[2696] | 1 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 2 | ! SDIRK-TLM - Tangent Linear Model of Singly-Diagonally-Implicit RK ! |
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| 3 | ! * Sdirk 2a, 2b: L-stable, 2 stages, order 2 ! |
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| 4 | ! * Sdirk 3a: L-stable, 3 stages, order 2, adj-invariant ! |
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| 5 | ! * Sdirk 4a, 4b: L-stable, 5 stages, order 4 ! |
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| 6 | ! By default the code employs the KPP sparse linear algebra routines ! |
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| 7 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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| 8 | ! ! |
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| 9 | ! (C) Adrian Sandu, July 2005 ! |
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| 10 | ! Virginia Polytechnic Institute and State University ! |
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| 11 | ! Contact: sandu@cs.vt.edu ! |
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| 12 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 ! |
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| 13 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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| 14 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 15 | |
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| 16 | MODULE KPP_ROOT_Integrator |
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| 17 | |
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| 18 | USE KPP_ROOT_Precision |
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| 19 | USE KPP_ROOT_Global, ONLY: FIX, RCONST, TIME |
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| 20 | USE KPP_ROOT_Parameters, ONLY: NVAR, NSPEC, NFIX, LU_NONZERO |
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| 21 | USE KPP_ROOT_JacobianSP, ONLY: LU_DIAG |
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| 22 | USE KPP_ROOT_Jacobian, ONLY: Jac_SP_Vec |
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| 23 | USE KPP_ROOT_LinearAlgebra, ONLY: KppDecomp, & |
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| 24 | KppSolve, Set2zero, WLAMCH, WCOPY, WAXPY, WSCAL, WADD |
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| 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | PUBLIC |
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| 28 | SAVE |
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| 29 | |
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| 30 | !~~~> Statistics on the work performed by the SDIRK method |
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| 31 | INTEGER, PARAMETER :: Nfun=1, Njac=2, Nstp=3, Nacc=4, & |
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| 32 | Nrej=5, Ndec=6, Nsol=7, Nsng=8, & |
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| 33 | Ntexit=1, Nhexit=2, Nhnew=3 |
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| 34 | |
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| 35 | CONTAINS |
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| 36 | |
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| 37 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 38 | SUBROUTINE INTEGRATE_TLM( NTLM, Y, Y_tlm, TIN, TOUT, ATOL_tlm,RTOL_tlm, & |
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| 39 | ICNTRL_U, RCNTRL_U, ISTATUS_U, RSTATUS_U, IERR_U ) |
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| 40 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 41 | |
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| 42 | USE KPP_ROOT_Parameters, ONLY: NVAR,ind_O3 |
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| 43 | USE KPP_ROOT_Global, ONLY: ATOL,RTOL,VAR |
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| 44 | |
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| 45 | IMPLICIT NONE |
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| 46 | |
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| 47 | !~~~> Y - Concentrations |
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| 48 | KPP_REAL :: Y(NVAR) |
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| 49 | !~~~> NTLM - No. of sensitivity coefficients |
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| 50 | INTEGER NTLM |
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| 51 | !~~~> Y_tlm - Sensitivities of concentrations |
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| 52 | ! Note: Y_tlm (1:NVAR,j) contains sensitivities of |
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| 53 | ! Y(1:NVAR) w.r.t. the j-th parameter, j=1...NTLM |
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| 54 | KPP_REAL :: Y_tlm(NVAR,NTLM) |
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| 55 | KPP_REAL :: TIN ! TIN - Start Time |
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| 56 | KPP_REAL :: TOUT ! TOUT - End Time |
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| 57 | KPP_REAL, INTENT(IN), OPTIONAL :: RTOL_tlm(NVAR,NTLM),ATOL_tlm(NVAR,NTLM) |
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| 58 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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| 59 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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| 60 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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| 61 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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| 62 | INTEGER, INTENT(OUT), OPTIONAL :: IERR_U |
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| 63 | |
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| 64 | INTEGER :: IERR |
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| 65 | |
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| 66 | KPP_REAL :: RCNTRL(20), RSTATUS(20), T1, T2 |
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| 67 | INTEGER :: ICNTRL(20), ISTATUS(20) |
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| 68 | INTEGER, SAVE :: Ntotal = 0 |
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| 69 | |
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| 70 | ICNTRL(1:20) = 0 |
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| 71 | RCNTRL(1:20) = 0.0_dp |
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| 72 | |
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| 73 | !~~~> fine-tune the integrator: |
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| 74 | ICNTRL(2) = 0 ! 0=vector tolerances, 1=scalar tolerances |
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| 75 | ICNTRL(5) = 8 ! Max no. of Newton iterations |
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| 76 | ICNTRL(6) = 0 ! Starting values for Newton are interpolated (0) or zero (1) |
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| 77 | ICNTRL(7) = 0 ! How to solve TLM: 0=modified Newton, 1=direct |
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| 78 | ICNTRL(9) = 0 ! TLM Newton Iterations influence |
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| 79 | ICNTRL(12) = 0 ! TLM Truncation Error influence |
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| 80 | |
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| 81 | !~~~> if optional parameters are given, and if they are >0, |
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| 82 | ! then use them to overwrite default settings |
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| 83 | IF (PRESENT(ICNTRL_U)) THEN |
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| 84 | WHERE(ICNTRL_U(:) > 0) ICNTRL(:) = ICNTRL_U(:) |
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| 85 | END IF |
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| 86 | IF (PRESENT(RCNTRL_U)) THEN |
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| 87 | WHERE(RCNTRL_U(:) > 0) RCNTRL(:) = RCNTRL_U(:) |
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| 88 | END IF |
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| 89 | |
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| 90 | |
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| 91 | T1 = TIN; T2 = TOUT |
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| 92 | CALL SdirkTLM( NVAR, NTLM, T1, T2, Y, Y_tlm, RTOL, ATOL, & |
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| 93 | RTOL_tlm, ATOL_tlm, RCNTRL,ICNTRL,RSTATUS,ISTATUS,IERR ) |
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| 94 | |
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| 95 | !~~~> Debug option: print number of steps |
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| 96 | ! Ntotal = Ntotal + ISTATUS(Nstp) |
