[2696] | 1 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 2 | ! SDIRK - Singly-Diagonally-Implicit Runge-Kutta method ! |
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| 3 | ! (L-stable, 5 stages, order 4) ! |
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| 4 | ! By default the code employs the KPP sparse linear algebra routines ! |
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| 5 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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| 6 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 7 | ! A. Sandu - version of July 10, 2005 |
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| 8 | |
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| 9 | MODULE KPP_ROOT_Integrator |
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| 10 | |
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| 11 | USE KPP_ROOT_Precision |
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| 12 | USE KPP_ROOT_Global, ONLY: FIX, RCONST, TIME |
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| 13 | USE KPP_ROOT_Parameters, ONLY: NVAR, NSPEC, NFIX, LU_NONZERO |
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| 14 | USE KPP_ROOT_JacobianSP, ONLY: LU_DIAG |
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| 15 | USE KPP_ROOT_LinearAlgebra, ONLY: KppDecomp, KppSolve, & |
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| 16 | Set2zero, WLAMCH, WAXPY, WCOPY |
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| 17 | |
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| 18 | IMPLICIT NONE |
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| 19 | PUBLIC |
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| 20 | SAVE |
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| 21 | |
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| 22 | !~~~> Statistics on the work performed by the SDIRK method |
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| 23 | INTEGER :: Nfun,Njac,Nstp,Nacc,Nrej,Ndec,Nsol,Nsng |
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| 24 | INTEGER, PARAMETER :: ifun=1, ijac=2, istp=3, iacc=4, & |
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| 25 | irej=5, idec=6, isol=7, isng=8, itexit=1, ihexit=2 |
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| 26 | ! SDIRK method coefficients |
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| 27 | KPP_REAL :: rkAlpha(5,4), rkBeta(5,4), rkD(4,5), & |
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| 28 | rkGamma, rkA(5,5), rkB(5), rkC(5) |
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| 29 | |
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| 30 | ! description of the error numbers IERR |
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| 31 | CHARACTER(LEN=50), PARAMETER, DIMENSION(-8:1) :: IERR_NAMES = (/ & |
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| 32 | 'Matrix is repeatedly singular ', & ! -8 |
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| 33 | 'Step size too small: T + 10*H = T or H < Roundoff ', & ! -7 |
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| 34 | 'No of steps exceeds maximum bound ', & ! -6 |
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| 35 | 'Improper tolerance values ', & ! -5 |
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| 36 | 'FacMin/FacMax/FacRej must be positive ', & ! -4 |
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| 37 | 'Hmin/Hmax/Hstart must be positive ', & ! -3 |
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| 38 | 'Improper value for maximal no of Newton iterations', & ! -2 |
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| 39 | 'Improper value for maximal no of steps ', & ! -1 |
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| 40 | ' ', & ! 0 (not used) |
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| 41 | 'Success ' /) ! 1 |
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| 42 | |
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| 43 | CONTAINS |
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| 44 | |
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| 45 | SUBROUTINE INTEGRATE( TIN, TOUT, & |
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| 46 | ICNTRL_U, RCNTRL_U, ISTATUS_U, RSTATUS_U, IERR_U ) |
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| 47 | |
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| 48 | USE KPP_ROOT_Parameters |
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| 49 | USE KPP_ROOT_Global |
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| 50 | IMPLICIT NONE |
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| 51 | |
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| 52 | KPP_REAL, INTENT(IN) :: TIN ! Start Time |
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| 53 | KPP_REAL, INTENT(IN) :: TOUT ! End Time |
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| 54 | ! Optional input parameters and statistics |
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| 55 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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| 56 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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| 57 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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| 58 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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| 59 | INTEGER, INTENT(OUT), OPTIONAL :: IERR_U |
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| 60 | |
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| 61 | !INTEGER, SAVE :: Ntotal = 0 |
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| 62 | KPP_REAL :: RCNTRL(20), RSTATUS(20) |
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| 63 | INTEGER :: ICNTRL(20), ISTATUS(20), IERR |
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| 64 | |
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| 65 | ICNTRL(:) = 0 |
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| 66 | RCNTRL(:) = 0.0_dp |
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| 67 | ISTATUS(:) = 0 |
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| 68 | |
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| 69 | ! If optional parameters are given, and if they are >0, |
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| 70 | ! then they overwrite default settings. |
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| 71 | IF (PRESENT(ICNTRL_U)) THEN |
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| 72 | WHERE(ICNTRL_U(:) > 0) ICNTRL(:) = ICNTRL_U(:) |
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| 73 | END IF |
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| 74 | IF (PRESENT(RCNTRL_U)) THEN |
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| 75 | WHERE(RCNTRL_U(:) > 0) RCNTRL(:) = RCNTRL_U(:) |
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| 76 | END IF |
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| 77 | |
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| 78 | CALL SDIRK( NVAR,TIN,TOUT,VAR,RTOL,ATOL, & |
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| 79 | RCNTRL,ICNTRL,RSTATUS,ISTATUS,IERR ) |
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| 80 | |
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| 81 | ! mz_rs_20050716: IERR and ISTATUS(istp) are returned to the user who then |
