | PRINT *,'User-selected FacRej: RCNTRL(6) =',RCNTRL(6) |
|---|
| 1397 | CALL ros_errormsg(- 4,tstart,zero,ierr) |
|---|
| 1398 | RETURN |
|---|
| 1399 | ENDIF |
|---|
| 1400 | !~~~> facsafe: safety factor in the computation of new step size |
|---|
| 1401 | IF (rcntrl(7) == zero)THEN |
|---|
| 1402 | facsafe = 0.9_dp |
|---|
| 1403 | ELSEIF (rcntrl(7)> zero)THEN |
|---|
| 1404 | facsafe = rcntrl(7) |
|---|
| 1405 | ELSE |
|---|
| 1406 | PRINT *,'User-selected FacSafe: RCNTRL(7) =',RCNTRL(7) |
|---|
| 1407 | CALL ros_errormsg(- 4,tstart,zero,ierr) |
|---|
| 1408 | RETURN |
|---|
| 1409 | ENDIF |
|---|
| 1410 | !~~~> check IF tolerances are reasonable |
|---|
| 1411 | DO i=1,uplimtol |
|---|
| 1412 | IF((abstol(i)<= zero).or. (reltol(i)<= 10.0_dp*roundoff)& |
|---|
| 1413 | .or. (reltol(i)>= 1.0_dp))THEN |
|---|
| 1414 | PRINT *,' AbsTol(',i,') = ',AbsTol(i) |
|---|
| 1415 | PRINT *,' RelTol(',i,') = ',RelTol(i) |
|---|
| 1416 | CALL ros_errormsg(- 5,tstart,zero,ierr) |
|---|
| 1417 | RETURN |
|---|
| 1418 | ENDIF |
|---|
| 1419 | ENDDO |
|---|
| 1420 | |
|---|
| 1421 | |
|---|
| 1422 | !~~~> CALL rosenbrock method |
|---|
| 1423 | CALL ros_integrator(y,tstart,tend,texit, & |
|---|
| 1424 | abstol,reltol, & |
|---|
| 1425 | ! Integration parameters |
|---|
| 1426 | autonomous,vectortol,max_no_steps, & |
|---|
| 1427 | roundoff,hmin,hmax,hstart, & |
|---|
| 1428 | facmin,facmax,facrej,facsafe, & |
|---|
| 1429 | ! Error indicator |
|---|
| 1430 | ierr) |
|---|
| 1431 | |
|---|
| 1432 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1433 | CONTAINS ! SUBROUTINEs internal to rosenbrock |
|---|
| 1434 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1435 | |
|---|
| 1436 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1437 | SUBROUTINE ros_errormsg(code,t,h,ierr) |
|---|
| 1438 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1439 | ! Handles all error messages |
|---|
| 1440 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1441 | |
|---|
| 1442 | REAL(kind=dp),INTENT(in):: t,h |
|---|
| 1443 | INTEGER,INTENT(in) :: code |
|---|
| 1444 | INTEGER,INTENT(out):: ierr |
|---|
| 1445 | |
|---|
| 1446 | ierr = code |
|---|
| 1447 | print *,& |
|---|
| 1448 | 'Forced exit from Rosenbrock due to the following error:' |
|---|
| 1449 | |
|---|
| 1450 | select CASE (code) |
|---|
| 1451 | CASE (- 1) |
|---|
| 1452 | PRINT *,'--> Improper value for maximal no of steps' |
|---|
| 1453 | CASE (- 2) |
|---|
| 1454 | PRINT *,'--> Selected Rosenbrock method not implemented' |
|---|
| 1455 | CASE (- 3) |
|---|
| 1456 | PRINT *,'--> Hmin/Hmax/Hstart must be positive' |
|---|
| 1457 | CASE (- 4) |
|---|
| 1458 | PRINT *,'--> FacMin/FacMax/FacRej must be positive' |
|---|
| 1459 | CASE (- 5) |
|---|
| 1460 | PRINT *,'--> Improper tolerance values' |
|---|
| 1461 | CASE (- 6) |
|---|
| 1462 | PRINT *,'--> No of steps exceeds maximum bound' |
|---|
| 1463 | CASE (- 7) |
|---|
| 1464 | PRINT *,'--> Step size too small: T + 10*H = T',& |
|---|
| 1465 | ' or H < Roundoff' |
|---|
| 1466 | CASE (- 8) |
|---|
| 1467 | PRINT *,'--> Matrix is repeatedly singular' |
|---|
| 1468 | CASE default |
|---|
| 1469 | PRINT *,'Unknown Error code: ',Code |
|---|
| 1470 | END select |
|---|
| 1471 | |
|---|
| 1472 | print *,"t=",t,"and h=",h |
|---|
| 1473 | |
|---|
| 1474 | END SUBROUTINE ros_errormsg |
|---|
| 1475 | |
|---|
| 1476 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1477 | SUBROUTINE ros_integrator (y,tstart,tend,t, & |
|---|
| 1478 | abstol,reltol, & |
|---|
| 1479 | !~~~> integration PARAMETERs |
|---|
| 1480 | autonomous,vectortol,max_no_steps, & |
|---|
| 1481 | roundoff,hmin,hmax,hstart, & |
|---|
| 1482 | facmin,facmax,facrej,facsafe, & |
|---|
| 1483 | !~~~> error indicator |
|---|
| 1484 | ierr) |
|---|
| 1485 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1486 | ! Template for the implementation of a generic Rosenbrock method |
|---|
| 1487 | ! defined by ros_S (no of stages) |
|---|
| 1488 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
|---|
| 1489 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1490 | |
|---|
| 1491 | |
|---|
| 1492 | !~~~> input: the initial condition at tstart; output: the solution at t |
|---|
| 1493 | REAL(kind=dp),INTENT(inout):: y(n) |
|---|
| 1494 | !~~~> input: integration interval |
|---|
| 1495 | REAL(kind=dp),INTENT(in):: tstart,tend |
|---|
| 1496 | !~~~> output: time at which the solution is RETURNed (t=tENDIF success) |
|---|
| 1497 | REAL(kind=dp),INTENT(out):: t |
|---|
| 1498 | !~~~> input: tolerances |
|---|
| 1499 | REAL(kind=dp),INTENT(in):: abstol(n),reltol(n) |
|---|
| 1500 | !~~~> input: integration PARAMETERs |
|---|
| 1501 | LOGICAL,INTENT(in):: autonomous,vectortol |
|---|
| 1502 | REAL(kind=dp),INTENT(in):: hstart,hmin,hmax |
|---|
| 1503 | INTEGER,INTENT(in):: max_no_steps |
|---|
| 1504 | REAL(kind=dp),INTENT(in):: roundoff,facmin,facmax,facrej,facsafe |
|---|
| 1505 | !~~~> output: error indicator |
|---|
| 1506 | INTEGER,INTENT(out):: ierr |
|---|
| 1507 | ! ~~~~ Local variables |
|---|
| 1508 | REAL(kind=dp):: ynew(n),fcn0(n),fcn(n) |
|---|
| 1509 | REAL(kind=dp):: k(n*ros_s),dfdt(n) |
|---|
| 1510 | #ifdef full_algebra |
|---|
| 1511 | REAL(kind=dp):: jac0(n,n),ghimj(n,n) |
|---|
| 1512 | #else |
|---|
| 1513 | REAL(kind=dp):: jac0(lu_nonzero),ghimj(lu_nonzero) |
|---|
| 1514 | #endif |
|---|
| 1515 | REAL(kind=dp):: h,hnew,hc,hg,fac,tau |
|---|
| 1516 | REAL(kind=dp):: err,yerr(n) |
|---|
| 1517 | INTEGER :: pivot(n),direction,ioffset,j,istage |
|---|
| 1518 | LOGICAL :: rejectlasth,rejectmoreh,singular |