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| 97 | ! PRINT*,'NSTEPS=',ISTATUS(Nstp),' (',Ntotal,')',' O3=', VAR(ind_O3) |
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| 98 | |
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| 99 | ! if optional parameters are given for output |
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| 100 | ! use them to store information in them |
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| 101 | IF (PRESENT(ISTATUS_U)) ISTATUS_U(:) = ISTATUS(:) |
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| 102 | IF (PRESENT(RSTATUS_U)) RSTATUS_U(:) = RSTATUS(:) |
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| 103 | IF (PRESENT(IERR_U)) IERR_U = IERR |
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| 104 | |
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| 105 | IF (IERR < 0) THEN |
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| 106 | PRINT *,'SDIRK-TLM: Unsuccessful exit at T=', TIN,' (IERR=',IERR,')' |
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| 107 | ENDIF |
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| 108 | |
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| 109 | END SUBROUTINE INTEGRATE_TLM |
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| 110 | |
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| 111 | |
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| 112 | |
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| 113 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 114 | SUBROUTINE SdirkTLM(N, NTLM, Tinitial, Tfinal, Y, Y_tlm, RelTol, AbsTol, & |
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| 115 | RelTol_tlm, AbsTol_tlm, & |
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| 116 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, Ierr) |
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| 117 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 118 | ! |
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| 119 | ! Solves the system y'=F(t,y) using a Singly-Diagonally-Implicit |
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| 120 | ! Runge-Kutta (SDIRK) method. |
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| 121 | ! |
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| 122 | ! This implementation is based on the book and the code Sdirk4: |
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| 123 | ! |
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| 124 | ! E. Hairer and G. Wanner |
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| 125 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
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| 126 | ! Springer series in computational mathematics, Springer-Verlag, 1996. |
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| 127 | ! This code is based on the SDIRK4 routine in the above book. |
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| 128 | ! |
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| 129 | ! Methods: |
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| 130 | ! * Sdirk 2a, 2b: L-stable, 2 stages, order 2 |
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| 131 | ! * Sdirk 3a: L-stable, 3 stages, order 2, adjoint-invariant |
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| 132 | ! * Sdirk 4a, 4b: L-stable, 5 stages, order 4 |
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| 133 | ! |
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| 134 | ! (C) Adrian Sandu, July 2005 |
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| 135 | ! Virginia Polytechnic Institute and State University |
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| 136 | ! Contact: sandu@cs.vt.edu |
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| 137 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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| 138 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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| 139 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 140 | ! |
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| 141 | !~~~> INPUT ARGUMENTS: |
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| 142 | ! |
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| 143 | !- Y(NVAR) = vector of initial conditions (at T=Tinitial) |
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| 144 | !- [Tinitial,Tfinal] = time range of integration |
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| 145 | ! (if Tinitial>Tfinal the integration is performed backwards in time) |
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| 146 | !- RelTol, AbsTol = user precribed accuracy |
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| 147 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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| 148 | ! returns Ydot = Y' = F(T,Y) |
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| 149 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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| 150 | ! returns Jcb = dF/dY |
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| 151 | !- ICNTRL(1:20) = integer inputs parameters |
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| 152 | !- RCNTRL(1:20) = real inputs parameters |
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| 153 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 154 | ! |
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| 155 | !~~~> OUTPUT ARGUMENTS: |
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| 156 | ! |
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| 157 | !- Y(NVAR) -> vector of final states (at T->Tfinal) |
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| 158 | !- ISTATUS(1:20) -> integer output parameters |
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| 159 | !- RSTATUS(1:20) -> real output parameters |
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| 160 | !- Ierr -> job status upon return |
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| 161 | ! success (positive value) or |
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| 162 | ! failure (negative value) |
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| 163 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 164 | ! |
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| 165 | !~~~> INPUT PARAMETERS: |
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| 166 | ! |
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| 167 | ! Note: For input parameters equal to zero the default values of the |
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| 168 | ! corresponding variables are used. |
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| 169 | ! |
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| 170 | ! Note: For input parameters equal to zero the default values of the |
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| 171 | ! corresponding variables are used. |
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| 172 | !~~~> |
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| 173 | ! ICNTRL(1) = not used |
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| 174 | ! |
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| 175 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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| 176 | ! = 1: AbsTol, RelTol are scalars |
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| 177 | ! |
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| 178 | ! ICNTRL(3) = Method |
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| 179 | ! |
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| 180 | ! ICNTRL(4) -> maximum number of integration steps |
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| 181 | ! For ICNTRL(4)=0 the default value of 100000 is used |
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| 182 | ! |
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| 183 | ! ICNTRL(5) -> maximum number of Newton iterations |
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| 184 | ! For ICNTRL(5)=0 the default value of 8 is used |
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| 185 | ! |
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| 186 | ! ICNTRL(6) -> starting values of Newton iterations: |
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| 187 | ! ICNTRL(6)=0 : starting values are interpolated (the default) |
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| 188 | ! ICNTRL(6)=1 : starting values are zero |
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| 189 | ! |
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| 190 | ! ICNTRL(7) -> method to solve TLM equations: |