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| 82 | ! decides what to do about it, i.e. either stop the run or ignore it. |
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| 83 | !!$ IF (IERR < 0) THEN |
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| 84 | !!$ PRINT *,'SDIRK: Unsuccessful exit at T=',TIN,' (IERR=',IERR,')' |
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| 85 | !!$ ENDIF |
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| 86 | !!$ Ntotal = Ntotal + Nstp |
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| 87 | !!$ PRINT*,'NSTEPS=',Nstp, '(',Ntotal,')' |
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| 88 | |
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| 89 | STEPMIN = RSTATUS(ihexit) ! Save last step |
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| 90 | |
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| 91 | ! if optional parameters are given for output they to return information |
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| 92 | IF (PRESENT(ISTATUS_U)) ISTATUS_U(:) = ISTATUS(:) |
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| 93 | IF (PRESENT(RSTATUS_U)) THEN |
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| 94 | RSTATUS_U(:) = RSTATUS(:) |
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| 95 | RSTATUS_U(1) = TOUT ! final time |
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| 96 | END IF |
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| 97 | IF (PRESENT(IERR_U)) IERR_U = IERR |
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| 98 | |
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| 99 | END SUBROUTINE INTEGRATE |
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| 100 | |
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| 101 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 102 | SUBROUTINE SDIRK(N, Tinitial, Tfinal, Y, RelTol, AbsTol, & |
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| 103 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, IDID) |
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| 104 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 105 | ! |
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| 106 | ! Solves the system y'=F(t,y) using a Singly-Diagonally-Implicit |
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| 107 | ! Runge-Kutta (SDIRK) method. |
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| 108 | ! |
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| 109 | ! For details on SDIRK methods and their implementation consult: |
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| 110 | ! E. Hairer and G. Wanner |
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| 111 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
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| 112 | ! Springer series in computational mathematics, Springer-Verlag, 1996. |
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| 113 | ! This code is based on the SDIRK4 routine in the above book. |
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| 114 | ! |
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| 115 | ! (C) Adrian Sandu, July 2005 |
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| 116 | ! Virginia Polytechnic Institute and State University |
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| 117 | ! Contact: sandu@cs.vt.edu |
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| 118 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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| 119 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 120 | ! |
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| 121 | !~~~> INPUT ARGUMENTS: |
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| 122 | ! |
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| 123 | !- Y(NVAR) = vector of initial conditions (at T=Tinitial) |
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| 124 | !- [Tinitial,Tfinal] = time range of integration |
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| 125 | ! (if Tinitial>Tfinal the integration is performed backwards in time) |
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| 126 | !- RelTol, AbsTol = user precribed accuracy |
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| 127 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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| 128 | ! returns Ydot = Y' = F(T,Y) |
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| 129 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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| 130 | ! returns Jcb = dF/dY |
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| 131 | !- ICNTRL(1:20) = integer inputs parameters |
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| 132 | !- RCNTRL(1:20) = real inputs parameters |
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| 133 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 134 | ! |
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| 135 | !~~~> OUTPUT ARGUMENTS: |
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| 136 | ! |
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| 137 | !- Y(NVAR) -> vector of final states (at T->Tfinal) |
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| 138 | !- ISTATUS(1:20) -> integer output parameters |
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| 139 | !- RSTATUS(1:20) -> real output parameters |
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| 140 | !- IDID -> job status upon return |
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| 141 | ! success (positive value) or |
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| 142 | ! failure (negative value) |
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| 143 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 144 | ! |
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| 145 | !~~~> INPUT PARAMETERS: |
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| 146 | ! |
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| 147 | ! Note: For input parameters equal to zero the default values of the |
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| 148 | ! corresponding variables are used. |
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| 149 | ! |
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| 150 | ! Note: For input parameters equal to zero the default values of the |
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| 151 | ! corresponding variables are used. |
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| 152 | !~~~> |
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| 153 | ! ICNTRL(1) = not used |
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| 154 | ! |
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| 155 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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| 156 | ! = 1: AbsTol, RelTol are scalars |
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| 157 | ! |
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| 158 | ! ICNTRL(3) = not used |
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| 159 | ! |
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| 160 | ! ICNTRL(4) -> maximum number of integration steps |
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| 161 | ! For ICNTRL(4)=0 the default value of 100000 is used |