|---|
| 1519 | !~~~> local PARAMETERs |
|---|
| 1520 | REAL(kind=dp),PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
|---|
| 1521 | REAL(kind=dp),PARAMETER :: deltamin = 1.0e-5_dp |
|---|
| 1522 | !~~~> locally called FUNCTIONs |
|---|
| 1523 | ! REAL(kind=dp) WLAMCH |
|---|
| 1524 | ! EXTERNAL WLAMCH |
|---|
| 1525 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1526 | |
|---|
| 1527 | |
|---|
| 1528 | !~~~> initial preparations |
|---|
| 1529 | t = tstart |
|---|
| 1530 | rstatus(nhexit) = zero |
|---|
| 1531 | h = min( max(abs(hmin),abs(hstart)),abs(hmax)) |
|---|
| 1532 | IF (abs(h)<= 10.0_dp*roundoff)h = deltamin |
|---|
| 1533 | |
|---|
| 1534 | IF (tEND >= tstart)THEN |
|---|
| 1535 | direction = + 1 |
|---|
| 1536 | ELSE |
|---|
| 1537 | direction = - 1 |
|---|
| 1538 | ENDIF |
|---|
| 1539 | h = direction*h |
|---|
| 1540 | |
|---|
| 1541 | rejectlasth=.false. |
|---|
| 1542 | rejectmoreh=.false. |
|---|
| 1543 | |
|---|
| 1544 | !~~~> time loop begins below |
|---|
| 1545 | |
|---|
| 1546 | timeloop: DO WHILE((direction > 0).and.((t- tEND)+ roundoff <= zero)& |
|---|
| 1547 | .or. (direction < 0).and.((tend-t)+ roundoff <= zero)) |
|---|
| 1548 | |
|---|
| 1549 | IF(istatus(nstp)> max_no_steps)THEN ! too many steps |
|---|
| 1550 | CALL ros_errormsg(- 6,t,h,ierr) |
|---|
| 1551 | RETURN |
|---|
| 1552 | ENDIF |
|---|
| 1553 | IF(((t+ 0.1_dp*h) == t).or.(h <= roundoff))THEN ! step size too small |
|---|
| 1554 | CALL ros_errormsg(- 7,t,h,ierr) |
|---|
| 1555 | RETURN |
|---|
| 1556 | ENDIF |
|---|
| 1557 | |
|---|
| 1558 | !~~~> limit h IF necessary to avoid going beyond tend |
|---|
| 1559 | h = min(h,abs(tend-t)) |
|---|
| 1560 | |
|---|
| 1561 | !~~~> compute the FUNCTION at current time |
|---|
| 1562 | CALL funtemplate(t,y,fcn0) |
|---|
| 1563 | istatus(nfun) = istatus(nfun)+ 1 |
|---|
| 1564 | |
|---|
| 1565 | !~~~> compute the FUNCTION derivative with respect to t |
|---|
| 1566 | IF (.not.autonomous)THEN |
|---|
| 1567 | CALL ros_funtimederivative(t,roundoff,y,& |
|---|
| 1568 | fcn0,dfdt) |
|---|
| 1569 | ENDIF |
|---|
| 1570 | |
|---|
| 1571 | !~~~> compute the jacobian at current time |
|---|
| 1572 | CALL jactemplate(t,y,jac0) |
|---|
| 1573 | istatus(njac) = istatus(njac)+ 1 |
|---|
| 1574 | |
|---|
| 1575 | !~~~> repeat step calculation until current step accepted |
|---|
| 1576 | untilaccepted: do |
|---|
| 1577 | |
|---|
| 1578 | CALL ros_preparematrix(h,direction,ros_gamma(1),& |
|---|
| 1579 | jac0,ghimj,pivot,singular) |
|---|
| 1580 | IF (singular)THEN ! more than 5 consecutive failed decompositions |
|---|
| 1581 | CALL ros_errormsg(- 8,t,h,ierr) |
|---|
| 1582 | RETURN |
|---|
| 1583 | ENDIF |
|---|
| 1584 | |
|---|
| 1585 | !~~~> compute the stages |
|---|
| 1586 | stage: DO istage = 1,ros_s |
|---|
| 1587 | |
|---|
| 1588 | ! current istage offset. current istage vector is k(ioffset+ 1:ioffset+ n) |
|---|
| 1589 | ioffset = n*(istage-1) |
|---|
| 1590 | |
|---|
| 1591 | ! for the 1st istage the FUNCTION has been computed previously |
|---|
| 1592 | IF(istage == 1)THEN |
|---|
| 1593 | !slim: CALL wcopy(n,fcn0,1,fcn,1) |
|---|
| 1594 | fcn(1:n) = fcn0(1:n) |
|---|
| 1595 | ! istage>1 and a new FUNCTION evaluation is needed at the current istage |
|---|
| 1596 | ELSEIF(ros_newf(istage))THEN |
|---|
| 1597 | !slim: CALL wcopy(n,y,1,ynew,1) |
|---|
| 1598 | ynew(1:n) = y(1:n) |
|---|
| 1599 | DO j = 1,istage-1 |
|---|
| 1600 | CALL waxpy(n,ros_a((istage-1)*(istage-2)/2+ j),& |
|---|
| 1601 | k(n*(j- 1)+ 1),1,ynew,1) |
|---|
| 1602 | ENDDO |
|---|
| 1603 | tau = t + ros_alpha(istage)*direction*h |
|---|
| 1604 | CALL funtemplate(tau,ynew,fcn) |
|---|
| 1605 | istatus(nfun) = istatus(nfun)+ 1 |
|---|
| 1606 | ENDIF ! IF istage == 1 ELSEIF ros_newf(istage) |
|---|
| 1607 | !slim: CALL wcopy(n,fcn,1,k(ioffset+ 1),1) |
|---|
| 1608 | k(ioffset+ 1:ioffset+ n) = fcn(1:n) |
|---|
| 1609 | DO j = 1,istage-1 |
|---|
| 1610 | hc = ros_c((istage-1)*(istage-2)/2+ j)/(direction*h) |
|---|
| 1611 | CALL waxpy(n,hc,k(n*(j- 1)+ 1),1,k(ioffset+ 1),1) |
|---|
| 1612 | ENDDO |
|---|
| 1613 | IF ((.not. autonomous).and.(ros_gamma(istage).ne.zero))THEN |
|---|
| 1614 | hg = direction*h*ros_gamma(istage) |
|---|
| 1615 | CALL waxpy(n,hg,dfdt,1,k(ioffset+ 1),1) |
|---|
| 1616 | ENDIF |
|---|
| 1617 | CALL ros_solve(ghimj,pivot,k(ioffset+ 1)) |
|---|
| 1618 | |
|---|
| 1619 | END DO stage |
|---|
| 1620 | |
|---|
| 1621 | |
|---|
| 1622 | !~~~> compute the new solution |
|---|
| 1623 | !slim: CALL wcopy(n,y,1,ynew,1) |
|---|
| 1624 | ynew(1:n) = y(1:n) |
|---|
| 1625 | DO j=1,ros_s |
|---|
| 1626 | CALL waxpy(n,ros_m(j),k(n*(j- 1)+ 1),1,ynew,1) |
|---|
| 1627 | ENDDO |
|---|
| 1628 | |
|---|
| 1629 | !~~~> compute the error estimation |
|---|
| 1630 | !slim: CALL wscal(n,zero,yerr,1) |
|---|
| 1631 | yerr(1:n) = zero |
|---|
| 1632 | DO j=1,ros_s |
|---|
| 1633 | CALL waxpy(n,ros_e(j),k(n*(j- 1)+ 1),1,yerr,1) |
|---|
| 1634 | ENDDO |
|---|
| 1635 | err = ros_errornorm(y,ynew,yerr,abstol,reltol,vectortol) |
|---|
| 1636 | |
|---|
| 1637 | !~~~> new step size is bounded by facmin <= hnew/h <= facmax |
|---|
| 1638 | fac = min(facmax,max(facmin,facsafe/err**(one/ros_elo))) |
|---|
| 1639 | hnew = h*fac |
|---|
| 1640 | |
|---|
| 1641 | !~~~> check the error magnitude and adjust step size |
|---|
| 1642 | istatus(nstp) = istatus(nstp)+ 1 |
|---|
| 1643 | IF((err <= one).or.(h <= hmin))THEN !~~~> accept step |
|---|
| 1644 | istatus(nacc) = istatus(nacc)+ 1 |
|---|
| 1645 | !slim: CALL wcopy(n,ynew,1,y,1) |
|---|
| 1646 | y(1:n) = ynew(1:n) |
|---|
| 1647 | t = t + direction*h |