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| 191 | ! ICNTRL(7)=0 : modified Newton re-using LU (the default) |
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| 192 | ! ICNTRL(7)=1 : direct solution (additional one LU factorization per stage) |
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| 193 | ! |
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| 194 | ! ICNTRL(9) -> switch for TLM Newton iteration error estimation strategy |
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| 195 | ! ICNTRL(9) = 0: base number of iterations as forward solution |
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| 196 | ! ICNTRL(9) = 1: use RTOL_tlm and ATOL_tlm to calculate |
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| 197 | ! error estimation for TLM at Newton stages |
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| 198 | ! |
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| 199 | ! ICNTRL(12) -> switch for TLM truncation error control |
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| 200 | ! ICNTRL(12) = 0: TLM error is not used |
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| 201 | ! ICNTRL(12) = 1: TLM error is computed and used |
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| 202 | ! |
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| 203 | ! |
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| 204 | !~~~> Real parameters |
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| 205 | ! |
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| 206 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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| 207 | ! It is strongly recommended to keep Hmin = ZERO |
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| 208 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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| 209 | ! RCNTRL(3) -> Hstart, starting value for the integration step size |
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| 210 | ! |
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| 211 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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| 212 | ! RCNTRL(5) -> FacMax, upper bound on step increase factor (default=6) |
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| 213 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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| 214 | ! (default=0.1) |
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| 215 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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| 216 | ! than the predicted value (default=0.9) |
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| 217 | ! RCNTRL(8) -> ThetaMin. If Newton convergence rate smaller |
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| 218 | ! than ThetaMin the Jacobian is not recomputed; |
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| 219 | ! (default=0.001) |
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| 220 | ! RCNTRL(9) -> NewtonTol, stopping criterion for Newton's method |
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| 221 | ! (default=0.03) |
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| 222 | ! RCNTRL(10) -> Qmin |
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| 223 | ! RCNTRL(11) -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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| 224 | ! step size is kept constant and the LU factorization |
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| 225 | ! reused (default Qmin=1, Qmax=1.2) |
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| 226 | ! |
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| 227 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 228 | ! |
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| 229 | !~~~> OUTPUT PARAMETERS: |
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| 230 | ! |
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| 231 | ! Note: each call to Rosenbrock adds the current no. of fcn calls |
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| 232 | ! to previous value of ISTATUS(1), and similar for the other params. |
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| 233 | ! Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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| 234 | ! |
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| 235 | ! ISTATUS(1) = No. of function calls |
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| 236 | ! ISTATUS(2) = No. of jacobian calls |
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| 237 | ! ISTATUS(3) = No. of steps |
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| 238 | ! ISTATUS(4) = No. of accepted steps |
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| 239 | ! ISTATUS(5) = No. of rejected steps (except at the beginning) |
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| 240 | ! ISTATUS(6) = No. of LU decompositions |
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| 241 | ! ISTATUS(7) = No. of forward/backward substitutions |
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| 242 | ! ISTATUS(8) = No. of singular matrix decompositions |
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| 243 | ! |
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| 244 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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| 245 | ! computed Y upon return |
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| 246 | ! RSTATUS(2) -> Hexit,last accepted step before return |
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| 247 | ! RSTATUS(3) -> Hnew, last predicted step before return |
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| 248 | ! For multiple restarts, use Hnew as Hstart in the following run |
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| 249 | ! |
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| 250 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 251 | IMPLICIT NONE |
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| 252 | |
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| 253 | ! Arguments |
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| 254 | INTEGER, INTENT(IN) :: N, NTLM, ICNTRL(20) |
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| 255 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal, & |
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| 256 | RelTol(N), AbsTol(N), RCNTRL(20), & |
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| 257 | RelTol_tlm(N,NTLM), AbsTol_tlm(N,NTLM) |
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| 258 | KPP_REAL, INTENT(INOUT) :: Y(NVAR), Y_tlm(N,NTLM) |
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| 259 | INTEGER, INTENT(OUT) :: Ierr |
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| 260 | INTEGER, INTENT(INOUT) :: ISTATUS(20) |
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| 261 | KPP_REAL, INTENT(OUT) :: RSTATUS(20) |
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| 262 | |
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| 263 | !~~~> SDIRK method coefficients, up to 5 stages |
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| 264 | INTEGER, PARAMETER :: Smax = 5 |
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| 265 | INTEGER, PARAMETER :: S2A=1, S2B=2, S3A=3, S4A=4, S4B=5 |
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| 266 | KPP_REAL :: rkGamma, rkA(Smax,Smax), rkB(Smax), rkC(Smax), & |
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| 267 | rkD(Smax), rkE(Smax), rkBhat(Smax), rkELO, & |
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| 268 | rkAlpha(Smax,Smax), rkTheta(Smax,Smax) |
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| 269 | INTEGER :: sdMethod, rkS ! The number of stages |
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| 270 | |
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| 271 | ! Local variables |
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| 272 | KPP_REAL :: Hmin, Hmax, Hstart, Roundoff, & |
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| 273 | FacMin, Facmax, FacSafe, FacRej, & |
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| 274 | ThetaMin, NewtonTol, Qmin, Qmax |
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| 275 | INTEGER :: ITOL, NewtonMaxit, Max_no_steps, i |
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| 276 | LOGICAL :: StartNewton, DirectTLM, TLMNewtonEst, TLMtruncErr |
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| 277 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
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| 278 | |
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| 279 | |