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| 162 | ! |
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| 163 | ! ICNTRL(5) -> maximum number of Newton iterations |
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| 164 | ! For ICNTRL(5)=0 the default value of 8 is used |
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| 165 | ! |
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| 166 | ! ICNTRL(6) -> starting values of Newton iterations: |
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| 167 | ! ICNTRL(6)=0 : starting values are interpolated (the default) |
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| 168 | ! ICNTRL(6)=1 : starting values are zero |
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| 169 | ! |
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| 170 | !~~~> Real parameters |
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| 171 | ! |
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| 172 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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| 173 | ! It is strongly recommended to keep Hmin = ZERO |
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| 174 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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| 175 | ! RCNTRL(3) -> Hstart, starting value for the integration step size |
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| 176 | ! |
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| 177 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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| 178 | ! RCNTRL(5) -> FacMax, upper bound on step increase factor (default=6) |
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| 179 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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| 180 | ! (default=0.1) |
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| 181 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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| 182 | ! than the predicted value (default=0.9) |
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| 183 | ! RCNTRL(8) -> ThetaMin. If Newton convergence rate smaller |
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| 184 | ! than ThetaMin the Jacobian is not recomputed; |
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| 185 | ! (default=0.001) |
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| 186 | ! RCNTRL(9) -> NewtonTol, stopping criterion for Newton's method |
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| 187 | ! (default=0.03) |
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| 188 | ! RCNTRL(10) -> Qmin |
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| 189 | ! RCNTRL(11) -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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| 190 | ! step size is kept constant and the LU factorization |
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| 191 | ! reused (default Qmin=1, Qmax=1.2) |
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| 192 | ! |
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| 193 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 194 | ! |
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| 195 | !~~~> OUTPUT PARAMETERS: |
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| 196 | ! |
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| 197 | ! Note: each call to Rosenbrock adds the current no. of fcn calls |
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| 198 | ! to previous value of ISTATUS(1), and similar for the other params. |
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| 199 | ! Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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| 200 | ! |
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| 201 | ! ISTATUS(1) = No. of function calls |
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| 202 | ! ISTATUS(2) = No. of jacobian calls |
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| 203 | ! ISTATUS(3) = No. of steps |
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| 204 | ! ISTATUS(4) = No. of accepted steps |
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| 205 | ! ISTATUS(5) = No. of rejected steps (except at the beginning) |
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| 206 | ! ISTATUS(6) = No. of LU decompositions |
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| 207 | ! ISTATUS(7) = No. of forward/backward substitutions |
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| 208 | ! ISTATUS(8) = No. of singular matrix decompositions |
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| 209 | ! |
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| 210 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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| 211 | ! computed Y upon return |
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| 212 | ! RSTATUS(2) -> Hexit, last predicted step before exit |
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| 213 | ! For multiple restarts, use Hexit as Hstart in the following run |
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| 214 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 215 | IMPLICIT NONE |
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| 216 | |
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| 217 | ! Arguments |
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| 218 | INTEGER, INTENT(IN) :: N, ICNTRL(20) |
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| 219 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal, & |
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| 220 | RelTol(NVAR), AbsTol(NVAR), RCNTRL(20) |
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| 221 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
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| 222 | INTEGER, INTENT(OUT) :: IDID |
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| 223 | INTEGER, INTENT(INOUT) :: ISTATUS(20) |
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| 224 | KPP_REAL, INTENT(OUT) :: RSTATUS(20) |
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| 225 | |
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| 226 | ! Local variables |
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| 227 | KPP_REAL :: Hmin, Hmax, Hstart, Roundoff, & |
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| 228 | FacMin, Facmax, FacSafe, FacRej, & |
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| 229 | ThetaMin, NewtonTol, Qmin, Qmax, & |
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| 230 | Texit, Hexit |
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| 231 | INTEGER :: ITOL, NewtonMaxit, Max_no_steps, i |
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| 232 | KPP_REAL, PARAMETER :: ZERO = 0.0d0 |
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| 233 | |
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| 234 | !~~~> Initialize statistics |
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| 235 | Nfun = ISTATUS(ifun) |
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| 236 | Njac = ISTATUS(ijac) |
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| 237 | Nstp = ISTATUS(istp) |
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| 238 | Nacc = ISTATUS(iacc) |