|---|
| 1648 | hnew = max(hmin,min(hnew,hmax)) |
|---|
| 1649 | IF (rejectlasth)THEN ! no step size increase after a rejected step |
|---|
| 1650 | hnew = min(hnew,h) |
|---|
| 1651 | ENDIF |
|---|
| 1652 | rstatus(nhexit) = h |
|---|
| 1653 | rstatus(nhnew) = hnew |
|---|
| 1654 | rstatus(ntexit) = t |
|---|
| 1655 | rejectlasth = .false. |
|---|
| 1656 | rejectmoreh = .false. |
|---|
| 1657 | h = hnew |
|---|
| 1658 | exit untilaccepted ! exit the loop: WHILE step not accepted |
|---|
| 1659 | ELSE !~~~> reject step |
|---|
| 1660 | IF (rejectmoreh)THEN |
|---|
| 1661 | hnew = h*facrej |
|---|
| 1662 | ENDIF |
|---|
| 1663 | rejectmoreh = rejectlasth |
|---|
| 1664 | rejectlasth = .true. |
|---|
| 1665 | h = hnew |
|---|
| 1666 | IF (istatus(nacc)>= 1) istatus(nrej) = istatus(nrej)+ 1 |
|---|
| 1667 | ENDIF ! err <= 1 |
|---|
| 1668 | |
|---|
| 1669 | END DO untilaccepted |
|---|
| 1670 | |
|---|
| 1671 | END DO timeloop |
|---|
| 1672 | |
|---|
| 1673 | !~~~> succesful exit |
|---|
| 1674 | ierr = 1 !~~~> the integration was successful |
|---|
| 1675 | |
|---|
| 1676 | END SUBROUTINE ros_integrator |
|---|
| 1677 | |
|---|
| 1678 | |
|---|
| 1679 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1680 | REAL(kind=dp)FUNCTION ros_errornorm(y,ynew,yerr,& |
|---|
| 1681 | abstol,reltol,vectortol) |
|---|
| 1682 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1683 | !~~~> computes the "scaled norm" of the error vector yerr |
|---|
| 1684 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1685 | |
|---|
| 1686 | ! Input arguments |
|---|
| 1687 | REAL(kind=dp),INTENT(in):: y(n),ynew(n),& |
|---|
| 1688 | yerr(n),abstol(n),reltol(n) |
|---|
| 1689 | LOGICAL,INTENT(in):: vectortol |
|---|
| 1690 | ! Local variables |
|---|
| 1691 | REAL(kind=dp):: err,scale,ymax |
|---|
| 1692 | INTEGER :: i |
|---|
| 1693 | REAL(kind=dp),PARAMETER :: zero = 0.0_dp |
|---|
| 1694 | |
|---|
| 1695 | err = zero |
|---|
| 1696 | DO i=1,n |
|---|
| 1697 | ymax = max(abs(y(i)),abs(ynew(i))) |
|---|
| 1698 | IF (vectortol)THEN |
|---|
| 1699 | scale = abstol(i)+ reltol(i)*ymax |
|---|
| 1700 | ELSE |
|---|
| 1701 | scale = abstol(1)+ reltol(1)*ymax |
|---|
| 1702 | ENDIF |
|---|
| 1703 | err = err+(yerr(i)/scale)**2 |
|---|
| 1704 | ENDDO |
|---|
| 1705 | err = sqrt(err/n) |
|---|
| 1706 | |
|---|
| 1707 | ros_errornorm = max(err,1.0d-10) |
|---|
| 1708 | |
|---|
| 1709 | END FUNCTION ros_errornorm |
|---|
| 1710 | |
|---|
| 1711 | |
|---|
| 1712 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1713 | SUBROUTINE ros_funtimederivative(t,roundoff,y,& |
|---|
| 1714 | fcn0,dfdt) |
|---|
| 1715 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1716 | !~~~> the time partial derivative of the FUNCTION by finite differences |
|---|
| 1717 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1718 | |
|---|
| 1719 | !~~~> input arguments |
|---|
| 1720 | REAL(kind=dp),INTENT(in):: t,roundoff,y(n),fcn0(n) |
|---|
| 1721 | !~~~> output arguments |
|---|
| 1722 | REAL(kind=dp),INTENT(out):: dfdt(n) |
|---|
| 1723 | !~~~> local variables |
|---|
| 1724 | REAL(kind=dp):: delta |
|---|
| 1725 | REAL(kind=dp),PARAMETER :: one = 1.0_dp, deltamin = 1.0e-6_dp |
|---|
| 1726 | |
|---|
| 1727 | delta = sqrt(roundoff)*max(deltamin,abs(t)) |
|---|
| 1728 | CALL funtemplate(t+ delta,y,dfdt) |
|---|
| 1729 | istatus(nfun) = istatus(nfun)+ 1 |
|---|
| 1730 | CALL waxpy(n,(- one),fcn0,1,dfdt,1) |
|---|
| 1731 | CALL wscal(n,(one/delta),dfdt,1) |
|---|
| 1732 | |
|---|
| 1733 | END SUBROUTINE ros_funtimederivative |
|---|
| 1734 | |
|---|
| 1735 | |
|---|
| 1736 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1737 | SUBROUTINE ros_preparematrix(h,direction,gam,& |
|---|
| 1738 | jac0,ghimj,pivot,singular) |
|---|
| 1739 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
|---|
| 1740 | ! Prepares the LHS matrix for stage calculations |
|---|
| 1741 | ! 1. Construct Ghimj = 1/(H*ham) - Jac0 |
|---|
| 1742 | ! "(Gamma H) Inverse Minus Jacobian" |
|---|
| 1743 | ! 2. Repeat LU decomposition of Ghimj until successful. |
|---|
| 1744 | ! -half the step size if LU decomposition fails and retry |
|---|
| 1745 | ! -exit after 5 consecutive fails |
|---|
| 1746 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
|---|
| 1747 | |
|---|
| 1748 | !~~~> input arguments |
|---|
| 1749 | #ifdef full_algebra |
|---|
| 1750 | REAL(kind=dp),INTENT(in):: jac0(n,n) |
|---|
| 1751 | #else |
|---|
| 1752 | REAL(kind=dp),INTENT(in):: jac0(lu_nonzero) |
|---|
| 1753 | #endif |
|---|
| 1754 | REAL(kind=dp),INTENT(in):: gam |
|---|
| 1755 | INTEGER,INTENT(in):: direction |
|---|
| 1756 | !~~~> output arguments |
|---|
| 1757 | #ifdef full_algebra |
|---|
| 1758 | REAL(kind=dp),INTENT(out):: ghimj(n,n) |
|---|
| 1759 | #else |
|---|
| 1760 | REAL(kind=dp),INTENT(out):: ghimj(lu_nonzero) |
|---|
| 1761 | #endif |
|---|
| 1762 | LOGICAL,INTENT(out):: singular |
|---|
| 1763 | INTEGER,INTENT(out):: pivot(n) |
|---|
| 1764 | !~~~> inout arguments |
|---|
| 1765 | REAL(kind=dp),INTENT(inout):: h ! step size is decreased when lu fails |
|---|
| 1766 | !~~~> local variables |
|---|
| 1767 | INTEGER :: i,ising,nconsecutive |
|---|
| 1768 | REAL(kind=dp):: ghinv |
|---|
| 1769 | REAL(kind=dp),PARAMETER :: one = 1.0_dp, half = 0.5_dp |
|---|
| 1770 | |
|---|
| 1771 | nconsecutive = 0 |
|---|
| 1772 | singular = .true. |
|---|
| 1773 | |
|---|
| 1774 | DO WHILE (singular) |
|---|
| 1775 | |
|---|
| 1776 | !~~~> construct ghimj = 1/(h*gam)- jac0 |
|---|
| 1777 | #ifdef full_algebra |
|---|
| 1778 | !slim: CALL wcopy(n*n,jac0,1,ghimj,1) |