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| 280 | Ierr = 0 |
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| 281 | ISTATUS(1:20) = 0 |
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| 282 | RSTATUS(1:20) = ZERO |
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| 283 | |
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| 284 | !~~~> For Scalar tolerances (ICNTRL(2).NE.0) the code uses AbsTol(1) and RelTol(1) |
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| 285 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:NVAR) and RelTol(1:NVAR) |
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| 286 | IF (ICNTRL(2) == 0) THEN |
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| 287 | ITOL = 1 |
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| 288 | ELSE |
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| 289 | ITOL = 0 |
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| 290 | END IF |
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| 291 | |
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| 292 | !~~~> ICNTRL(3) - method selection |
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| 293 | SELECT CASE (ICNTRL(3)) |
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| 294 | CASE (0,1) |
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| 295 | CALL Sdirk2a |
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| 296 | CASE (2) |
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| 297 | CALL Sdirk2b |
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| 298 | CASE (3) |
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| 299 | CALL Sdirk3a |
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| 300 | CASE (4) |
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| 301 | CALL Sdirk4a |
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| 302 | CASE (5) |
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| 303 | CALL Sdirk4b |
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| 304 | CASE DEFAULT |
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| 305 | CALL Sdirk2a |
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| 306 | END SELECT |
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| 307 | |
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| 308 | !~~~> The maximum number of time steps admitted |
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| 309 | IF (ICNTRL(4) == 0) THEN |
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| 310 | Max_no_steps = 200000 |
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| 311 | ELSEIF (ICNTRL(4) > 0) THEN |
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| 312 | Max_no_steps=ICNTRL(4) |
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| 313 | ELSE |
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| 314 | PRINT * ,'User-selected ICNTRL(4)=',ICNTRL(4) |
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| 315 | CALL SDIRK_ErrorMsg(-1,Tinitial,ZERO,Ierr) |
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| 316 | END IF |
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| 317 | !~~~> The maximum number of Newton iterations admitted |
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| 318 | IF(ICNTRL(5) == 0)THEN |
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| 319 | NewtonMaxit=8 |
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| 320 | ELSE |
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| 321 | NewtonMaxit=ICNTRL(5) |
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| 322 | IF(NewtonMaxit <= 0)THEN |
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| 323 | PRINT * ,'User-selected ICNTRL(5)=',ICNTRL(5) |
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| 324 | CALL SDIRK_ErrorMsg(-2,Tinitial,ZERO,Ierr) |
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| 325 | END IF |
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| 326 | END IF |
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| 327 | !~~~> StartNewton: Use extrapolation for starting values of Newton iterations |
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| 328 | IF (ICNTRL(6) == 0) THEN |
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| 329 | StartNewton = .TRUE. |
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| 330 | ELSE |
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| 331 | StartNewton = .FALSE. |
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| 332 | END IF |
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| 333 | !~~~> Solve TLM equations directly or by Newton iterations |
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| 334 | DirectTLM = (ICNTRL(7) == 1) |
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| 335 | !~~~> Newton iteration error control selection |
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| 336 | IF (ICNTRL(9) == 0) THEN |
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| 337 | TLMNewtonEst = .FALSE. |
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| 338 | ELSE |
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| 339 | TLMNewtonEst = .TRUE. |
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| 340 | END IF |
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| 341 | !~~~> TLM truncation error control selection |
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| 342 | IF (ICNTRL(12) == 0) THEN |
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| 343 | TLMtruncErr = .FALSE. |
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| 344 | ELSE |
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| 345 | TLMtruncErr = .TRUE. |
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| 346 | END IF |
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| 347 | |
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| 348 | !~~~> Unit roundoff (1+Roundoff>1) |
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| 349 | Roundoff = WLAMCH('E') |
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| 350 | |
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| 351 | !~~~> Lower bound on the step size: (positive value) |
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| 352 | IF (RCNTRL(1) == ZERO) THEN |
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| 353 | Hmin = ZERO |
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| 354 | ELSEIF (RCNTRL(1) > ZERO) THEN |
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| 355 | Hmin = RCNTRL(1) |
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| 356 | ELSE |
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| 357 | PRINT * , 'User-selected RCNTRL(1)=', RCNTRL(1) |
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| 358 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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| 359 | END IF |
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| 360 | |
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| 361 | !~~~> Upper bound on the step size: (positive value) |
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| 362 | IF (RCNTRL(2) == ZERO) THEN |
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| 363 | Hmax = ABS(Tfinal-Tinitial) |
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| 364 | ELSEIF (RCNTRL(2) > ZERO) THEN |
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| 365 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tfinal-Tinitial)) |
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| 366 | ELSE |
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| 367 | PRINT * , 'User-selected RCNTRL(2)=', RCNTRL(2) |
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| 368 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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| 369 | END IF |
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| 370 | |
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| 371 | !~~~> Starting step size: (positive value) |
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| 372 | IF (RCNTRL(3) == ZERO) THEN |
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| 373 | Hstart = MAX(Hmin,Roundoff) |
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| 374 | ELSEIF (RCNTRL(3) > ZERO) THEN |
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| 375 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tfinal-Tinitial)) |
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| 376 | ELSE |
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| 377 | PRINT * , 'User-selected Hstart: RCNTRL(3)=', RCNTRL(3) |
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| 378 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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| 379 | END IF |
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| 380 | |