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| 239 | Nrej = ISTATUS(irej) |
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| 240 | Ndec = ISTATUS(idec) |
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| 241 | Nsol = ISTATUS(isol) |
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| 242 | Nsng = ISTATUS(isng) |
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| 243 | ! Nfun=0; Njac=0; Nstp=0; Nacc=0 |
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| 244 | ! Nrej=0; Ndec=0; Nsol=0; Nsng=0 |
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| 245 | |
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| 246 | IDID = 0 |
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| 247 | |
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| 248 | !~~~> For Scalar tolerances (ICNTRL(2).NE.0) the code uses AbsTol(1) and RelTol(1) |
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| 249 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:NVAR) and RelTol(1:NVAR) |
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| 250 | IF (ICNTRL(2) == 0) THEN |
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| 251 | ITOL = 1 |
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| 252 | ELSE |
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| 253 | ITOL = 0 |
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| 254 | END IF |
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| 255 | |
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| 256 | !~~~> The maximum number of time steps admitted |
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| 257 | IF (ICNTRL(3) == 0) THEN |
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| 258 | Max_no_steps = 100000 |
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| 259 | ELSEIF (Max_no_steps > 0) THEN |
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| 260 | Max_no_steps=ICNTRL(3) |
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| 261 | ELSE |
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| 262 | PRINT * ,'User-selected ICNTRL(3)=',ICNTRL(3) |
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| 263 | CALL SDIRK_ErrorMsg(-1,Tinitial,ZERO,IDID) |
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| 264 | END IF |
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| 265 | |
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| 266 | |
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| 267 | !~~~> The maximum number of Newton iterations admitted |
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| 268 | IF(ICNTRL(4) == 0)THEN |
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| 269 | NewtonMaxit=8 |
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| 270 | ELSE |
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| 271 | NewtonMaxit=ICNTRL(4) |
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| 272 | IF(NewtonMaxit <= 0)THEN |
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| 273 | PRINT * ,'User-selected ICNTRL(4)=',ICNTRL(4) |
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| 274 | CALL SDIRK_ErrorMsg(-2,Tinitial,ZERO,IDID) |
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| 275 | END IF |
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| 276 | END IF |
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| 277 | |
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| 278 | !~~~> Unit roundoff (1+Roundoff>1) |
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| 279 | Roundoff = WLAMCH('E') |
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| 280 | |
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| 281 | !~~~> Lower bound on the step size: (positive value) |
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| 282 | IF (RCNTRL(1) == ZERO) THEN |
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| 283 | Hmin = ZERO |
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| 284 | ELSEIF (RCNTRL(1) > ZERO) THEN |
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| 285 | Hmin = RCNTRL(1) |
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| 286 | ELSE |
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| 287 | PRINT * , 'User-selected RCNTRL(1)=', RCNTRL(1) |
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| 288 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,IDID) |
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| 289 | END IF |
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| 290 | |
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| 291 | !~~~> Upper bound on the step size: (positive value) |
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| 292 | IF (RCNTRL(2) == ZERO) THEN |
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| 293 | Hmax = ABS(Tfinal-Tinitial) |
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| 294 | ELSEIF (RCNTRL(2) > ZERO) THEN |
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| 295 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tfinal-Tinitial)) |
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| 296 | ELSE |
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| 297 | PRINT * , 'User-selected RCNTRL(2)=', RCNTRL(2) |
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| 298 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,IDID) |
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| 299 | END IF |
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| 300 | |
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| 301 | !~~~> Starting step size: (positive value) |
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| 302 | IF (RCNTRL(3) == ZERO) THEN |
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| 303 | Hstart = MAX(Hmin,Roundoff) |
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| 304 | ELSEIF (RCNTRL(3) > ZERO) THEN |
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| 305 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tfinal-Tinitial)) |
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| 306 | ELSE |
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| 307 | PRINT * , 'User-selected Hstart: RCNTRL(3)=', RCNTRL(3) |
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| 308 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,IDID) |
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| 309 | END IF |
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| 310 | |
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| 311 | !~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax |
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| 312 | IF (RCNTRL(4) == ZERO) THEN |
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| 313 | FacMin = 0.2_dp |
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| 314 | ELSEIF (RCNTRL(4) > ZERO) THEN |
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| 315 | FacMin = RCNTRL(4) |
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| 316 | ELSE |
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| 317 | PRINT * , 'User-selected FacMin: RCNTRL(4)=', RCNTRL(4) |
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| 318 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,IDID) |
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| 319 | END IF |
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| 320 | IF (RCNTRL(5) == ZERO) THEN |
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| 321 | FacMax = 10.0_dp |