|---|
| 1779 | !slim: CALL wscal(n*n,(- one),ghimj,1) |
|---|
| 1780 | ghimj = - jac0 |
|---|
| 1781 | ghinv = one/(direction*h*gam) |
|---|
| 1782 | DO i=1,n |
|---|
| 1783 | ghimj(i,i) = ghimj(i,i)+ ghinv |
|---|
| 1784 | ENDDO |
|---|
| 1785 | #else |
|---|
| 1786 | !slim: CALL wcopy(lu_nonzero,jac0,1,ghimj,1) |
|---|
| 1787 | !slim: CALL wscal(lu_nonzero,(- one),ghimj,1) |
|---|
| 1788 | ghimj(1:lu_nonzero) = - jac0(1:lu_nonzero) |
|---|
| 1789 | ghinv = one/(direction*h*gam) |
|---|
| 1790 | DO i=1,n |
|---|
| 1791 | ghimj(lu_diag(i)) = ghimj(lu_diag(i))+ ghinv |
|---|
| 1792 | ENDDO |
|---|
| 1793 | #endif |
|---|
| 1794 | !~~~> compute lu decomposition |
|---|
| 1795 | CALL ros_decomp( ghimj,pivot,ising) |
|---|
| 1796 | IF (ising == 0)THEN |
|---|
| 1797 | !~~~> IF successful done |
|---|
| 1798 | singular = .false. |
|---|
| 1799 | ELSE ! ising .ne. 0 |
|---|
| 1800 | !~~~> IF unsuccessful half the step size; IF 5 consecutive fails THEN RETURN |
|---|
| 1801 | istatus(nsng) = istatus(nsng)+ 1 |
|---|
| 1802 | nconsecutive = nconsecutive+1 |
|---|
| 1803 | singular = .true. |
|---|
| 1804 | PRINT*,'Warning: LU Decomposition returned ISING = ',ISING |
|---|
| 1805 | IF (nconsecutive <= 5)THEN ! less than 5 consecutive failed decompositions |
|---|
| 1806 | h = h*half |
|---|
| 1807 | ELSE ! more than 5 consecutive failed decompositions |
|---|
| 1808 | RETURN |
|---|
| 1809 | ENDIF ! nconsecutive |
|---|
| 1810 | ENDIF ! ising |
|---|
| 1811 | |
|---|
| 1812 | END DO ! WHILE singular |
|---|
| 1813 | |
|---|
| 1814 | END SUBROUTINE ros_preparematrix |
|---|
| 1815 | |
|---|
| 1816 | |
|---|
| 1817 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1818 | SUBROUTINE ros_decomp( a,pivot,ising) |
|---|
| 1819 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1820 | ! Template for the LU decomposition |
|---|
| 1821 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1822 | !~~~> inout variables |
|---|
| 1823 | #ifdef full_algebra |
|---|
| 1824 | REAL(kind=dp),INTENT(inout):: a(n,n) |
|---|
| 1825 | #else |
|---|
| 1826 | REAL(kind=dp),INTENT(inout):: a(lu_nonzero) |
|---|
| 1827 | #endif |
|---|
| 1828 | !~~~> output variables |
|---|
| 1829 | INTEGER,INTENT(out):: pivot(n),ising |
|---|
| 1830 | |
|---|
| 1831 | #ifdef full_algebra |
|---|
| 1832 | CALL dgetrf( n,n,a,n,pivot,ising) |
|---|
| 1833 | #else |
|---|
| 1834 | CALL kppdecomp(a,ising) |
|---|
| 1835 | pivot(1) = 1 |
|---|
| 1836 | #endif |
|---|
| 1837 | istatus(ndec) = istatus(ndec)+ 1 |
|---|
| 1838 | |
|---|
| 1839 | END SUBROUTINE ros_decomp |
|---|
| 1840 | |
|---|
| 1841 | |
|---|
| 1842 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1843 | SUBROUTINE ros_solve( a,pivot,b) |
|---|
| 1844 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1845 | ! Template for the forward/backward substitution (using pre-computed LU decomposition) |
|---|
| 1846 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1847 | !~~~> input variables |
|---|
| 1848 | #ifdef full_algebra |
|---|
| 1849 | REAL(kind=dp),INTENT(in):: a(n,n) |
|---|
| 1850 | INTEGER :: ising |
|---|
| 1851 | #else |
|---|
| 1852 | REAL(kind=dp),INTENT(in):: a(lu_nonzero) |
|---|
| 1853 | #endif |
|---|
| 1854 | INTEGER,INTENT(in):: pivot(n) |
|---|
| 1855 | !~~~> inout variables |
|---|
| 1856 | REAL(kind=dp),INTENT(inout):: b(n) |
|---|
| 1857 | |
|---|
| 1858 | #ifdef full_algebra |
|---|
| 1859 | CALL DGETRS( 'N',N ,1,A,N,Pivot,b,N,ISING) |
|---|
| 1860 | IF(info < 0)THEN |
|---|
| 1861 | print*,"error in dgetrs. ising=",ising |
|---|
| 1862 | ENDIF |
|---|
| 1863 | #else |
|---|
| 1864 | CALL kppsolve( a,b) |
|---|
| 1865 | #endif |
|---|
| 1866 | |
|---|
| 1867 | istatus(nsol) = istatus(nsol)+ 1 |
|---|
| 1868 | |
|---|
| 1869 | END SUBROUTINE ros_solve |
|---|
| 1870 | |
|---|
| 1871 | |
|---|
| 1872 | |
|---|
| 1873 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1874 | SUBROUTINE ros2 |
|---|
| 1875 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1876 | ! --- AN L-STABLE METHOD,2 stages,order 2 |
|---|
| 1877 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1878 | |
|---|
| 1879 | double precision g |
|---|
| 1880 | |
|---|
| 1881 | g = 1.0_dp + 1.0_dp/sqrt(2.0_dp) |
|---|
| 1882 | rosmethod = rs2 |
|---|
| 1883 | !~~~> name of the method |
|---|
| 1884 | ros_Name = 'ROS-2' |
|---|
| 1885 | !~~~> number of stages |
|---|
| 1886 | ros_s = 2 |
|---|
| 1887 | |
|---|
| 1888 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 1889 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 1890 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 1891 | ! The general mapping formula is: |
|---|
| 1892 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 1893 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 1894 | |
|---|
| 1895 | ros_a(1) = (1.0_dp)/g |
|---|
| 1896 | ros_c(1) = (- 2.0_dp)/g |
|---|
| 1897 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 1898 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 1899 | ros_newf(1) = .true. |
|---|
| 1900 | ros_newf(2) = .true. |
|---|
| 1901 | !~~~> m_i = coefficients for new step solution |
|---|
| 1902 | ros_m(1) = (3.0_dp)/(2.0_dp*g) |
|---|
| 1903 | ros_m(2) = (1.0_dp)/(2.0_dp*g) |
|---|
| 1904 | ! E_i = Coefficients for error estimator |
|---|
| 1905 | ros_e(1) = 1.0_dp/(2.0_dp*g) |
|---|
| 1906 | ros_e(2) = 1.0_dp/(2.0_dp*g) |
|---|
| 1907 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 1908 | ! main and the embedded scheme orders plus one |
|---|
| 1909 | ros_elo = 2.0_dp |
|---|
| 1910 | !~~~> y_stage_i ~ y( t + h*alpha_i) |
|---|
| 1911 | ros_alpha(1) = 0.0_dp |