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| 381 | !~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax |
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| 382 | IF (RCNTRL(4) == ZERO) THEN |
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| 383 | FacMin = 0.2_dp |
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| 384 | ELSEIF (RCNTRL(4) > ZERO) THEN |
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| 385 | FacMin = RCNTRL(4) |
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| 386 | ELSE |
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| 387 | PRINT * , 'User-selected FacMin: RCNTRL(4)=', RCNTRL(4) |
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| 388 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
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| 389 | END IF |
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| 390 | IF (RCNTRL(5) == ZERO) THEN |
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| 391 | FacMax = 10.0_dp |
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| 392 | ELSEIF (RCNTRL(5) > ZERO) THEN |
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| 393 | FacMax = RCNTRL(5) |
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| 394 | ELSE |
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| 395 | PRINT * , 'User-selected FacMax: RCNTRL(5)=', RCNTRL(5) |
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| 396 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
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| 397 | END IF |
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| 398 | !~~~> FacRej: Factor to decrease step after 2 succesive rejections |
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| 399 | IF (RCNTRL(6) == ZERO) THEN |
---|
| 400 | FacRej = 0.1_dp |
---|
| 401 | ELSEIF (RCNTRL(6) > ZERO) THEN |
---|
| 402 | FacRej = RCNTRL(6) |
---|
| 403 | ELSE |
---|
| 404 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
---|
| 405 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
| 406 | END IF |
---|
| 407 | !~~~> FacSafe: Safety Factor in the computation of new step size |
---|
| 408 | IF (RCNTRL(7) == ZERO) THEN |
---|
| 409 | FacSafe = 0.9_dp |
---|
| 410 | ELSEIF (RCNTRL(7) > ZERO) THEN |
---|
| 411 | FacSafe = RCNTRL(7) |
---|
| 412 | ELSE |
---|
| 413 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
---|
| 414 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
| 415 | END IF |
---|
| 416 | |
---|
| 417 | !~~~> ThetaMin: decides whether the Jacobian should be recomputed |
---|
| 418 | IF(RCNTRL(8) == 0.D0)THEN |
---|
| 419 | ThetaMin = 1.0d-3 |
---|
| 420 | ELSE |
---|
| 421 | ThetaMin = RCNTRL(8) |
---|
| 422 | END IF |
---|
| 423 | |
---|
| 424 | !~~~> Stopping criterion for Newton's method |
---|
| 425 | IF(RCNTRL(9) == ZERO)THEN |
---|
| 426 | NewtonTol = 3.0d-2 |
---|
| 427 | ELSE |
---|
| 428 | NewtonTol = RCNTRL(9) |
---|
| 429 | END IF |
---|
| 430 | |
---|
| 431 | !~~~> Qmin, Qmax: IF Qmin < Hnew/Hold < Qmax, STEP SIZE = CONST. |
---|
| 432 | IF(RCNTRL(10) == ZERO)THEN |
---|
| 433 | Qmin=ONE |
---|
| 434 | ELSE |
---|
| 435 | Qmin=RCNTRL(10) |
---|
| 436 | END IF |
---|
| 437 | IF(RCNTRL(11) == ZERO)THEN |
---|
| 438 | Qmax=1.2D0 |
---|
| 439 | ELSE |
---|
| 440 | Qmax=RCNTRL(11) |
---|
| 441 | END IF |
---|
| 442 | |
---|
| 443 | !~~~> Check if tolerances are reasonable |
---|
| 444 | IF (ITOL == 0) THEN |
---|
| 445 | IF (AbsTol(1) <= ZERO .OR. RelTol(1) <= 10.D0*Roundoff) THEN |
---|
| 446 | PRINT * , ' Scalar AbsTol = ',AbsTol(1) |
---|
| 447 | PRINT * , ' Scalar RelTol = ',RelTol(1) |
---|
| 448 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr) |
---|
| 449 | END IF |
---|
| 450 | ELSE |
---|
| 451 | DO i=1,N |
---|
| 452 | IF (AbsTol(i) <= 0.D0.OR.RelTol(i) <= 10.D0*Roundoff) THEN |
---|
| 453 | PRINT * , ' AbsTol(',i,') = ',AbsTol(i) |
---|
| 454 | PRINT * , ' RelTol(',i,') = ',RelTol(i) |
---|
| 455 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr) |
---|
| 456 | END IF |
---|
| 457 | END DO |
---|
| 458 | END IF |
---|
| 459 | |
---|
| 460 | IF (Ierr < 0) RETURN |
---|
| 461 | |
---|
| 462 | CALL SDIRK_IntegratorTLM( N,NTLM,Tinitial,Tfinal,Y,Y_tlm,Ierr ) |
---|
| 463 | |
---|
| 464 | |
---|
| 465 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 466 | CONTAINS ! PROCEDURES INTERNAL TO SDIRK |
---|
| 467 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 468 | |
---|
| 469 | |
---|
| 470 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 471 | SUBROUTINE SDIRK_IntegratorTLM( N,NTLM,Tinitial,Tfinal,Y,Y_tlm,Ierr ) |
---|
| 472 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 473 | |
---|
| 474 | USE KPP_ROOT_Parameters |
---|
| 475 | IMPLICIT NONE |
---|
| 476 | |
---|
| 477 | !~~~> Arguments: |
---|
| 478 | INTEGER, INTENT(IN) :: N, NTLM |
---|
| 479 | KPP_REAL, INTENT(INOUT) :: Y(N), Y_tlm(N,NTLM) |
---|
| 480 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal |
---|
| 481 | INTEGER, INTENT(OUT) :: Ierr |
---|
| 482 | |
---|
| 483 | !~~~> Local variables: |
---|
| 484 | KPP_REAL :: Z(NVAR,rkS), G(NVAR), TMP(NVAR), & |
---|
| 485 | NewtonRate, SCAL(NVAR), DZ(NVAR), & |
---|
| 486 | T, H, Theta, Hratio, NewtonPredictedErr, & |
---|
| 487 | Qnewton, Err, Fac, Hnew, Tdirection, & |
---|
| 488 | NewtonIncrement, NewtonIncrementOld, & |
---|
| 489 | SCAL_tlm(NVAR), Yerr(N), Yerr_tlm(N,NTLM), ThetaTLM |
---|
| 490 | KPP_REAL :: Z_tlm(NVAR,rkS,NTLM) |
---|
| 491 | INTEGER :: itlm, j, IER, istage, NewtonIter, saveNiter, NewtonIterTLM |
---|
| 492 | INTEGER :: IP(NVAR), IP_tlm(NVAR) |
---|
| 493 | LOGICAL :: Reject, FirstStep, SkipJac, SkipLU, NewtonDone |
---|
| 494 | |
---|
| 495 | #ifdef FULL_ALGEBRA |
---|
| 496 | KPP_REAL, DIMENSION(NVAR,NVAR) :: FJAC, E, Jac, E_tlm |
---|
| 497 | #else |
---|
| 498 | KPP_REAL, DIMENSION(LU_NONZERO) :: FJAC, E, Jac, E_tlm |
---|
| 499 | #endif |
---|
| 500 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
| 501 | |
---|
| 502 | |
---|
| 503 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 504 | !~~~> Initializations |
---|
| 505 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 506 | |
---|
| 507 | T = Tinitial |
---|
| 508 | Tdirection = SIGN(ONE,Tfinal-Tinitial) |
---|
| 509 | H = MAX(ABS(Hmin),ABS(Hstart)) |
---|
| 510 | IF (ABS(H) <= 10.D0*Roundoff) H=1.0D-6 |
---|
| 511 | H=MIN(ABS(H),Hmax) |
---|
| 512 | H=SIGN(H,Tdirection) |
---|
| 513 | SkipLU = .FALSE. |
---|
| 514 | SkipJac = .FALSE. |
---|
| 515 | Reject = .FALSE. |
---|
| 516 | FirstStep=.TRUE. |
---|
| 517 | |
---|
| 518 | CALL SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 519 | |
---|
| 520 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 521 | !~~~> Time loop begins |
---|
| 522 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 523 | Tloop: DO WHILE ( (Tfinal-T)*Tdirection - Roundoff > ZERO ) |
---|
| 524 | |
---|
| 525 | |
---|
| 526 | !~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition |
---|
| 527 | IF ( .NOT.SkipLU ) THEN ! This time around skip the Jac update and LU |
---|
| 528 | CALL SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
| 529 | SkipJac, SkipLU, E, IP, Reject, IER ) |
---|
| 530 | IF (IER /= 0) THEN |
---|
| 531 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
| 532 | END IF |
---|
| 533 | END IF |
---|
| 534 | |
---|
| 535 | IF (ISTATUS(Nstp) > Max_no_steps) THEN |
---|
| 536 | CALL SDIRK_ErrorMsg(-6,T,H,Ierr); RETURN |
---|
| 537 | END IF |
---|
| 538 | IF ( (T+0.1d0*H == T) .OR. (ABS(H) <= Roundoff) ) THEN |
---|
| 539 | CALL SDIRK_ErrorMsg(-7,T,H,Ierr); RETURN |
---|
| 540 | END IF |
---|
| 541 | |
---|
| 542 | stages:DO istage = 1, rkS |
---|
| 543 | |
---|
| 544 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 545 | !~~~> Simplified Newton iterations |
---|
| 546 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 547 | |
---|
| 548 | !~~~> Starting values for Newton iterations |
---|
| 549 | CALL Set2zero(N,Z(1,istage)) |
---|
| 550 | |
---|
| 551 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
| 552 | CALL Set2zero(N,G) |
---|
| 553 | IF (istage > 1) THEN |
---|
| 554 | DO j = 1, istage-1 |
---|
| 555 | ! Gj(:) = sum_j Theta(i,j)*Zj(:) = H * sum_j A(i,j)*Fun(Zj(:)) |
---|
| 556 | CALL WAXPY(N,rkTheta(istage,j),Z(1,j),1,G,1) |
---|
| 557 | ! Zi(:) = sum_j Alpha(i,j)*Zj(:) |
---|
| 558 | IF (StartNewton) THEN |
---|
| 559 | CALL WAXPY(N,rkAlpha(istage,j),Z(1,j),1,Z(1,istage),1) |
---|
| 560 | END IF |
---|
| 561 | END DO |
---|
| 562 | END IF |
---|
| 563 | |
---|
| 564 | !~~~> Initializations for Newton iteration |
---|
| 565 | NewtonDone = .FALSE. |
---|
| 566 | Fac = 0.5d0 ! Step reduction factor if too many iterations |
---|
| 567 | |
---|
| 568 | NewtonLoop:DO NewtonIter = 1, NewtonMaxit |
---|
| 569 | |
---|
| 570 | !~~~> Prepare the loop-dependent part of the right-hand side |