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| 322 | ELSEIF (RCNTRL(5) > ZERO) THEN |
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| 323 | FacMax = RCNTRL(5) |
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| 324 | ELSE |
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| 325 | PRINT * , 'User-selected FacMax: RCNTRL(5)=', RCNTRL(5) |
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| 326 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,IDID) |
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| 327 | END IF |
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| 328 | !~~~> FacRej: Factor to decrease step after 2 succesive rejections |
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| 329 | IF (RCNTRL(6) == ZERO) THEN |
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| 330 | FacRej = 0.1_dp |
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| 331 | ELSEIF (RCNTRL(6) > ZERO) THEN |
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| 332 | FacRej = RCNTRL(6) |
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| 333 | ELSE |
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| 334 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
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| 335 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,IDID) |
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| 336 | END IF |
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| 337 | !~~~> FacSafe: Safety Factor in the computation of new step size |
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| 338 | IF (RCNTRL(7) == ZERO) THEN |
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| 339 | FacSafe = 0.9_dp |
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| 340 | ELSEIF (RCNTRL(7) > ZERO) THEN |
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| 341 | FacSafe = RCNTRL(7) |
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| 342 | ELSE |
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| 343 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
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| 344 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,IDID) |
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| 345 | END IF |
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| 346 | |
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| 347 | !~~~> DECIDES WHETHER THE JACOBIAN SHOULD BE RECOMPUTED; |
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| 348 | IF(RCNTRL(8) == 0.D0)THEN |
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| 349 | ThetaMin = 1.0d-3 |
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| 350 | ELSE |
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| 351 | ThetaMin = RCNTRL(8) |
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| 352 | END IF |
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| 353 | |
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| 354 | !~~~> STOPPING CRITERION FOR NEWTON'S METHOD |
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| 355 | IF(RCNTRL(9) == 0.0d0)THEN |
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| 356 | NewtonTol = 3.0d-2 |
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| 357 | ELSE |
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| 358 | NewtonTol =RCNTRL(9) |
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| 359 | END IF |
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| 360 | |
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| 361 | !~~~> Qmin AND Qmax: IF Qmin < Hnew/Hold < Qmax, STEP SIZE = CONST. |
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| 362 | IF(RCNTRL(10) == 0.D0)THEN |
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| 363 | Qmin=1.D0 |
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| 364 | ELSE |
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| 365 | Qmin=RCNTRL(10) |
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| 366 | END IF |
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| 367 | IF(RCNTRL(11) == 0.D0)THEN |
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| 368 | Qmax=1.2D0 |
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| 369 | ELSE |
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| 370 | Qmax=RCNTRL(11) |
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| 371 | END IF |
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| 372 | |
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| 373 | !~~~> Check if tolerances are reasonable |
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| 374 | IF (ITOL == 0) THEN |
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| 375 | IF (AbsTol(1) <= 0.D0.OR.RelTol(1) <= 10.D0*Roundoff) THEN |
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| 376 | PRINT * , ' Scalar AbsTol = ',AbsTol(1) |
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| 377 | PRINT * , ' Scalar RelTol = ',RelTol(1) |
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| 378 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,IDID) |
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| 379 | END IF |
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| 380 | ELSE |
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| 381 | DO i=1,N |
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| 382 | IF (AbsTol(i) <= 0.D0.OR.RelTol(i) <= 10.D0*Roundoff) THEN |
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| 383 | PRINT * , ' AbsTol(',i,') = ',AbsTol(i) |
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| 384 | PRINT * , ' RelTol(',i,') = ',RelTol(i) |
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| 385 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,IDID) |
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| 386 | END IF |
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| 387 | END DO |
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| 388 | END IF |
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| 389 | |
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| 390 | IF (IDID < 0) RETURN |
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| 391 | |
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| 392 | |
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| 393 | !~~~> CALL TO CORE INTEGRATOR |
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| 394 | CALL SDIRK_Integrator( N,Tinitial,Tfinal,Y,Hmin,Hmax,Hstart, & |
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| 395 | RelTol,AbsTol,ITOL, Max_no_steps, NewtonMaxit, & |
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| 396 | Roundoff, FacMin, FacMax, FacRej, FacSafe, ThetaMin, & |
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| 397 | NewtonTol, Qmin, Qmax, Hexit, Texit, IDID ) |
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| 398 | |
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| 399 | !~~~> Collect run statistics |
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| 400 | ISTATUS(ifun) = Nfun |
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| 401 | ISTATUS(ijac) = Njac |
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| 402 | ISTATUS(istp) = Nstp |
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| 403 | ISTATUS(iacc) = Nacc |
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| 404 | ISTATUS(irej) = Nrej |
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| 405 | ISTATUS(idec) = Ndec |
---|
| 406 | ISTATUS(isol) = Nsol |
---|