|---|
| 1912 | ros_alpha(2) = 1.0_dp |
|---|
| 1913 | !~~~> gamma_i = \sum_j gamma_{i,j} |
|---|
| 1914 | ros_gamma(1) = g |
|---|
| 1915 | ros_gamma(2) =- g |
|---|
| 1916 | |
|---|
| 1917 | END SUBROUTINE ros2 |
|---|
| 1918 | |
|---|
| 1919 | |
|---|
| 1920 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1921 | SUBROUTINE ros3 |
|---|
| 1922 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1923 | ! --- AN L-STABLE METHOD,3 stages,order 3,2 function evaluations |
|---|
| 1924 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1925 | |
|---|
| 1926 | rosmethod = rs3 |
|---|
| 1927 | !~~~> name of the method |
|---|
| 1928 | ros_Name = 'ROS-3' |
|---|
| 1929 | !~~~> number of stages |
|---|
| 1930 | ros_s = 3 |
|---|
| 1931 | |
|---|
| 1932 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 1933 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 1934 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 1935 | ! The general mapping formula is: |
|---|
| 1936 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 1937 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 1938 | |
|---|
| 1939 | ros_a(1) = 1.0_dp |
|---|
| 1940 | ros_a(2) = 1.0_dp |
|---|
| 1941 | ros_a(3) = 0.0_dp |
|---|
| 1942 | |
|---|
| 1943 | ros_c(1) = - 0.10156171083877702091975600115545e+01_dp |
|---|
| 1944 | ros_c(2) = 0.40759956452537699824805835358067e+01_dp |
|---|
| 1945 | ros_c(3) = 0.92076794298330791242156818474003e+01_dp |
|---|
| 1946 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 1947 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 1948 | ros_newf(1) = .true. |
|---|
| 1949 | ros_newf(2) = .true. |
|---|
| 1950 | ros_newf(3) = .false. |
|---|
| 1951 | !~~~> m_i = coefficients for new step solution |
|---|
| 1952 | ros_m(1) = 0.1e+01_dp |
|---|
| 1953 | ros_m(2) = 0.61697947043828245592553615689730e+01_dp |
|---|
| 1954 | ros_m(3) = - 0.42772256543218573326238373806514_dp |
|---|
| 1955 | ! E_i = Coefficients for error estimator |
|---|
| 1956 | ros_e(1) = 0.5_dp |
|---|
| 1957 | ros_e(2) = - 0.29079558716805469821718236208017e+01_dp |
|---|
| 1958 | ros_e(3) = 0.22354069897811569627360909276199_dp |
|---|
| 1959 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 1960 | ! main and the embedded scheme orders plus 1 |
|---|
| 1961 | ros_elo = 3.0_dp |
|---|
| 1962 | !~~~> y_stage_i ~ y( t + h*alpha_i) |
|---|
| 1963 | ros_alpha(1) = 0.0_dp |
|---|
| 1964 | ros_alpha(2) = 0.43586652150845899941601945119356_dp |
|---|
| 1965 | ros_alpha(3) = 0.43586652150845899941601945119356_dp |
|---|
| 1966 | !~~~> gamma_i = \sum_j gamma_{i,j} |
|---|
| 1967 | ros_gamma(1) = 0.43586652150845899941601945119356_dp |
|---|
| 1968 | ros_gamma(2) = 0.24291996454816804366592249683314_dp |
|---|
| 1969 | ros_gamma(3) = 0.21851380027664058511513169485832e+01_dp |
|---|
| 1970 | |
|---|
| 1971 | END SUBROUTINE ros3 |
|---|
| 1972 | |
|---|
| 1973 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1974 | |
|---|
| 1975 | |
|---|
| 1976 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1977 | SUBROUTINE ros4 |
|---|
| 1978 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1979 | ! L-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 4 STAGES |
|---|
| 1980 | ! L-STABLE EMBEDDED ROSENBROCK METHOD OF ORDER 3 |
|---|
| 1981 | ! |
|---|
| 1982 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
|---|
| 1983 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
|---|
| 1984 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
|---|
| 1985 | ! SPRINGER-VERLAG (1990) |
|---|
| 1986 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1987 | |
|---|
| 1988 | |
|---|
| 1989 | rosmethod = rs4 |
|---|
| 1990 | !~~~> name of the method |
|---|
| 1991 | ros_Name = 'ROS-4' |
|---|
| 1992 | !~~~> number of stages |
|---|
| 1993 | ros_s = 4 |
|---|
| 1994 | |
|---|
| 1995 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 1996 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 1997 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 1998 | ! The general mapping formula is: |
|---|
| 1999 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 2000 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 2001 | |
|---|
| 2002 | ros_a(1) = 0.2000000000000000e+01_dp |
|---|
| 2003 | ros_a(2) = 0.1867943637803922e+01_dp |
|---|
| 2004 | ros_a(3) = 0.2344449711399156_dp |
|---|
| 2005 | ros_a(4) = ros_a(2) |
|---|
| 2006 | ros_a(5) = ros_a(3) |
|---|
| 2007 | ros_a(6) = 0.0_dp |
|---|
| 2008 | |
|---|
| 2009 | ros_c(1) =- 0.7137615036412310e+01_dp |
|---|
| 2010 | ros_c(2) = 0.2580708087951457e+01_dp |
|---|
| 2011 | ros_c(3) = 0.6515950076447975_dp |
|---|
| 2012 | ros_c(4) =- 0.2137148994382534e+01_dp |
|---|
| 2013 | ros_c(5) =- 0.3214669691237626_dp |
|---|
| 2014 | ros_c(6) =- 0.6949742501781779_dp |
|---|
| 2015 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2016 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2017 | ros_newf(1) = .true. |
|---|
| 2018 | ros_newf(2) = .true. |
|---|
| 2019 | ros_newf(3) = .true. |
|---|
| 2020 | ros_newf(4) = .false. |
|---|
| 2021 | !~~~> m_i = coefficients for new step solution |
|---|
| 2022 | ros_m(1) = 0.2255570073418735e+01_dp |
|---|
| 2023 | ros_m(2) = 0.2870493262186792_dp |
|---|
| 2024 | ros_m(3) = 0.4353179431840180_dp |
|---|
| 2025 | ros_m(4) = 0.1093502252409163e+01_dp |
|---|
| 2026 | !~~~> e_i = coefficients for error estimator |
|---|
| 2027 | ros_e(1) =- 0.2815431932141155_dp |
|---|
| 2028 | ros_e(2) =- 0.7276199124938920e-01_dp |
|---|
| 2029 | ros_e(3) =- 0.1082196201495311_dp |
|---|
| 2030 | ros_e(4) =- 0.1093502252409163e+01_dp |