---|
| 571 | CALL WADD(N,Y,Z(1,istage),TMP) ! TMP <- Y + Zi |
---|
| 572 | CALL FUN_CHEM(T+rkC(istage)*H,TMP,DZ) ! DZ <- Fun(Y+Zi) |
---|
| 573 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 574 | ! DZ(1:N) = G(1:N) - Z(1:N,istage) + (H*rkGamma)*DZ(1:N) |
---|
| 575 | CALL WSCAL(N, H*rkGamma, DZ, 1) |
---|
| 576 | CALL WAXPY (N, -ONE, Z(1,istage), 1, DZ, 1) |
---|
| 577 | CALL WAXPY (N, ONE, G,1, DZ,1) |
---|
| 578 | |
---|
| 579 | !~~~> Solve the linear system |
---|
| 580 | CALL SDIRK_Solve ( H, N, E, IP, IER, DZ ) |
---|
| 581 | |
---|
| 582 | !~~~> Check convergence of Newton iterations |
---|
| 583 | CALL SDIRK_ErrorNorm(N, DZ, SCAL, NewtonIncrement) |
---|
| 584 | IF ( NewtonIter == 1 ) THEN |
---|
| 585 | Theta = ABS(ThetaMin) |
---|
| 586 | NewtonRate = 2.0d0 |
---|
| 587 | ELSE |
---|
| 588 | Theta = NewtonIncrement/NewtonIncrementOld |
---|
| 589 | IF (Theta < 0.99d0) THEN |
---|
| 590 | NewtonRate = Theta/(ONE-Theta) |
---|
| 591 | ! Predict error at the end of Newton process |
---|
| 592 | NewtonPredictedErr = NewtonIncrement & |
---|
| 593 | *Theta**(NewtonMaxit-NewtonIter)/(ONE-Theta) |
---|
| 594 | IF (NewtonPredictedErr >= NewtonTol) THEN |
---|
| 595 | ! Non-convergence of Newton: predicted error too large |
---|
| 596 | Qnewton = MIN(10.0d0,NewtonPredictedErr/NewtonTol) |
---|
| 597 | Fac = 0.8d0*Qnewton**(-ONE/(1+NewtonMaxit-NewtonIter)) |
---|
| 598 | EXIT NewtonLoop |
---|
| 599 | END IF |
---|
| 600 | ELSE ! Non-convergence of Newton: Theta too large |
---|
| 601 | EXIT NewtonLoop |
---|
| 602 | END IF |
---|
| 603 | END IF |
---|
| 604 | NewtonIncrementOld = NewtonIncrement |
---|
| 605 | ! Update solution: Z(:) <-- Z(:)+DZ(:) |
---|
| 606 | CALL WAXPY(N,ONE,DZ,1,Z(1,istage),1) |
---|
| 607 | |
---|
| 608 | ! Check error in Newton iterations |
---|
| 609 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
| 610 | IF (NewtonDone) THEN |
---|
| 611 | ! Tune error in TLM variables by defining the minimal number of Newton iterations. |
---|
| 612 | saveNiter = NewtonIter+1 |
---|
| 613 | EXIT NewtonLoop |
---|
| 614 | END IF |
---|
| 615 | |
---|
| 616 | END DO NewtonLoop |
---|
| 617 | |
---|
| 618 | IF (.NOT.NewtonDone) THEN |
---|
| 619 | !CALL RK_ErrorMsg(-12,T,H,Ierr); |
---|
| 620 | H = Fac*H; Reject=.TRUE. |
---|
| 621 | SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
| 622 | CYCLE Tloop |
---|
| 623 | END IF |
---|
| 624 | |
---|
| 625 | !~~~> End of simplified Newton iterations for forward variables |
---|
| 626 | |
---|
| 627 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 628 | !~~~> Solve for TLM variables |
---|
| 629 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 630 | |
---|
| 631 | !~~~> Direct solution for TLM variables |
---|
| 632 | DirTLM:IF (DirectTLM) THEN |
---|
| 633 | |
---|
| 634 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
| 635 | SkipJac = .FALSE. |
---|
| 636 | CALL SDIRK_PrepareMatrix ( H, T+rkC(istage)*H, TMP, Jac, & |
---|
| 637 | SkipJac, SkipLU, E_tlm, IP_tlm, Reject, IER ) |
---|
| 638 | IF (IER /= 0) CYCLE TLoop |
---|
| 639 | |
---|
| 640 | TlmL: DO itlm = 1, NTLM |
---|
| 641 | G(1:N) = Y_tlm(1:N,itlm) |
---|
| 642 | IF (istage > 1) THEN |
---|
| 643 | ! Gj(:) = sum_j Theta(i,j)*Zj_tlm(:) |
---|
| 644 | ! = H * sum_j A(i,j)*Jac(Zj(:))*(Yj_tlm+Zj_tlm) |
---|
| 645 | DO j = 1, istage-1 |
---|
| 646 | CALL WAXPY(N,rkTheta(istage,j),Z_tlm(1,j,itlm),1,G,1) |
---|
| 647 | END DO |
---|
| 648 | END IF |
---|
| 649 | CALL SDIRK_Solve ( H, N, E_tlm, IP_tlm, IER, G ) |
---|
| 650 | Z_tlm(1:N,istage,itlm) = G(1:N) - Y_tlm(1:N,itlm) |
---|
| 651 | END DO TlmL |
---|
| 652 | |
---|
| 653 | ELSE DirTLM |
---|
| 654 | |
---|
| 655 | !~~~> Jacobian of the current stage solution |
---|
| 656 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
| 657 | CALL JAC_CHEM(T+rkC(istage)*H,TMP,Jac) |
---|
| 658 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 659 | |
---|
| 660 | !~~~> Simplified Newton iterations for TLM variables |
---|
| 661 | TlmLoop:DO itlm = 1,NTLM |
---|
| 662 | NewtonRate = MAX(NewtonRate,Roundoff)**0.8d0 |
---|
| 663 | |
---|
| 664 | !~~~> Starting values for Newton iterations |
---|
| 665 | CALL Set2zero(N,Z_tlm(1,istage,itlm)) |
---|
| 666 | |
---|
| 667 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
| 668 | #ifdef FULL_ALGEBRA |
---|
| 669 | DZ = MATMUL(Jac,Y_tlm(1,itlm)) ! DZ <- Jac(Y+Z)*Y_tlm |
---|
| 670 | #else |
---|
| 671 | CALL Jac_SP_Vec ( Jac, Y_tlm(1,itlm), DZ ) |
---|
| 672 | #endif |
---|
| 673 | G(1:N) = (H*rkGamma)*DZ(1:N) |
---|
| 674 | IF (istage > 1) THEN |
---|
| 675 | ! Gj(:) = sum_j Theta(i,j)*Zj_tlm(:) |
---|
| 676 | ! = H * sum_j A(i,j)*Jac(Zj(:))*(Yj_tlm+Zj_tlm) |
---|
| 677 | DO j = 1, istage-1 |
---|
| 678 | CALL WAXPY(N,rkTheta(istage,j),Z_tlm(1,j,itlm),1,G,1) |
---|
| 679 | END DO |
---|
| 680 | END IF |
---|
| 681 | |
---|
| 682 | |
---|
| 683 | !~~~> Initializations for Newton iteration |
---|
| 684 | IF (TLMNewtonEst) THEN |
---|
| 685 | NewtonDone = .FALSE. |
---|
| 686 | Fac = 0.5d0 ! Step reduction factor if too many iterations |
---|
| 687 | |
---|
| 688 | CALL SDIRK_ErrorScale(N,ITOL,AbsTol_tlm(1,itlm),RelTol_tlm(1,itlm), & |
---|
| 689 | Y_tlm(1,itlm),SCAL_tlm) |
---|
| 690 | END IF |
---|
| 691 | |
---|
| 692 | NewtonLoopTLM:DO NewtonIterTLM = 1, NewtonMaxit |
---|
| 693 | |
---|
| 694 | !~~~> Prepare the loop-dependent part of the right-hand side |
---|
| 695 | #ifdef FULL_ALGEBRA |
---|
| 696 | DZ = MATMUL(Jac,Z_tlm(1,istage,itlm)) ! DZ <- Jac(Y+Z)*Z_tlm |
---|
| 697 | #else |
---|
| 698 | CALL Jac_SP_Vec ( Jac, Z_tlm(1,istage,itlm), DZ ) |
---|
| 699 | #endif |
---|
| 700 | DZ(1:N) = (H*rkGamma)*DZ(1:N)+G(1:N)-Z_tlm(1:N,istage,itlm) |
---|
| 701 | |
---|
| 702 | CALL SDIRK_Solve ( H, N, E, IP, IER, DZ ) |
---|
| 703 | |
---|
| 704 | IF (TLMNewtonEst) THEN |
---|
| 705 | !~~~> Check convergence of Newton iterations |
---|
| 706 | CALL SDIRK_ErrorNorm(N, DZ, SCAL_tlm, NewtonIncrement) |
---|
| 707 | IF ( NewtonIterTLM <= 1 ) THEN |
---|
| 708 | ThetaTLM = ABS(ThetaMin) |
---|
| 709 | NewtonRate = 2.0d0 |
---|
| 710 | ELSE |
---|
| 711 | ThetaTLM = NewtonIncrement/NewtonIncrementOld |
---|
| 712 | IF (ThetaTLM < 0.99d0) THEN |
---|
| 713 | NewtonRate = ThetaTLM/(ONE-ThetaTLM) |
---|
| 714 | ! Predict error at the end of Newton process |
---|
| 715 | NewtonPredictedErr = NewtonIncrement & |
---|
| 716 | *ThetaTLM**(NewtonMaxit-NewtonIterTLM)/(ONE-ThetaTLM) |
---|
| 717 | IF (NewtonPredictedErr >= NewtonTol) THEN |
---|
| 718 | ! Non-convergence of Newton: predicted error too large |
---|
| 719 | Qnewton = MIN(10.0d0,NewtonPredictedErr/NewtonTol) |
---|
| 720 | Fac = 0.8d0*Qnewton**(-ONE/(1+NewtonMaxit-NewtonIterTLM)) |
---|
| 721 | EXIT NewtonLoopTLM |
---|
| 722 | END IF |
---|
| 723 | ELSE ! Non-convergence of Newton: Theta too large |
---|
| 724 | EXIT NewtonLoopTLM |
---|
| 725 | END IF |
---|
| 726 | END IF |
---|
| 727 | NewtonIncrementOld = NewtonIncrement |
---|
| 728 | END IF !(TLMNewtonEst) |
---|
| 729 | |
---|
| 730 | ! Update solution: Z_tlm(:) <-- Z_tlm(:)+DZ(:) |
---|
| 731 | CALL WAXPY(N,ONE,DZ,1,Z_tlm(1,istage,itlm),1) |
---|
| 732 | |
---|
| 733 | ! Check error in Newton iterations |
---|
| 734 | IF (TLMNewtonEst) THEN |
---|
| 735 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
| 736 | IF (NewtonDone) EXIT NewtonLoopTLM |
---|
| 737 | ELSE |
---|
| 738 | ! Minimum number of iterations same as FWD iterations |
---|
| 739 | IF (NewtonIterTLM>=saveNiter) EXIT NewtonLoopTLM |
---|
| 740 | END IF |
---|
| 741 | |
---|
| 742 | END DO NewtonLoopTLM |
---|
| 743 | |
---|
| 744 | IF ((TLMNewtonEst) .AND. (.NOT.NewtonDone)) THEN |
---|
| 745 | !CALL RK_ErrorMsg(-12,T,H,Ierr); |
---|
| 746 | H = Fac*H; Reject=.TRUE. |
---|
| 747 | SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
| 748 | CYCLE Tloop |
---|
| 749 | END IF |
---|
| 750 | |
---|
| 751 | END DO TlmLoop |
---|
| 752 | !~~~> End of simplified Newton iterations for TLM |
---|
| 753 | |
---|
| 754 | END IF DirTLM |
---|
| 755 | |
---|
| 756 | END DO stages |
---|
| 757 | |
---|
| 758 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 759 | !~~~> Error estimation |
---|
| 760 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 761 | ISTATUS(Nstp) = ISTATUS(Nstp) + 1 |
---|
| 762 | CALL Set2zero(N,Yerr) |
---|
| 763 | DO i = 1,rkS |
---|
| 764 | IF (rkE(i)/=ZERO) CALL WAXPY(N,rkE(i),Z(1,i),1,Yerr,1) |
---|
| 765 | END DO |
---|
| 766 | |
---|
| 767 | CALL SDIRK_Solve ( H, N, E, IP, IER, Yerr ) |
---|
| 768 | CALL SDIRK_ErrorNorm(N, Yerr, SCAL, Err) |
---|
| 769 | |
---|
| 770 | IF (TLMtruncErr) THEN |
---|
| 771 | CALL Set2zero(NVAR*NTLM,Yerr_tlm) |
---|
| 772 | DO itlm=1,NTLM |
---|
| 773 | DO j=1,rkS |
---|
| 774 | IF (rkE(j) /= ZERO) CALL WAXPY(N,rkE(j),Z_tlm(1,j,itlm),1,Yerr_tlm(1,itlm),1) |