| 407 | ISTATUS(isng) = Nsng |
---|
| 408 | !~~~> Last T and H |
---|
| 409 | RSTATUS(:) = 0.0_dp |
---|
| 410 | RSTATUS(itexit) = Texit |
---|
| 411 | RSTATUS(ihexit) = Hexit |
---|
| 412 | |
---|
| 413 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 414 | CONTAINS ! PROCEDURES INTERNAL TO SDIRK |
---|
| 415 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 416 | |
---|
| 417 | |
---|
| 418 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 419 | SUBROUTINE SDIRK_Integrator( N,Tinitial,Tfinal,Y,Hmin,Hmax,Hstart, & |
---|
| 420 | RelTol,AbsTol,ITOL, Max_no_steps, NewtonMaxit, & |
---|
| 421 | Roundoff, FacMin, FacMax, FacRej, FacSafe, ThetaMin, & |
---|
| 422 | NewtonTol, Qmin, Qmax, Hexit, Texit, IDID ) |
---|
| 423 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 424 | ! CORE INTEGRATOR FOR SDIRK4 |
---|
| 425 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 426 | |
---|
| 427 | USE KPP_ROOT_Parameters |
---|
| 428 | IMPLICIT NONE |
---|
| 429 | |
---|
| 430 | !~~~> Arguments: |
---|
| 431 | INTEGER :: N |
---|
| 432 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
---|
| 433 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal, Hmin, Hmax, Hstart, & |
---|
| 434 | RelTol(NVAR), AbsTol(NVAR), Roundoff, & |
---|
| 435 | FacMin, FacMax, FacRej, FacSafe, ThetaMin, & |
---|
| 436 | NewtonTol, Qmin, Qmax |
---|
| 437 | KPP_REAL, INTENT(OUT) :: Hexit, Texit |
---|
| 438 | INTEGER, INTENT(IN) :: ITOL, Max_no_steps, NewtonMaxit |
---|
| 439 | INTEGER, INTENT(OUT) :: IDID |
---|
| 440 | |
---|
| 441 | !~~~> Local variables: |
---|
| 442 | KPP_REAL :: Z(NVAR,5), FV(NVAR,5), CONT(NVAR,4), & |
---|
| 443 | NewtonFactor(5), SCAL(NVAR), RHS(NVAR), & |
---|
| 444 | G(NVAR), Yhat(NVAR), TMP(NVAR), & |
---|
| 445 | T, H, Hold, Theta, Hratio, Hmax1, W, & |
---|
| 446 | HGammaInv, DYTH, QNEWT, ERR, Fac, Hnew, & |
---|
| 447 | Tdirection, NewtonErr, NewtonErrOld |
---|
| 448 | INTEGER :: i, j, IER, istage, NewtonIter, IP(NVAR) |
---|
| 449 | LOGICAL :: Reject, FIRST, NewtonReject, FreshJac, SkipJacUpdate, SkipLU |
---|
| 450 | |
---|
| 451 | #ifdef FULL_ALGEBRA |
---|
| 452 | KPP_REAL FJAC(NVAR,NVAR), E(NVAR,NVAR) |
---|
| 453 | #else |
---|
| 454 | KPP_REAL FJAC(LU_NONZERO), E(LU_NONZERO) |
---|
| 455 | #endif |
---|
| 456 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
| 457 | |
---|
| 458 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 459 | ! INITIALISATIONS |
---|
| 460 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 461 | CALL SDIRK_Coefficients |
---|
| 462 | T = Tinitial |
---|
| 463 | Tdirection = SIGN(1.D0,Tfinal-Tinitial) |
---|
| 464 | Hmax1=MIN(ABS(Hmax),ABS(Tfinal-Tinitial)) |
---|
| 465 | H = MAX(ABS(Hmin),ABS(Hstart)) |
---|
| 466 | IF (ABS(H) <= 10.D0*Roundoff) H=1.0D-6 |
---|
| 467 | H=MIN(ABS(H),Hmax1) |
---|
| 468 | H=SIGN(H,Tdirection) |
---|
| 469 | Hold=H |
---|
| 470 | NewtonReject=.FALSE. |
---|
| 471 | SkipLU =.FALSE. |
---|
| 472 | FreshJac = .FALSE. |
---|
| 473 | SkipJacUpdate = .FALSE. |
---|
| 474 | Reject=.FALSE. |
---|
| 475 | FIRST=.TRUE. |
---|
| 476 | NewtonFactor(1:5)=ONE |
---|
| 477 | |
---|
| 478 | CALL SDIRK_ErrorScale(ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 479 | |
---|
| 480 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 481 | !~~~> Time loop begins |
---|
| 482 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 483 | Tloop: DO WHILE ( (Tfinal-T)*Tdirection - Roundoff > ZERO ) |
---|
| 484 | |
---|
| 485 | |
---|
| 486 | !~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition |
---|
| 487 | IF ( SkipLU ) THEN ! This time around skip the Jac update and LU |
---|
| 488 | SkipLU = .FALSE.; FreshJac = .FALSE.; SkipJacUpdate = .FALSE. |
---|
| 489 | ELSE |
---|
| 490 | CALL SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
| 491 | FreshJac, SkipJacUpdate, E, IP, Reject, IER ) |
---|
| 492 | IF (IER /= 0) THEN |
---|
| 493 | CALL SDIRK_ErrorMsg(-8,T,H,IDID); RETURN |
---|
| 494 | END IF |
---|
| 495 | END IF |
---|
| 496 | |
---|
| 497 | IF (Nstp>Max_no_steps) THEN |
---|
| 498 | CALL SDIRK_ErrorMsg(-6,T,H,IDID); RETURN |
---|
| 499 | END IF |
---|
| 500 | IF ( (T+0.1d0*H == T) .OR. (ABS(H) <= Roundoff) ) THEN |
---|
| 501 | CALL SDIRK_ErrorMsg(-7,T,H,IDID); RETURN |
---|
| 502 | END IF |
---|
| 503 | |
---|
| 504 | HGammaInv = ONE/(H*rkGamma) |
---|
| 505 | |
---|
| 506 | !~~~> NEWTON ITERATION |
---|
| 507 | stages:DO istage=1,5 |
---|
| 508 | |
---|
| 509 | NewtonFactor(istage) = MAX(NewtonFactor(istage),Roundoff)**0.8d0 |
---|
| 510 | |
---|
| 511 | !~~~> STARTING VALUES FOR NEWTON ITERATION |
---|
| 512 | CALL Set2zero(N,G) |
---|
| 513 | CALL Set2zero(N,Z(1,istage)) |
---|
| 514 | IF (istage==1) THEN |
---|
| 515 | IF (FIRST.OR.NewtonReject) THEN |
---|
| 516 | CALL Set2zero(N,Z(1,istage)) |
---|
| 517 | ELSE |
---|
| 518 | W=ONE+rkGamma*H/Hold |
---|
| 519 | DO i=1,N |
---|
| 520 | Z(i,istage)=W*(CONT(i,1)+W*(CONT(i,2)+W*(CONT(i,3)+W*CONT(i,4))))-Yhat(i) |
---|
| 521 | END DO |
---|
| 522 | END IF |
---|
| 523 | ELSE |
---|
| 524 | DO j = 1, istage-1 |
---|
| 525 | ! Gj(:) = sum_j Beta(i,j)*Zj(:) = H * sum_j A(i,j)*Fun(Zj(:)) |
---|
| 526 | CALL WAXPY(N,rkBeta(istage,j),Z(1,j),1,G,1) |
---|
| 527 | ! CALL WAXPY(N,H*rkA(istage,j),FV(1,j),1,G,1) |
---|
| 528 | ! Zi(:) = sum_j Alpha(i,j)*Zj(:) |
---|
| 529 | CALL WAXPY(N,rkAlpha(istage,j),Z(1,j),1,Z(1,istage),1) |
---|
| 530 | END DO |
---|
| 531 | IF (istage==5) CALL WCOPY(N,Z(1,istage),1,Yhat,1) ! Yhat(:) <- Z5(:) |
---|
| 532 | END IF |
---|
| 533 | |
---|
| 534 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 535 | ! LOOP FOR THE SIMPLIFIED NEWTON ITERATION |
---|
| 536 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 537 | NewtonIter=0 |
---|
| 538 | Theta=ABS(ThetaMin) |
---|
| 539 | IF (Reject) Theta=2*ABS(ThetaMin) |
---|
| 540 | NewtonErr = 1.0e+6 ! To force-enter Newton loop |
---|
| 541 | |
---|
| 542 | Newton: DO WHILE (NewtonFactor(istage)*NewtonErr > NewtonTol) |
---|
| 543 | |
---|
| 544 | IF (NewtonIter >= NewtonMaxit) THEN |
---|
| 545 | H=H*0.5d0 |
---|
| 546 | Reject=.TRUE. |
---|
| 547 | NewtonReject=.TRUE. |
---|
| 548 | CYCLE Tloop |
---|
| 549 | END IF |
---|
| 550 | NewtonIter=NewtonIter+1 |
---|
| 551 | |
---|
| 552 | !~~~> COMPUTE THE RIGHT-HAND SIDE |
---|
| 553 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
| 554 | CALL FUN_CHEM(T+rkC(istage)*H,TMP,RHS) |
---|
| 555 | TMP(1:N) = G(1:N) - Z(1:N,istage) |
---|
| 556 | CALL WAXPY(N,HGammaInv,TMP,1,RHS,1) ! RHS(:) <- RHS(:) + HGammaInv*(G(:)-Z(:)) |
---|
| 557 | |
---|
| 558 | !~~~> SOLVE THE LINEAR SYSTEMS |
---|
| 559 | #ifdef FULL_ALGEBRA |
---|
| 560 | CALL DGETRS( 'N', N, 1, E, N, IP, RHS, N, IER ) |
---|
| 561 | #else |
---|
| 562 | CALL KppSolve(E, RHS) |
---|
| 563 | #endif |
---|
| 564 | Nsol=Nsol+1 |
---|
| 565 | |
---|
| 566 | !~~~> CHECK CONVERGENCE OR IF NUMBER OF ITERATIONS TOO LARGE |
---|
| 567 | CALL SDIRK_ErrorNorm(N, RHS, SCAL, NewtonErr) |
---|
| 568 | IF ( (NewtonIter >= 2) .AND. (NewtonIter < NewtonMaxit) ) THEN |
---|
| 569 | Theta = NewtonErr/NewtonErrOld |
---|
| 570 | IF (Theta < 0.99d0) THEN |
---|
| 571 | NewtonFactor(istage)=Theta/(ONE-Theta) |
---|
| 572 | DYTH = NewtonFactor(istage)*NewtonErr* & |
---|
| 573 | Theta**(NewtonMaxit-1-NewtonIter) |
---|
| 574 | QNEWT = MAX(1.0d-4,MIN(16.0d0,DYTH/NewtonTol)) |
---|
| 575 | IF (QNEWT >= ONE) THEN |
---|
| 576 | H=.8D0*H*QNEWT**(-ONE/(NewtonMaxit-NewtonIter)) |
---|
| 577 | Reject=.TRUE. |