|---|
| 2031 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2032 | ! main and the embedded scheme orders plus 1 |
|---|
| 2033 | ros_elo = 4.0_dp |
|---|
| 2034 | !~~~> y_stage_i ~ y( t + h*alpha_i) |
|---|
| 2035 | ros_alpha(1) = 0.0_dp |
|---|
| 2036 | ros_alpha(2) = 0.1145640000000000e+01_dp |
|---|
| 2037 | ros_alpha(3) = 0.6552168638155900_dp |
|---|
| 2038 | ros_alpha(4) = ros_alpha(3) |
|---|
| 2039 | !~~~> gamma_i = \sum_j gamma_{i,j} |
|---|
| 2040 | ros_gamma(1) = 0.5728200000000000_dp |
|---|
| 2041 | ros_gamma(2) =- 0.1769193891319233e+01_dp |
|---|
| 2042 | ros_gamma(3) = 0.7592633437920482_dp |
|---|
| 2043 | ros_gamma(4) =- 0.1049021087100450_dp |
|---|
| 2044 | |
|---|
| 2045 | END SUBROUTINE ros4 |
|---|
| 2046 | |
|---|
| 2047 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2048 | SUBROUTINE rodas3 |
|---|
| 2049 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2050 | ! --- A STIFFLY-STABLE METHOD,4 stages,order 3 |
|---|
| 2051 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2052 | |
|---|
| 2053 | |
|---|
| 2054 | rosmethod = rd3 |
|---|
| 2055 | !~~~> name of the method |
|---|
| 2056 | ros_Name = 'RODAS-3' |
|---|
| 2057 | !~~~> number of stages |
|---|
| 2058 | ros_s = 4 |
|---|
| 2059 | |
|---|
| 2060 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 2061 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 2062 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 2063 | ! The general mapping formula is: |
|---|
| 2064 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 2065 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 2066 | |
|---|
| 2067 | ros_a(1) = 0.0_dp |
|---|
| 2068 | ros_a(2) = 2.0_dp |
|---|
| 2069 | ros_a(3) = 0.0_dp |
|---|
| 2070 | ros_a(4) = 2.0_dp |
|---|
| 2071 | ros_a(5) = 0.0_dp |
|---|
| 2072 | ros_a(6) = 1.0_dp |
|---|
| 2073 | |
|---|
| 2074 | ros_c(1) = 4.0_dp |
|---|
| 2075 | ros_c(2) = 1.0_dp |
|---|
| 2076 | ros_c(3) =- 1.0_dp |
|---|
| 2077 | ros_c(4) = 1.0_dp |
|---|
| 2078 | ros_c(5) =- 1.0_dp |
|---|
| 2079 | ros_c(6) =- (8.0_dp/3.0_dp) |
|---|
| 2080 | |
|---|
| 2081 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2082 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2083 | ros_newf(1) = .true. |
|---|
| 2084 | ros_newf(2) = .false. |
|---|
| 2085 | ros_newf(3) = .true. |
|---|
| 2086 | ros_newf(4) = .true. |
|---|
| 2087 | !~~~> m_i = coefficients for new step solution |
|---|
| 2088 | ros_m(1) = 2.0_dp |
|---|
| 2089 | ros_m(2) = 0.0_dp |
|---|
| 2090 | ros_m(3) = 1.0_dp |
|---|
| 2091 | ros_m(4) = 1.0_dp |
|---|
| 2092 | !~~~> e_i = coefficients for error estimator |
|---|
| 2093 | ros_e(1) = 0.0_dp |
|---|
| 2094 | ros_e(2) = 0.0_dp |
|---|
| 2095 | ros_e(3) = 0.0_dp |
|---|
| 2096 | ros_e(4) = 1.0_dp |
|---|
| 2097 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2098 | ! main and the embedded scheme orders plus 1 |
|---|
| 2099 | ros_elo = 3.0_dp |
|---|
| 2100 | !~~~> y_stage_i ~ y( t + h*alpha_i) |
|---|
| 2101 | ros_alpha(1) = 0.0_dp |
|---|
| 2102 | ros_alpha(2) = 0.0_dp |
|---|
| 2103 | ros_alpha(3) = 1.0_dp |
|---|
| 2104 | ros_alpha(4) = 1.0_dp |
|---|
| 2105 | !~~~> gamma_i = \sum_j gamma_{i,j} |
|---|
| 2106 | ros_gamma(1) = 0.5_dp |
|---|
| 2107 | ros_gamma(2) = 1.5_dp |
|---|
| 2108 | ros_gamma(3) = 0.0_dp |
|---|
| 2109 | ros_gamma(4) = 0.0_dp |
|---|
| 2110 | |
|---|
| 2111 | END SUBROUTINE rodas3 |
|---|
| 2112 | |
|---|
| 2113 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2114 | SUBROUTINE rodas4 |
|---|
| 2115 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2116 | ! STIFFLY-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 6 STAGES |
|---|
| 2117 | ! |
|---|
| 2118 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
|---|
| 2119 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
|---|
| 2120 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
|---|
| 2121 | ! SPRINGER-VERLAG (1996) |
|---|
| 2122 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2123 | |
|---|
| 2124 | |
|---|
| 2125 | rosmethod = rd4 |
|---|
| 2126 | !~~~> name of the method |
|---|
| 2127 | ros_Name = 'RODAS-4' |
|---|
| 2128 | !~~~> number of stages |
|---|
| 2129 | ros_s = 6 |
|---|
| 2130 | |
|---|
| 2131 | !~~~> y_stage_i ~ y( t + h*alpha_i) |
|---|
| 2132 | ros_alpha(1) = 0.000_dp |
|---|
| 2133 | ros_alpha(2) = 0.386_dp |
|---|
| 2134 | ros_alpha(3) = 0.210_dp |
|---|
| 2135 | ros_alpha(4) = 0.630_dp |
|---|
| 2136 | ros_alpha(5) = 1.000_dp |
|---|
| 2137 | ros_alpha(6) = 1.000_dp |
|---|
| 2138 | |
|---|
| 2139 | !~~~> gamma_i = \sum_j gamma_{i,j} |
|---|
| 2140 | ros_gamma(1) = 0.2500000000000000_dp |
|---|
| 2141 | ros_gamma(2) =- 0.1043000000000000_dp |
|---|
| 2142 | ros_gamma(3) = 0.1035000000000000_dp |
|---|
| 2143 | ros_gamma(4) =- 0.3620000000000023e-01_dp |
|---|
| 2144 | ros_gamma(5) = 0.0_dp |
|---|
| 2145 | ros_gamma(6) = 0.0_dp |
|---|
| 2146 | |
|---|
| 2147 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 2148 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 2149 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 2150 | ! The general mapping formula is: A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 2151 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 2152 | |
|---|
| 2153 | ros_a(1) = 0.1544000000000000e+01_dp |
|---|
| 2154 | ros_a(2) = 0.9466785280815826_dp |
|---|
| 2155 | ros_a(3) = 0.2557011698983284_dp |
|---|
| 2156 | ros_a(4) = 0.3314825187068521e+01_dp |
|---|
| 2157 | ros_a(5) = 0.2896124015972201e+01_dp |
|---|
| 2158 | ros_a(6) = 0.9986419139977817_dp |
|---|