---|
| 775 | END DO |
---|
| 776 | CALL SDIRK_Solve (H, N, E, IP, IER, Yerr_tlm(1,itlm)) |
---|
| 777 | END DO |
---|
| 778 | CALL SDIRK_ErrorNorm_tlm(N,NTLM, Yerr_tlm, Err) |
---|
| 779 | END IF |
---|
| 780 | |
---|
| 781 | !~~~> Computation of new step size Hnew |
---|
| 782 | Fac = FacSafe*(Err)**(-ONE/rkELO) |
---|
| 783 | Fac = MAX(FacMin,MIN(FacMax,Fac)) |
---|
| 784 | Hnew = H*Fac |
---|
| 785 | |
---|
| 786 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 787 | !~~~> Accept/Reject step |
---|
| 788 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 789 | accept: IF ( Err < ONE ) THEN !~~~> Step is accepted |
---|
| 790 | |
---|
| 791 | FirstStep=.FALSE. |
---|
| 792 | ISTATUS(Nacc) = ISTATUS(Nacc) + 1 |
---|
| 793 | |
---|
| 794 | !~~~> Update time and solution |
---|
| 795 | T = T + H |
---|
| 796 | ! Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) |
---|
| 797 | DO i = 1,rkS |
---|
| 798 | IF (rkD(i)/=ZERO) THEN |
---|
| 799 | CALL WAXPY(N,rkD(i),Z(1,i),1,Y,1) |
---|
| 800 | DO itlm = 1, NTLM |
---|
| 801 | CALL WAXPY(N,rkD(i),Z_tlm(1,i,itlm),1,Y_tlm(1,itlm),1) |
---|
| 802 | END DO |
---|
| 803 | END IF |
---|
| 804 | END DO |
---|
| 805 | |
---|
| 806 | !~~~> Update scaling coefficients |
---|
| 807 | CALL SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 808 | |
---|
| 809 | !~~~> Next time step |
---|
| 810 | Hnew = Tdirection*MIN(ABS(Hnew),Hmax) |
---|
| 811 | ! Last T and H |
---|
| 812 | RSTATUS(Ntexit) = T |
---|
| 813 | RSTATUS(Nhexit) = H |
---|
| 814 | RSTATUS(Nhnew) = Hnew |
---|
| 815 | ! No step increase after a rejection |
---|
| 816 | IF (Reject) Hnew = Tdirection*MIN(ABS(Hnew),ABS(H)) |
---|
| 817 | Reject = .FALSE. |
---|
| 818 | IF ((T+Hnew/Qmin-Tfinal)*Tdirection > ZERO) THEN |
---|
| 819 | H = Tfinal-T |
---|
| 820 | ELSE |
---|
| 821 | Hratio=Hnew/H |
---|
| 822 | ! If step not changed too much keep Jacobian and reuse LU |
---|
| 823 | SkipLU = ( (Theta <= ThetaMin) .AND. (Hratio >= Qmin) & |
---|
| 824 | .AND. (Hratio <= Qmax) ) |
---|
| 825 | ! For TLM: do not skip LU (decrease TLM error) |
---|
| 826 | SkipLU = .FALSE. |
---|
| 827 | IF (.NOT.SkipLU) H = Hnew |
---|
| 828 | END IF |
---|
| 829 | ! If convergence is fast enough, do not update Jacobian |
---|
| 830 | ! SkipJac = (Theta <= ThetaMin) |
---|
| 831 | SkipJac = .FALSE. |
---|
| 832 | |
---|
| 833 | ELSE accept !~~~> Step is rejected |
---|
| 834 | |
---|
| 835 | IF (FirstStep .OR. Reject) THEN |
---|
| 836 | H = FacRej*H |
---|
| 837 | ELSE |
---|
| 838 | H = Hnew |
---|
| 839 | END IF |
---|
| 840 | Reject = .TRUE. |
---|
| 841 | SkipJac = .TRUE. |
---|
| 842 | SkipLU = .FALSE. |
---|
| 843 | IF (ISTATUS(Nacc) >= 1) ISTATUS(Nrej) = ISTATUS(Nrej) + 1 |
---|
| 844 | |
---|
| 845 | END IF accept |
---|
| 846 | |
---|
| 847 | END DO Tloop |
---|
| 848 | |
---|
| 849 | ! Successful return |
---|
| 850 | Ierr = 1 |
---|
| 851 | |
---|
| 852 | END SUBROUTINE SDIRK_IntegratorTLM |
---|
| 853 | |
---|
| 854 | |
---|
| 855 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 856 | SUBROUTINE SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 857 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 858 | IMPLICIT NONE |
---|
| 859 | INTEGER :: N, i, ITOL |
---|
| 860 | KPP_REAL :: AbsTol(NVAR), RelTol(NVAR), & |
---|
| 861 | Y(NVAR), SCAL(NVAR) |
---|
| 862 | IF (ITOL == 0) THEN |
---|
| 863 | DO i=1,N |
---|
| 864 | SCAL(i) = ONE / ( AbsTol(1)+RelTol(1)*ABS(Y(i)) ) |
---|
| 865 | END DO |
---|
| 866 | ELSE |
---|
| 867 | DO i=1,N |
---|
| 868 | SCAL(i) = ONE / ( AbsTol(i)+RelTol(i)*ABS(Y(i)) ) |
---|
| 869 | END DO |
---|
| 870 | END IF |
---|
| 871 | END SUBROUTINE SDIRK_ErrorScale |
---|
| 872 | |
---|
| 873 | |
---|
| 874 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 875 | SUBROUTINE SDIRK_ErrorNorm(N, Y, SCAL, Err) |
---|
| 876 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 877 | ! |
---|
| 878 | INTEGER :: i, N |
---|
| 879 | KPP_REAL :: Y(N), SCAL(N), Err |
---|
| 880 | Err = ZERO |
---|
| 881 | DO i=1,N |
---|
| 882 | Err = Err+(Y(i)*SCAL(i))**2 |
---|
| 883 | END DO |
---|
| 884 | Err = MAX( SQRT(Err/DBLE(N)), 1.0d-10 ) |
---|
| 885 | ! |
---|
| 886 | END SUBROUTINE SDIRK_ErrorNorm |
---|
| 887 | |
---|
| 888 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 889 | SUBROUTINE SDIRK_ErrorNorm_tlm(N,NTLM, Y_tlm, FWD_Err) |
---|
| 890 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 891 | ! |
---|
| 892 | INTEGER :: itlm, NTLM, N |
---|
| 893 | KPP_REAL :: Y_tlm(N,NTLM), SCAL_tlm(N), FWD_Err, Err |
---|
| 894 | |
---|
| 895 | DO itlm=1,NTLM |
---|
| 896 | CALL SDIRK_ErrorScale(N,ITOL,AbsTol_tlm(1,itlm),RelTol_tlm(1,itlm), & |
---|
| 897 | Y_tlm(1,itlm),SCAL_tlm) |
---|
| 898 | CALL SDIRK_ErrorNorm(N, Y_tlm(1,itlm), SCAL_tlm, Err) |
---|
| 899 | FWD_Err = MAX(FWD_Err, Err) |
---|
| 900 | END DO |
---|
| 901 | ! |
---|
| 902 | END SUBROUTINE SDIRK_ErrorNorm_tlm |
---|
| 903 | |
---|
| 904 | |
---|
| 905 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 906 | SUBROUTINE SDIRK_ErrorMsg(Code,T,H,Ierr) |
---|
| 907 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 908 | ! Handles all error messages |
---|
| 909 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 910 | |
---|
| 911 | KPP_REAL, INTENT(IN) :: T, H |
---|
| 912 | INTEGER, INTENT(IN) :: Code |
---|
| 913 | INTEGER, INTENT(OUT) :: Ierr |
---|
| 914 | |
---|
| 915 | Ierr = Code |
---|
| 916 | PRINT * , & |
---|
| 917 | 'Forced exit from SDIRK due to the following error:' |
---|
| 918 | |
---|
| 919 | SELECT CASE (Code) |
---|
| 920 | CASE (-1) |
---|
| 921 | PRINT * , '--> Improper value for maximal no of steps' |
---|
| 922 | CASE (-2) |
---|
| 923 | PRINT * , '--> Improper value for maximal no of Newton iterations' |
---|
| 924 | CASE (-3) |
---|
| 925 | PRINT * , '--> Hmin/Hmax/Hstart must be positive' |
---|
| 926 | CASE (-4) |
---|
| 927 | PRINT * , '--> FacMin/FacMax/FacRej must be positive' |
---|
| 928 | CASE (-5) |
---|
| 929 | PRINT * , '--> Improper tolerance values' |
---|
| 930 | CASE (-6) |
---|
| 931 | PRINT * , '--> No of steps exceeds maximum bound' |
---|
| 932 | CASE (-7) |
---|
| 933 | PRINT * , '--> Step size too small: T + 10*H = T', & |
---|
| 934 | ' or H < Roundoff' |
---|
| 935 | CASE (-8) |
---|
| 936 | PRINT * , '--> Matrix is repeatedly singular' |
---|
| 937 | CASE DEFAULT |
---|
| 938 | PRINT *, 'Unknown Error code: ', Code |
---|
| 939 | END SELECT |
---|
| 940 | |
---|
| 941 | PRINT *, "T=", T, "and H=", H |
---|
| 942 | |
---|
| 943 | END SUBROUTINE SDIRK_ErrorMsg |
---|
| 944 | |
---|
| 945 | |
---|
| 946 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 947 | SUBROUTINE SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
| 948 | SkipJac, SkipLU, E, IP, Reject, ISING ) |
---|
| 949 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 950 | !~~~> Compute the matrix E = I - 1/(H*Gamma)*Jac, and its decomposition |
---|
| 951 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 952 | |
---|
| 953 | IMPLICIT NONE |
---|
| 954 | |
---|
| 955 | KPP_REAL, INTENT(INOUT) :: H |
---|
| 956 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
---|
| 957 | LOGICAL, INTENT(INOUT) :: SkipJac,SkipLU,Reject |
---|
| 958 | INTEGER, INTENT(OUT) :: ISING, IP(NVAR) |
---|
| 959 | #ifdef FULL_ALGEBRA |
---|
| 960 | KPP_REAL, INTENT(INOUT) :: FJAC(NVAR,NVAR) |
---|
| 961 | KPP_REAL, INTENT(OUT) :: E(NVAR,NVAR) |
---|
| 962 | #else |
---|
| 963 | KPP_REAL, INTENT(INOUT) :: FJAC(LU_NONZERO) |
---|
| 964 | KPP_REAL, INTENT(OUT) :: E(LU_NONZERO) |
---|
| 965 | #endif |
---|
| 966 | KPP_REAL :: HGammaInv |
---|
| 967 | INTEGER :: i, j, ConsecutiveSng |
---|
| 968 | |
---|
| 969 | ConsecutiveSng = 0 |
---|
| 970 | ISING = 1 |
---|
| 971 | |
---|
| 972 | Hloop: DO WHILE (ISING /= 0) |
---|
| 973 | |
---|
| 974 | HGammaInv = ONE/(H*rkGamma) |
---|
| 975 | |
---|
| 976 | !~~~> Compute the Jacobian |
---|
| 977 | ! IF (SkipJac) THEN |
---|
| 978 | ! SkipJac = .FALSE. |
---|
| 979 | ! ELSE |
---|
| 980 | IF (.NOT. SkipJac) THEN |
---|
| 981 | CALL JAC_CHEM( T, Y, FJAC ) |
---|
| 982 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 983 | END IF |
---|
| 984 | |
---|
| 985 | #ifdef FULL_ALGEBRA |
---|
| 986 | DO j=1,NVAR |
---|
| 987 | DO i=1,NVAR |
---|
| 988 | E(i,j) = -FJAC(i,j) |
---|
| 989 | END DO |
---|
| 990 | E(j,j) = E(j,j)+HGammaInv |
---|
| 991 | END DO |
---|
| 992 | CALL DGETRF( NVAR, NVAR, E, NVAR, IP, ISING ) |
---|
| 993 | #else |
---|
| 994 | DO i = 1,LU_NONZERO |
---|
| 995 | E(i) = -FJAC(i) |
---|
| 996 | END DO |
---|
| 997 | DO i = 1,NVAR |
---|
| 998 | j = LU_DIAG(i); E(j) = E(j) + HGammaInv |
---|
| 999 | END DO |
---|
| 1000 | CALL KppDecomp ( E, ISING) |
---|
| 1001 | IP(1) = 1 |
---|
| 1002 | #endif |
---|
| 1003 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
| 1004 | |
---|