---|
| 578 | NewtonReject=.TRUE. |
---|
| 579 | CYCLE Tloop ! go back to the beginning of DO step |
---|
| 580 | END IF |
---|
| 581 | ELSE |
---|
| 582 | NewtonReject=.TRUE. |
---|
| 583 | H=H*0.5d0 |
---|
| 584 | Reject=.TRUE. |
---|
| 585 | CYCLE Tloop ! go back to the beginning of DO step |
---|
| 586 | END IF |
---|
| 587 | END IF |
---|
| 588 | NewtonErrOld = NewtonErr |
---|
| 589 | CALL WAXPY(N,ONE,RHS,1,Z(1,istage),1) ! Z(:) <-- Z(:)+RHS(:) |
---|
| 590 | |
---|
| 591 | END DO Newton |
---|
| 592 | |
---|
| 593 | !~~> END OF SIMPLIFIED NEWTON ITERATION |
---|
| 594 | ! Save function values |
---|
| 595 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
| 596 | CALL FUN_CHEM(T+rkC(istage)*H,TMP,FV(1,istage)) |
---|
| 597 | |
---|
| 598 | END DO stages |
---|
| 599 | |
---|
| 600 | |
---|
| 601 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 602 | ! ERROR ESTIMATION |
---|
| 603 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 604 | Nstp=Nstp+1 |
---|
| 605 | TMP(1:N)=HGammaInv*(Z(1:N,5)-Yhat(1:N)) |
---|
| 606 | |
---|
| 607 | #ifdef FULL_ALGEBRA |
---|
| 608 | CALL DGETRS( 'N', N, 1, E, N, IP, TMP, N, IER ) |
---|
| 609 | #else |
---|
| 610 | CALL KppSolve(E, TMP) |
---|
| 611 | #endif |
---|
| 612 | |
---|
| 613 | CALL SDIRK_ErrorNorm(N, TMP, SCAL, ERR) |
---|
| 614 | |
---|
| 615 | !~~~> COMPUTATION OF Hnew: WE REQUIRE FacMin <= Hnew/H <= FacMax |
---|
| 616 | !Safe = FacSafe*DBLE(1+2*NewtonMaxit)/DBLE(NewtonIter+2*NewtonMaxit) |
---|
| 617 | Fac = MAX(FacMin,MIN(FacMax,(ERR)**(-0.25d0)*FacSafe)) |
---|
| 618 | Hnew = H*Fac |
---|
| 619 | |
---|
| 620 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 621 | ! ACCEPT/Reject STEP |
---|
| 622 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 623 | accept: IF ( ERR < ONE ) THEN !~~~> STEP IS ACCEPTED |
---|
| 624 | |
---|
| 625 | FIRST=.FALSE. |
---|
| 626 | Nacc=Nacc+1 |
---|
| 627 | Hold=H |
---|
| 628 | |
---|
| 629 | !~~~> COEFFICIENTS FOR CONTINUOUS SOLUTION |
---|
| 630 | CALL WAXPY(N,ONE,Z(1,5),1,Y,1) ! Y(:) <-- Y(:)+Z5(:) |
---|
| 631 | CALL WCOPY(N,Z(1,5),1,Yhat,1) ! Yhat <-- Z5 |
---|
| 632 | |
---|
| 633 | DO i=1,4 ! CONTi <-- Sum_j rkD(i,j)*Zj |
---|
| 634 | CALL Set2zero(N,CONT(1,i)) |
---|
| 635 | DO j = 1,5 |
---|
| 636 | CALL WAXPY(N,rkD(i,j),Z(1,j),1,CONT(1,i),1) |
---|
| 637 | END DO |
---|
| 638 | END DO |
---|
| 639 | |
---|
| 640 | CALL SDIRK_ErrorScale(ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 641 | |
---|
| 642 | T=T+H |
---|
| 643 | FreshJac=.FALSE. |
---|
| 644 | |
---|
| 645 | Hnew = Tdirection*MIN(ABS(Hnew),Hmax1) |
---|
| 646 | Hexit = Hnew |
---|
| 647 | IF (Reject) Hnew=Tdirection*MIN(ABS(Hnew),ABS(H)) |
---|
| 648 | Reject = .FALSE. |
---|
| 649 | NewtonReject = .FALSE. |
---|
| 650 | IF ((T+Hnew/Qmin-Tfinal)*Tdirection > 0.D0) THEN |
---|
| 651 | H = Tfinal-T |
---|
| 652 | ELSE |
---|
| 653 | Hratio=Hnew/H |
---|
| 654 | ! If step not changed too much, keep it as is; |
---|
| 655 | ! do not update Jacobian and reuse LU |
---|
| 656 | IF ( (Theta <= ThetaMin) .AND. (Hratio >= Qmin) & |
---|
| 657 | .AND. (Hratio <= Qmax) ) THEN |
---|
| 658 | SkipJacUpdate = .TRUE. |
---|
| 659 | SkipLU = .TRUE. |
---|
| 660 | ELSE |
---|
| 661 | H = Hnew |
---|
| 662 | END IF |
---|
| 663 | END IF |
---|
| 664 | ! If convergence is fast enough, do not update Jacobian |
---|
| 665 | IF (Theta <= ThetaMin) SkipJacUpdate = .TRUE. |
---|
| 666 | |
---|
| 667 | ELSE accept !~~~> STEP IS REJECTED |
---|
| 668 | |
---|
| 669 | Reject=.TRUE. |
---|
| 670 | IF (FIRST) THEN |
---|
| 671 | H=H*FacRej |
---|
| 672 | ELSE |
---|
| 673 | H=Hnew |
---|
| 674 | END IF |
---|
| 675 | IF (Nacc >= 1) Nrej=Nrej+1 |
---|
| 676 | |
---|
| 677 | END IF accept |
---|
| 678 | |
---|
| 679 | END DO Tloop |
---|
| 680 | |
---|
| 681 | ! Successful return |
---|
| 682 | Texit = T |
---|
| 683 | IDID = 1 |
---|
| 684 | |
---|
| 685 | END SUBROUTINE SDIRK_Integrator |
---|
| 686 | |
---|
| 687 | |
---|
| 688 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 689 | SUBROUTINE SDIRK_ErrorScale(ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 690 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 691 | IMPLICIT NONE |
---|
| 692 | INTEGER :: i, ITOL |
---|
| 693 | KPP_REAL :: AbsTol(NVAR), RelTol(NVAR), & |
---|
| 694 | Y(NVAR), SCAL(NVAR) |
---|
| 695 | IF (ITOL == 0) THEN |
---|
| 696 | DO i=1,NVAR |
---|
| 697 | SCAL(i) = 1.0d0 / ( AbsTol(1)+RelTol(1)*ABS(Y(i)) ) |
---|
| 698 | END DO |
---|
| 699 | ELSE |
---|
| 700 | DO i=1,NVAR |
---|
| 701 | SCAL(i) = 1.0d0 / ( AbsTol(i)+RelTol(i)*ABS(Y(i)) ) |
---|
| 702 | END DO |
---|
| 703 | END IF |
---|
| 704 | END SUBROUTINE SDIRK_ErrorScale |
---|
| 705 | |
---|
| 706 | |
---|
| 707 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 708 | SUBROUTINE SDIRK_ErrorNorm(N, Y, SCAL, ERR) |
---|
| 709 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 710 | ! |
---|
| 711 | INTEGER :: i, N |
---|
| 712 | KPP_REAL :: Y(N), SCAL(N), ERR |
---|
| 713 | ERR=0.0d0 |
---|
| 714 | DO i=1,N |
---|
| 715 | ERR = ERR+(Y(i)*SCAL(i))**2 |
---|
| 716 | END DO |
---|
| 717 | ERR = MAX( SQRT(ERR/DBLE(N)), 1.0d-10 ) |
---|
| 718 | ! |
---|
| 719 | END SUBROUTINE SDIRK_ErrorNorm |
---|
| 720 | |
---|
| 721 | |
---|
| 722 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 723 | SUBROUTINE SDIRK_ErrorMsg(Code,T,H,IERR) |
---|
| 724 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 725 | ! Handles all error messages |
---|
| 726 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 727 | |
---|
| 728 | KPP_REAL, INTENT(IN) :: T, H |
---|
| 729 | INTEGER, INTENT(IN) :: Code |
---|
| 730 | INTEGER, INTENT(OUT) :: IERR |
---|
| 731 | |
---|
| 732 | IERR = Code |
---|
| 733 | PRINT * , & |
---|
| 734 | 'Forced exit from SDIRK due to the following error:' |
---|
| 735 | IF ((Code>=-8).AND.(Code<=-1)) THEN |
---|
| 736 | PRINT *, IERR_NAMES(Code) |
---|
| 737 | ELSE |
---|
| 738 | PRINT *, 'Unknown Error code: ', Code |
---|
| 739 | ENDIF |
---|
| 740 | |
---|
| 741 | PRINT *, "T=", T, "and H=", H |
---|
| 742 | |
---|
| 743 | END SUBROUTINE SDIRK_ErrorMsg |
---|
| 744 | |
---|
| 745 | |
---|
| 746 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 747 | SUBROUTINE SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
| 748 | FreshJac, SkipJacUpdate, E, IP, Reject, IER ) |
---|
| 749 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 750 | ! |
---|
| 751 | IMPLICIT NONE |
---|
| 752 | |
---|
| 753 | KPP_REAL, INTENT(INOUT) :: H |
---|
| 754 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
---|
| 755 | LOGICAL, INTENT(INOUT) :: FreshJac, SkipJacUpdate |
---|
| 756 | INTEGER, INTENT(OUT) :: IER, IP(NVAR) |
---|
| 757 | LOGICAL, INTENT(INOUT) :: Reject |
---|
| 758 | #ifdef FULL_ALGEBRA |
---|
| 759 | KPP_REAL, INTENT(INOUT) :: FJAC(NVAR,NVAR) |
---|
| 760 | KPP_REAL, INTENT(OUT) :: E(NVAR,NVAR) |
---|
| 761 | #else |
---|
| 762 | KPP_REAL, INTENT(INOUT) :: FJAC(LU_NONZERO) |
---|
| 763 | KPP_REAL, INTENT(OUT) :: E(LU_NONZERO) |
---|
| 764 | #endif |
---|
| 765 | KPP_REAL :: HGammaInv |
---|
| 766 | INTEGER :: i, j, ConsecutiveSng |
---|
| 767 | KPP_REAL, PARAMETER :: ONE = 1.0d0 |
---|
| 768 | |
---|
| 769 | 20 CONTINUE |
---|
| 770 | |
---|
| 771 | !~~~> COMPUTE THE JACOBIAN |
---|
| 772 | IF (SkipJacUpdate) THEN |
---|
| 773 | SkipJacUpdate = .FALSE. |
---|
| 774 | ELSE IF ( .NOT.FreshJac ) THEN |
---|
| 775 | CALL JAC_CHEM( T, Y, FJAC ) |
---|