| 2159 | ros_a(7) = 0.1221224509226641e+01_dp |
|---|
| 2160 | ros_a(8) = 0.6019134481288629e+01_dp |
|---|
| 2161 | ros_a(9) = 0.1253708332932087e+02_dp |
|---|
| 2162 | ros_a(10) =- 0.6878860361058950_dp |
|---|
| 2163 | ros_a(11) = ros_a(7) |
|---|
| 2164 | ros_a(12) = ros_a(8) |
|---|
| 2165 | ros_a(13) = ros_a(9) |
|---|
| 2166 | ros_a(14) = ros_a(10) |
|---|
| 2167 | ros_a(15) = 1.0_dp |
|---|
| 2168 | |
|---|
| 2169 | ros_c(1) =- 0.5668800000000000e+01_dp |
|---|
| 2170 | ros_c(2) =- 0.2430093356833875e+01_dp |
|---|
| 2171 | ros_c(3) =- 0.2063599157091915_dp |
|---|
| 2172 | ros_c(4) =- 0.1073529058151375_dp |
|---|
| 2173 | ros_c(5) =- 0.9594562251023355e+01_dp |
|---|
| 2174 | ros_c(6) =- 0.2047028614809616e+02_dp |
|---|
| 2175 | ros_c(7) = 0.7496443313967647e+01_dp |
|---|
| 2176 | ros_c(8) =- 0.1024680431464352e+02_dp |
|---|
| 2177 | ros_c(9) =- 0.3399990352819905e+02_dp |
|---|
| 2178 | ros_c(10) = 0.1170890893206160e+02_dp |
|---|
| 2179 | ros_c(11) = 0.8083246795921522e+01_dp |
|---|
| 2180 | ros_c(12) =- 0.7981132988064893e+01_dp |
|---|
| 2181 | ros_c(13) =- 0.3152159432874371e+02_dp |
|---|
| 2182 | ros_c(14) = 0.1631930543123136e+02_dp |
|---|
| 2183 | ros_c(15) =- 0.6058818238834054e+01_dp |
|---|
| 2184 | |
|---|
| 2185 | !~~~> m_i = coefficients for new step solution |
|---|
| 2186 | ros_m(1) = ros_a(7) |
|---|
| 2187 | ros_m(2) = ros_a(8) |
|---|
| 2188 | ros_m(3) = ros_a(9) |
|---|
| 2189 | ros_m(4) = ros_a(10) |
|---|
| 2190 | ros_m(5) = 1.0_dp |
|---|
| 2191 | ros_m(6) = 1.0_dp |
|---|
| 2192 | |
|---|
| 2193 | !~~~> e_i = coefficients for error estimator |
|---|
| 2194 | ros_e(1) = 0.0_dp |
|---|
| 2195 | ros_e(2) = 0.0_dp |
|---|
| 2196 | ros_e(3) = 0.0_dp |
|---|
| 2197 | ros_e(4) = 0.0_dp |
|---|
| 2198 | ros_e(5) = 0.0_dp |
|---|
| 2199 | ros_e(6) = 1.0_dp |
|---|
| 2200 | |
|---|
| 2201 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2202 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2203 | ros_newf(1) = .true. |
|---|
| 2204 | ros_newf(2) = .true. |
|---|
| 2205 | ros_newf(3) = .true. |
|---|
| 2206 | ros_newf(4) = .true. |
|---|
| 2207 | ros_newf(5) = .true. |
|---|
| 2208 | ros_newf(6) = .true. |
|---|
| 2209 | |
|---|
| 2210 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2211 | ! main and the embedded scheme orders plus 1 |
|---|
| 2212 | ros_elo = 4.0_dp |
|---|
| 2213 | |
|---|
| 2214 | END SUBROUTINE rodas4 |
|---|
| 2215 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2216 | SUBROUTINE rang3 |
|---|
| 2217 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2218 | ! STIFFLY-STABLE W METHOD OF ORDER 3,WITH 4 STAGES |
|---|
| 2219 | ! |
|---|
| 2220 | ! J. RANG and L. ANGERMANN |
|---|
| 2221 | ! NEW ROSENBROCK W-METHODS OF ORDER 3 |
|---|
| 2222 | ! FOR PARTIAL DIFFERENTIAL ALGEBRAIC |
|---|
| 2223 | ! EQUATIONS OF INDEX 1 |
|---|
| 2224 | ! BIT Numerical Mathematics (2005) 45: 761-787 |
|---|
| 2225 | ! DOI: 10.1007/s10543-005-0035-y |
|---|
| 2226 | ! Table 4.1-4.2 |
|---|
| 2227 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2228 | |
|---|
| 2229 | |
|---|
| 2230 | rosmethod = rg3 |
|---|
| 2231 | !~~~> name of the method |
|---|
| 2232 | ros_Name = 'RANG-3' |
|---|
| 2233 | !~~~> number of stages |
|---|
| 2234 | ros_s = 4 |
|---|
| 2235 | |
|---|
| 2236 | ros_a(1) = 5.09052051067020d+00; |
|---|
| 2237 | ros_a(2) = 5.09052051067020d+00; |
|---|
| 2238 | ros_a(3) = 0.0d0; |
|---|
| 2239 | ros_a(4) = 4.97628111010787d+00; |
|---|
| 2240 | ros_a(5) = 2.77268164715849d-02; |
|---|
| 2241 | ros_a(6) = 2.29428036027904d-01; |
|---|
| 2242 | |
|---|
| 2243 | ros_c(1) = - 1.16790812312283d+01; |
|---|
| 2244 | ros_c(2) = - 1.64057326467367d+01; |
|---|
| 2245 | ros_c(3) = - 2.77268164715850d-01; |
|---|
| 2246 | ros_c(4) = - 8.38103960500476d+00; |
|---|
| 2247 | ros_c(5) = - 8.48328409199343d-01; |
|---|
| 2248 | ros_c(6) = 2.87009860433106d-01; |
|---|
| 2249 | |
|---|
| 2250 | ros_m(1) = 5.22582761233094d+00; |
|---|
| 2251 | ros_m(2) = - 5.56971148154165d-01; |
|---|
| 2252 | ros_m(3) = 3.57979469353645d-01; |
|---|
| 2253 | ros_m(4) = 1.72337398521064d+00; |
|---|
| 2254 | |
|---|
| 2255 | ros_e(1) = - 5.16845212784040d+00; |
|---|
| 2256 | ros_e(2) = - 1.26351942603842d+00; |
|---|
| 2257 | ros_e(3) = - 1.11022302462516d-16; |
|---|
| 2258 | ros_e(4) = 2.22044604925031d-16; |
|---|
| 2259 | |
|---|
| 2260 | ros_alpha(1) = 0.0d00; |
|---|
| 2261 | ros_alpha(2) = 2.21878746765329d+00; |
|---|
| 2262 | ros_alpha(3) = 2.21878746765329d+00; |
|---|
| 2263 | ros_alpha(4) = 1.55392337535788d+00; |
|---|
| 2264 | |
|---|
| 2265 | ros_gamma(1) = 4.35866521508459d-01; |
|---|
| 2266 | ros_gamma(2) = - 1.78292094614483d+00; |
|---|
| 2267 | ros_gamma(3) = - 2.46541900496934d+00; |
|---|
| 2268 | ros_gamma(4) = - 8.05529997906370d-01; |
|---|
| 2269 | |
|---|
| 2270 | |
|---|
| 2271 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2272 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2273 | ros_newf(1) = .true. |
|---|
| 2274 | ros_newf(2) = .true. |
|---|
| 2275 | ros_newf(3) = .true. |
|---|
| 2276 | ros_newf(4) = .true. |
|---|
| 2277 | |
|---|
| 2278 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2279 | ! main and the embedded scheme orders plus 1 |
|---|
| 2280 | ros_elo = 3.0_dp |
|---|
| 2281 | |
|---|
| 2282 | END SUBROUTINE rang3 |
|---|
| 2283 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2284 | |
|---|
| 2285 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2286 | ! End of the set of internal Rosenbrock subroutines |
|---|
| 2287 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2288 | END SUBROUTINE rosenbrock |
|---|
| 2289 | |
|---|
| 2290 | SUBROUTINE funtemplate( t,y,ydot) |
|---|
| 2291 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2292 | ! Template for the ODE function call. |
|---|
| 2293 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
|---|
| 2294 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2295 | !~~~> input variables |
|---|
| 2296 | REAL(kind=dp):: t,y(nvar) |
|---|
| 2297 | !~~~> output variables |
|---|
| 2298 | REAL(kind=dp):: ydot(nvar) |
|---|
| 2299 | !~~~> local variables |
|---|
| 2300 | REAL(kind=dp):: told |
|---|
| 2301 | |
|---|
| 2302 | told = time |
|---|
| 2303 | time = t |
|---|
| 2304 | CALL fun( y,fix,rconst,ydot) |
|---|
| 2305 | time = told |
|---|
| 2306 | |
|---|
| 2307 | END SUBROUTINE funtemplate |
|---|
| 2308 | |
|---|
| 2309 | SUBROUTINE jactemplate( t,y,jcb) |
|---|
| 2310 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2311 | ! Template for the ODE Jacobian call. |
|---|
| 2312 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
|---|
| 2313 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2314 | !~~~> input variables |
|---|
| 2315 | REAL(kind=dp):: t,y(nvar) |
|---|
| 2316 | !~~~> output variables |
|---|
| 2317 | #ifdef full_algebra |
|---|
| 2318 | REAL(kind=dp):: jv(lu_nonzero),jcb(nvar,nvar) |
|---|
| 2319 | #else |
|---|
| 2320 | REAL(kind=dp):: jcb(lu_nonzero) |
|---|
| 2321 | #endif |
|---|
| 2322 | !~~~> local variables |
|---|
| 2323 | REAL(kind=dp):: told |
|---|
| 2324 | #ifdef full_algebra |
|---|
| 2325 | INTEGER :: i,j |
|---|
| 2326 | #endif |
|---|
| 2327 | |
|---|
| 2328 | told = time |
|---|
| 2329 | time = t |
|---|
| 2330 | #ifdef full_algebra |
|---|
| 2331 | CALL jac_sp(y,fix,rconst,jv) |
|---|
| 2332 | DO j=1,nvar |
|---|
| 2333 | DO i=1,nvar |
|---|
| 2334 | jcb(i,j) = 0.0_dp |
|---|
| 2335 | ENDDO |
|---|
| 2336 | ENDDO |
|---|
| 2337 | DO i=1,lu_nonzero |
|---|
| 2338 | jcb(lu_irow(i),lu_icol(i)) = jv(i) |
|---|
| 2339 | ENDDO |
|---|
| 2340 | #else |
|---|
| 2341 | CALL jac_sp( y,fix,rconst,jcb) |
|---|
| 2342 | #endif |
|---|
| 2343 | time = told |
|---|
| 2344 | |
|---|
| 2345 | END SUBROUTINE jactemplate |
|---|
| 2346 | |
|---|
| 2347 | SUBROUTINE chem_gasphase_integrate (time_step_len,conc,tempk,photo,ierrf,xnacc,xnrej,istatus,l_debug,pe) |
|---|
| 2348 | |
|---|
| 2349 | IMPLICIT NONE |
|---|
| 2350 | |
|---|
| 2351 | REAL(dp), INTENT(IN) :: time_step_len |
|---|
| 2352 | REAL(dp), DIMENSION(:,:), INTENT(INOUT) :: conc |
|---|
| 2353 | REAL(dp), DIMENSION(:,:), INTENT(INOUT) :: photo |
|---|
| 2354 | REAL(dp), DIMENSION(:), INTENT(IN) :: tempk |
|---|
| 2355 | INTEGER, INTENT(OUT), OPTIONAL :: ierrf(:) |
|---|
| 2356 | INTEGER, INTENT(OUT), OPTIONAL :: xnacc(:) |
|---|
| 2357 | INTEGER, INTENT(OUT), OPTIONAL :: xnrej(:) |
|---|
| 2358 | INTEGER, INTENT(INOUT), OPTIONAL :: istatus(:) |
|---|
| 2359 | INTEGER, INTENT(IN), OPTIONAL :: pe |
|---|
| 2360 | LOGICAL, INTENT(IN), OPTIONAL :: l_debug |
|---|
| 2361 | |
|---|
| 2362 | INTEGER :: k ! loop variable |
|---|
| 2363 | REAL(dp) :: dt |
|---|
| 2364 | INTEGER, DIMENSION(20) :: istatus_u |
|---|
| 2365 | INTEGER :: ierr_u |
|---|
| 2366 | |
|---|
| 2367 | |
|---|
| 2368 | if (present (istatus)) istatus = 0 |
|---|
| 2369 | |
|---|
| 2370 | DO k=1,vl_glo,vl_dim |
|---|
| 2371 | is = k |
|---|
| 2372 | ie = min(k+vl_dim-1,vl_glo) |
|---|
| 2373 | vl = ie-is+1 |
|---|
| 2374 | |
|---|
| 2375 | c(:) = conc(is,:) |
|---|
| 2376 | |
|---|
| 2377 | temp = tempk(is) |
|---|
| 2378 | |
|---|
| 2379 | phot(:) = photo(is,:) |
|---|
| 2380 | |
|---|
| 2381 | CALL update_rconst |
|---|
| 2382 | |
|---|
| 2383 | dt = time_step_len |
|---|
| 2384 | |
|---|
| 2385 | ! integrate from t=0 to t=dt |
|---|
| 2386 | CALL integrate(0._dp, dt,icntrl,rcntrl,istatus_u = istatus_u,ierr_u=ierr_u) |
|---|
| 2387 | |
|---|
| 2388 | |
|---|
| 2389 | IF (PRESENT(l_debug) .AND. PRESENT(pe)) THEN |
|---|
| 2390 | IF (l_debug) CALL error_output(conc(is,:),ierr_u,pe) |
|---|
| 2391 | ENDIF |
|---|
| 2392 | conc(is,:) = c(:) |
|---|
| 2393 | |
|---|
| 2394 | ! Return Diagnostic Information |
|---|
| 2395 | |
|---|
| 2396 | if(PRESENT(ierrf)) ierrf(is) = ierr_u |
|---|
| 2397 | if(PRESENT(xnacc)) xnacc(is) = istatus_u(4) |
|---|
| 2398 | if(PRESENT(xnrej)) xnrej(is) = istatus_u(5) |
|---|
| 2399 | |
|---|
| 2400 | if (PRESENT (istatus)) then |
|---|
| 2401 | istatus(1:8) = istatus(1:8) + istatus_u(1:8) |
|---|
| 2402 | ENDIF |
|---|
| 2403 | |
|---|
| 2404 | END DO |
|---|
| 2405 | |
|---|
| 2406 | |
|---|
| 2407 | ! Deallocate input arrays |
|---|
| 2408 | |
|---|
| 2409 | if (ALLOCATED(temp)) DEALLOCATE(temp) |
|---|
| 2410 | |
|---|
| 2411 | data_loaded = .false. |
|---|
| 2412 | |
|---|
| 2413 | RETURN |
|---|
| 2414 | END SUBROUTINE chem_gasphase_integrate |
|---|
| 2415 | |
|---|
| 2416 | SUBROUTINE fill_temp(status,array) |
|---|
| 2417 | |
|---|
| 2418 | INTEGER, INTENT(OUT) :: status |
|---|
| 2419 | REAL(dp), INTENT(IN), DIMENSION(:) :: array |
|---|
| 2420 | |
|---|
| 2421 | status = 0 |
|---|
| 2422 | IF (.not. ALLOCATED(temp)) & |
|---|
| 2423 | ALLOCATE(temp(size(array))) |
|---|
| 2424 | |
|---|
| 2425 | IF (data_loaded .AND. (vl_glo /= size(array,1))) THEN |
|---|
| 2426 | status = 1 |
|---|
| 2427 | RETURN |
|---|
| 2428 | END IF |
|---|
| 2429 | |
|---|
| 2430 | vl_glo = size(array,1) |
|---|
| 2431 | temp = array |
|---|
| 2432 | data_loaded = .TRUE. |
|---|
| 2433 | |
|---|
| 2434 | RETURN |
|---|
| 2435 | |
|---|
| 2436 | END SUBROUTINE fill_temp |
|---|
| 2437 | |
|---|
| 2438 | END MODULE chem_gasphase_mod |
|---|
| 2439 | |
|---|