| 776 | FreshJac = .TRUE. |
---|
| 777 | END IF |
---|
| 778 | |
---|
| 779 | !~~~> Compute the matrix E = 1/(H*GAMMA)*Jac, and its decomposition |
---|
| 780 | ConsecutiveSng = 0 |
---|
| 781 | IER = 1 |
---|
| 782 | |
---|
| 783 | Hloop: DO WHILE (IER /= 0) |
---|
| 784 | |
---|
| 785 | HGammaInv = ONE/(H*rkGamma) |
---|
| 786 | |
---|
| 787 | #ifdef FULL_ALGEBRA |
---|
| 788 | DO j=1,NVAR |
---|
| 789 | DO i=1,NVAR |
---|
| 790 | E(i,j)=-FJAC(i,j) |
---|
| 791 | END DO |
---|
| 792 | E(j,j)=E(j,j)+HGammaInv |
---|
| 793 | END DO |
---|
| 794 | CALL DGETRF( NVAR, NVAR, E, NVAR, IP, IER ) |
---|
| 795 | #else |
---|
| 796 | DO i = 1,LU_NONZERO |
---|
| 797 | E(i) = -FJAC(i) |
---|
| 798 | END DO |
---|
| 799 | DO i = 1,NVAR |
---|
| 800 | j = LU_DIAG(i); E(j) = E(j) + HGammaInv |
---|
| 801 | END DO |
---|
| 802 | CALL KppDecomp ( E, IER) |
---|
| 803 | IP(1) = 1 |
---|
| 804 | #endif |
---|
| 805 | Ndec=Ndec+1 |
---|
| 806 | |
---|
| 807 | IF (IER /= 0) THEN |
---|
| 808 | WRITE (6,*) ' MATRIX IS SINGULAR, IER=',IER,' T=',T,' H=',H |
---|
| 809 | Nsng = Nsng+1; ConsecutiveSng = ConsecutiveSng + 1 |
---|
| 810 | IF (ConsecutiveSng >= 6) RETURN ! Failure |
---|
| 811 | H=H*0.5d0 |
---|
| 812 | Reject=.TRUE. |
---|
| 813 | !~~~> Update Jacobian if not fresh |
---|
| 814 | IF ( .NOT.FreshJac ) GOTO 20 |
---|
| 815 | END IF |
---|
| 816 | |
---|
| 817 | END DO Hloop |
---|
| 818 | |
---|
| 819 | END SUBROUTINE SDIRK_PrepareMatrix |
---|
| 820 | |
---|
| 821 | |
---|
| 822 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 823 | SUBROUTINE SDIRK_Coefficients |
---|
| 824 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 825 | rkGamma=4.0d0/15.0d0 |
---|
| 826 | |
---|
| 827 | rkA(1,1)= 4.d0/15.d0 |
---|
| 828 | rkA(2,1)= 1.d0/2.d0 |
---|
| 829 | rkA(2,2)= 4.d0/15.d0 |
---|
| 830 | rkA(3,1)= 51069.d0/144200.d0 |
---|
| 831 | rkA(3,2)=-7809.d0/144200.d0 |
---|
| 832 | rkA(3,3)= 4.d0/15.d0 |
---|
| 833 | rkA(4,1)= 12047244770625658.d0/141474406359725325.d0 |
---|
| 834 | rkA(4,2)=-3057890203562191.d0/47158135453241775.d0 |
---|
| 835 | rkA(4,3)= 2239631894905804.d0/28294881271945065.d0 |
---|
| 836 | rkA(4,4)= 4.d0/15.d0 |
---|
| 837 | rkA(5,1)= 181513.d0/86430.d0 |
---|
| 838 | rkA(5,2)=-89074.d0/116015.d0 |
---|
| 839 | rkA(5,3)= 83636.d0/34851.d0 |
---|
| 840 | rkA(5,4)=-69863904375173.d0/23297141763930.d0 |
---|
| 841 | rkA(5,5)= 4.d0/15.d0 |
---|
| 842 | |
---|
| 843 | rkB(1)= 181513.d0/86430.d0 |
---|
| 844 | rkB(2)=-89074.d0/116015.d0 |
---|
| 845 | rkB(3)= 83636.d0/34851.d0 |
---|
| 846 | rkB(4)=-69863904375173.d0/23297141763930.d0 |
---|
| 847 | rkB(5)= 4/15.d0 |
---|
| 848 | |
---|
| 849 | rkC(1)=4.d0/15.d0 |
---|
| 850 | rkC(2)=23.d0/30.d0 |
---|
| 851 | rkC(3)=17.d0/30.d0 |
---|
| 852 | rkC(4)=707.d0/1931.d0 |
---|
| 853 | rkC(5)=1.d0 |
---|
| 854 | |
---|
| 855 | rkBeta(2,1)=15.0d0/8.0d0 |
---|
| 856 | rkBeta(3,1)=1577061.0d0/922880.0d0 |
---|
| 857 | rkBeta(3,2)=-23427.0d0/115360.0d0 |
---|
| 858 | rkBeta(4,1)=647163682356923881.0d0/2414496535205978880.0d0 |
---|
| 859 | rkBeta(4,2)=-593512117011179.0d0/3245291041943520.0d0 |
---|
| 860 | rkBeta(4,3)=559907973726451.0d0/1886325418129671.0d0 |
---|
| 861 | rkBeta(5,1)=724545451.0d0/796538880.0d0 |
---|
| 862 | rkBeta(5,2)=-830832077.0d0/267298560.0d0 |
---|
| 863 | rkBeta(5,3)=30957577.0d0/2509272.0d0 |
---|
| 864 | rkBeta(5,4)=-69863904375173.0d0/6212571137048.0d0 |
---|
| 865 | |
---|
| 866 | rkAlpha(2,1)= 23.d0/8.d0 |
---|
| 867 | rkAlpha(3,1)= 0.9838473040915402d0 |
---|
| 868 | rkAlpha(3,2)= 0.3969226768377252d0 |
---|
| 869 | rkAlpha(4,1)= 0.6563374010466914d0 |
---|
| 870 | rkAlpha(4,2)= 0.0d0 |
---|
| 871 | rkAlpha(4,3)= 0.3372498196189311d0 |
---|
| 872 | rkAlpha(5,1)=7752107607.0d0/11393456128.0d0 |
---|
| 873 | rkAlpha(5,2)=-17881415427.0d0/11470078208.0d0 |
---|
| 874 | rkAlpha(5,3)=2433277665.0d0/179459416.0d0 |
---|
| 875 | rkAlpha(5,4)=-96203066666797.0d0/6212571137048.0d0 |
---|
| 876 | |
---|
| 877 | rkD(1,1)= 24.74416644927758d0 |
---|
| 878 | rkD(1,2)= -4.325375951824688d0 |
---|
| 879 | rkD(1,3)= 41.39683763286316d0 |
---|
| 880 | rkD(1,4)= -61.04144619901784d0 |
---|
| 881 | rkD(1,5)= -3.391332232917013d0 |
---|
| 882 | rkD(2,1)= -51.98245719616925d0 |
---|
| 883 | rkD(2,2)= 10.52501981094525d0 |
---|
| 884 | rkD(2,3)= -154.2067922191855d0 |
---|
| 885 | rkD(2,4)= 214.3082125319825d0 |
---|
| 886 | rkD(2,5)= 14.71166018088679d0 |
---|
| 887 | rkD(3,1)= 33.14347947522142d0 |
---|
| 888 | rkD(3,2)= -19.72986789558523d0 |
---|
| 889 | rkD(3,3)= 230.4878502285804d0 |
---|
| 890 | rkD(3,4)= -287.6629744338197d0 |
---|
| 891 | rkD(3,5)= -18.99932366302254d0 |
---|
| 892 | rkD(4,1)= -5.905188728329743d0 |
---|
| 893 | rkD(4,2)= 13.53022403646467d0 |
---|
| 894 | rkD(4,3)= -117.6778956422581d0 |
---|
| 895 | rkD(4,4)= 134.3962081008550d0 |
---|
| 896 | rkD(4,5)= 8.678995715052762d0 |
---|
| 897 | |
---|
| 898 | END SUBROUTINE SDIRK_Coefficients |
---|
| 899 | |
---|
| 900 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 901 | END SUBROUTINE SDIRK ! AND ALL ITS INTERNAL PROCEDURES |
---|
| 902 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 903 | |
---|
| 904 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 905 | SUBROUTINE FUN_CHEM( T, Y, P ) |
---|
| 906 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 907 | |
---|
| 908 | USE KPP_ROOT_Parameters, ONLY: NVAR, LU_NONZERO |
---|
| 909 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
| 910 | USE KPP_ROOT_Function |
---|
| 911 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST |
---|
| 912 | |
---|
| 913 | INTEGER N |
---|
| 914 | KPP_REAL T, Told |
---|
| 915 | KPP_REAL Y(NVAR), P(NVAR) |
---|
| 916 | |
---|
| 917 | Told = TIME |
---|
| 918 | TIME = T |
---|
| 919 | CALL Update_SUN() |
---|
| 920 | CALL Update_RCONST() |
---|
| 921 | |
---|
| 922 | CALL Fun( Y, FIX, RCONST, P ) |
---|
| 923 | |
---|
| 924 | TIME = Told |
---|
| 925 | Nfun=Nfun+1 |
---|
| 926 | |
---|
| 927 | END SUBROUTINE FUN_CHEM |
---|
| 928 | |
---|
| 929 | |
---|
| 930 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 931 | SUBROUTINE JAC_CHEM( T, Y, JV ) |
---|
| 932 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 933 | |
---|
| 934 | USE KPP_ROOT_Parameters, ONLY: NVAR, LU_NONZERO |
---|
| 935 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
| 936 | USE KPP_ROOT_Jacobian |
---|
| 937 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST |
---|
| 938 | |
---|
| 939 | INTEGER N |
---|
| 940 | KPP_REAL T, Told |
---|
| 941 | KPP_REAL Y(NVAR) |
---|
| 942 | #ifdef FULL_ALGEBRA |
---|
| 943 | KPP_REAL :: JS(LU_NONZERO), JV(NVAR,NVAR) |
---|
| 944 | INTEGER :: i, j |
---|
| 945 | #else |
---|
| 946 | KPP_REAL :: JV(LU_NONZERO) |
---|
| 947 | #endif |
---|
| 948 | |
---|
| 949 | Told = TIME |
---|
| 950 | TIME = T |
---|
| 951 | CALL Update_SUN() |
---|
| 952 | CALL Update_RCONST() |
---|
| 953 | |
---|
| 954 | #ifdef FULL_ALGEBRA |
---|
| 955 | CALL Jac_SP(Y, FIX, RCONST, JS) |
---|
| 956 | DO j=1,NVAR |
---|
| 957 | DO j=1,NVAR |
---|
| 958 | JV(i,j) = 0.0D0 |
---|
| 959 | END DO |
---|
| 960 | END DO |
---|
| 961 | DO i=1,LU_NONZERO |
---|
| 962 | JV(LU_IROW(i),LU_ICOL(i)) = JS(i) |
---|
| 963 | END DO |
---|
| 964 | #else |
---|
| 965 | CALL Jac_SP(Y, FIX, RCONST, JV) |
---|
| 966 | #endif |
---|
| 967 | TIME = Told |
---|
| 968 | Njac = Njac+1 |
---|
| 969 | |
---|
| 970 | END SUBROUTINE JAC_CHEM |
---|
| 971 | |
---|
| 972 | END MODULE KPP_ROOT_Integrator |
---|