| 1005 | IF (ISING /= 0) THEN |
---|
| 1006 | WRITE (6,*) ' MATRIX IS SINGULAR, ISING=',ISING,' T=',T,' H=',H |
---|
| 1007 | ISTATUS(Nsng) = ISTATUS(Nsng) + 1; ConsecutiveSng = ConsecutiveSng + 1 |
---|
| 1008 | IF (ConsecutiveSng >= 6) RETURN ! Failure |
---|
| 1009 | H = 0.5d0*H |
---|
| 1010 | SkipJac = .TRUE. |
---|
| 1011 | SkipLU = .FALSE. |
---|
| 1012 | Reject = .TRUE. |
---|
| 1013 | END IF |
---|
| 1014 | |
---|
| 1015 | END DO Hloop |
---|
| 1016 | |
---|
| 1017 | END SUBROUTINE SDIRK_PrepareMatrix |
---|
| 1018 | |
---|
| 1019 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1020 | SUBROUTINE SDIRK_Solve ( H, N, E, IP, ISING, RHS ) |
---|
| 1021 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1022 | !~~~> Solves the system (H*Gamma-Jac)*x = R |
---|
| 1023 | ! using the LU decomposition of E = I - 1/(H*Gamma)*Jac |
---|
| 1024 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1025 | IMPLICIT NONE |
---|
| 1026 | INTEGER, INTENT(IN) :: N, IP(N), ISING |
---|
| 1027 | KPP_REAL, INTENT(IN) :: H |
---|
| 1028 | #ifdef FULL_ALGEBRA |
---|
| 1029 | KPP_REAL, INTENT(IN) :: E(NVAR,NVAR) |
---|
| 1030 | #else |
---|
| 1031 | KPP_REAL, INTENT(IN) :: E(LU_NONZERO) |
---|
| 1032 | #endif |
---|
| 1033 | KPP_REAL, INTENT(INOUT) :: RHS(N) |
---|
| 1034 | KPP_REAL :: HGammaInv |
---|
| 1035 | |
---|
| 1036 | HGammaInv = ONE/(H*rkGamma) |
---|
| 1037 | CALL WSCAL(N,HGammaInv,RHS,1) |
---|
| 1038 | #ifdef FULL_ALGEBRA |
---|
| 1039 | CALL DGETRS( 'N', N, 1, E, N, IP, RHS, N, ISING ) |
---|
| 1040 | #else |
---|
| 1041 | CALL KppSolve(E, RHS) |
---|
| 1042 | #endif |
---|
| 1043 | ISTATUS(Nsol) = ISTATUS(Nsol) + 1 |
---|
| 1044 | |
---|
| 1045 | END SUBROUTINE SDIRK_Solve |
---|
| 1046 | |
---|
| 1047 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1048 | SUBROUTINE Sdirk4a |
---|
| 1049 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1050 | sdMethod = S4A |
---|
| 1051 | ! Number of stages |
---|
| 1052 | rkS = 5 |
---|
| 1053 | |
---|
| 1054 | ! Method coefficients |
---|
| 1055 | rkGamma = .2666666666666666666666666666666667d0 |
---|
| 1056 | |
---|
| 1057 | rkA(1,1) = .2666666666666666666666666666666667d0 |
---|
| 1058 | rkA(2,1) = .5000000000000000000000000000000000d0 |
---|
| 1059 | rkA(2,2) = .2666666666666666666666666666666667d0 |
---|
| 1060 | rkA(3,1) = .3541539528432732316227461858529820d0 |
---|
| 1061 | rkA(3,2) = -.5415395284327323162274618585298197d-1 |
---|
| 1062 | rkA(3,3) = .2666666666666666666666666666666667d0 |
---|
| 1063 | rkA(4,1) = .8515494131138652076337791881433756d-1 |
---|
| 1064 | rkA(4,2) = -.6484332287891555171683963466229754d-1 |
---|
| 1065 | rkA(4,3) = .7915325296404206392428857585141242d-1 |
---|
| 1066 | rkA(4,4) = .2666666666666666666666666666666667d0 |
---|
| 1067 | rkA(5,1) = 2.100115700566932777970612055999074d0 |
---|
| 1068 | rkA(5,2) = -.7677800284445976813343102185062276d0 |
---|
| 1069 | rkA(5,3) = 2.399816361080026398094746205273880d0 |
---|
| 1070 | rkA(5,4) = -2.998818699869028161397714709433394d0 |
---|
| 1071 | rkA(5,5) = .2666666666666666666666666666666667d0 |
---|
| 1072 | |
---|
| 1073 | rkB(1) = 2.100115700566932777970612055999074d0 |
---|
| 1074 | rkB(2) = -.7677800284445976813343102185062276d0 |
---|
| 1075 | rkB(3) = 2.399816361080026398094746205273880d0 |
---|
| 1076 | rkB(4) = -2.998818699869028161397714709433394d0 |
---|
| 1077 | rkB(5) = .2666666666666666666666666666666667d0 |
---|
| 1078 | |
---|
| 1079 | rkBhat(1)= 2.885264204387193942183851612883390d0 |
---|
| 1080 | rkBhat(2)= -.1458793482962771337341223443218041d0 |
---|
| 1081 | rkBhat(3)= 2.390008682465139866479830743628554d0 |
---|
| 1082 | rkBhat(4)= -4.129393538556056674929560012190140d0 |
---|
| 1083 | rkBhat(5)= 0.d0 |
---|
| 1084 | |
---|
| 1085 | rkC(1) = .2666666666666666666666666666666667d0 |
---|
| 1086 | rkC(2) = .7666666666666666666666666666666667d0 |
---|
| 1087 | rkC(3) = .5666666666666666666666666666666667d0 |
---|
| 1088 | rkC(4) = .3661315380631796996374935266701191d0 |
---|
| 1089 | rkC(5) = 1.d0 |
---|
| 1090 | |
---|
| 1091 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1092 | rkD(1) = 0.d0 |
---|
| 1093 | rkD(2) = 0.d0 |
---|
| 1094 | rkD(3) = 0.d0 |
---|
| 1095 | rkD(4) = 0.d0 |
---|
| 1096 | rkD(5) = 1.d0 |
---|
| 1097 | |
---|
| 1098 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1099 | rkE(1) = -.6804000050475287124787034884002302d0 |
---|
| 1100 | rkE(2) = 1.558961944525217193393931795738823d0 |
---|
| 1101 | rkE(3) = -13.55893003128907927748632408763868d0 |
---|
| 1102 | rkE(4) = 15.48522576958521253098585004571302d0 |
---|
| 1103 | rkE(5) = 1.d0 |
---|
| 1104 | |
---|
| 1105 | ! Local order of Err estimate |
---|
| 1106 | rkElo = 4 |
---|
| 1107 | |
---|
| 1108 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1109 | rkTheta(2,1) = 1.875000000000000000000000000000000d0 |
---|
| 1110 | rkTheta(3,1) = 1.708847304091539528432732316227462d0 |
---|
| 1111 | rkTheta(3,2) = -.2030773231622746185852981969486824d0 |
---|
| 1112 | rkTheta(4,1) = .2680325578937783958847157206823118d0 |
---|
| 1113 | rkTheta(4,2) = -.1828840955527181631794050728644549d0 |
---|
| 1114 | rkTheta(4,3) = .2968246986151577397160821594427966d0 |
---|
| 1115 | rkTheta(5,1) = .9096171815241460655379433581446771d0 |
---|
| 1116 | rkTheta(5,2) = -3.108254967778352416114774430509465d0 |
---|
| 1117 | rkTheta(5,3) = 12.33727431701306195581826123274001d0 |
---|
| 1118 | rkTheta(5,4) = -11.24557012450885560524143016037523d0 |
---|
| 1119 | |
---|
| 1120 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1121 | rkAlpha(2,1) = 2.875000000000000000000000000000000d0 |
---|
| 1122 | rkAlpha(3,1) = .8500000000000000000000000000000000d0 |
---|
| 1123 | rkAlpha(3,2) = .4434782608695652173913043478260870d0 |
---|
| 1124 | rkAlpha(4,1) = .7352046091658870564637910527807370d0 |
---|
| 1125 | rkAlpha(4,2) = -.9525565003057343527941920657462074d-1 |
---|
| 1126 | rkAlpha(4,3) = .4290111305453813852259481840631738d0 |
---|
| 1127 | rkAlpha(5,1) = -16.10898993405067684831655675112808d0 |
---|
| 1128 | rkAlpha(5,2) = 6.559571569643355712998131800797873d0 |
---|
| 1129 | rkAlpha(5,3) = -15.90772144271326504260996815012482d0 |
---|
| 1130 | rkAlpha(5,4) = 25.34908987169226073668861694892683d0 |
---|
| 1131 | |
---|
| 1132 | !~~~> Coefficients for continuous solution |
---|
| 1133 | ! rkD(1,1)= 24.74416644927758d0 |
---|
| 1134 | ! rkD(1,2)= -4.325375951824688d0 |
---|
| 1135 | ! rkD(1,3)= 41.39683763286316d0 |
---|
| 1136 | ! rkD(1,4)= -61.04144619901784d0 |
---|
| 1137 | ! rkD(1,5)= -3.391332232917013d0 |
---|
| 1138 | ! rkD(2,1)= -51.98245719616925d0 |
---|
| 1139 | ! rkD(2,2)= 10.52501981094525d0 |
---|
| 1140 | ! rkD(2,3)= -154.2067922191855d0 |
---|
| 1141 | ! rkD(2,4)= 214.3082125319825d0 |
---|
| 1142 | ! rkD(2,5)= 14.71166018088679d0 |
---|
| 1143 | ! rkD(3,1)= 33.14347947522142d0 |
---|
| 1144 | ! rkD(3,2)= -19.72986789558523d0 |
---|
| 1145 | ! rkD(3,3)= 230.4878502285804d0 |
---|
| 1146 | ! rkD(3,4)= -287.6629744338197d0 |
---|
| 1147 | ! rkD(3,5)= -18.99932366302254d0 |
---|
| 1148 | ! rkD(4,1)= -5.905188728329743d0 |
---|
| 1149 | ! rkD(4,2)= 13.53022403646467d0 |
---|
| 1150 | ! rkD(4,3)= -117.6778956422581d0 |
---|
| 1151 | ! rkD(4,4)= 134.3962081008550d0 |
---|
| 1152 | ! rkD(4,5)= 8.678995715052762d0 |
---|
| 1153 | ! |
---|
| 1154 | ! DO i=1,4 ! CONTi <-- Sum_j rkD(i,j)*Zj |
---|
| 1155 | ! CALL Set2zero(N,CONT(1,i)) |
---|
| 1156 | ! DO j = 1,rkS |
---|
| 1157 | ! CALL WAXPY(N,rkD(i,j),Z(1,j),1,CONT(1,i),1) |
---|
| 1158 | ! END DO |
---|
| 1159 | ! END DO |
---|
| 1160 | |
---|
| 1161 | rkELO = 4.0d0 |
---|
| 1162 | |
---|
| 1163 | END SUBROUTINE Sdirk4a |
---|
| 1164 | |
---|
| 1165 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1166 | SUBROUTINE Sdirk4b |
---|
| 1167 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1168 | sdMethod = S4B |
---|
| 1169 | ! Number of stages |
---|
| 1170 | rkS = 5 |
---|
| 1171 | |
---|
| 1172 | ! Method coefficients |
---|
| 1173 | rkGamma = .25d0 |
---|
| 1174 | |
---|
| 1175 | rkA(1,1) = 0.25d0 |
---|
| 1176 | rkA(2,1) = 0.5d00 |
---|
| 1177 | rkA(2,2) = 0.25d0 |
---|
| 1178 | rkA(3,1) = 0.34d0 |
---|
| 1179 | rkA(3,2) =-0.40d-1 |
---|
| 1180 | rkA(3,3) = 0.25d0 |
---|
| 1181 | rkA(4,1) = 0.2727941176470588235294117647058824d0 |
---|
| 1182 | rkA(4,2) =-0.5036764705882352941176470588235294d-1 |
---|
| 1183 | rkA(4,3) = 0.2757352941176470588235294117647059d-1 |
---|
| 1184 | rkA(4,4) = 0.25d0 |
---|
| 1185 | rkA(5,1) = 1.041666666666666666666666666666667d0 |
---|
| 1186 | rkA(5,2) =-1.020833333333333333333333333333333d0 |
---|
| 1187 | rkA(5,3) = 7.812500000000000000000000000000000d0 |
---|
| 1188 | rkA(5,4) =-7.083333333333333333333333333333333d0 |
---|
| 1189 | rkA(5,5) = 0.25d0 |
---|
| 1190 | |
---|
| 1191 | rkB(1) = 1.041666666666666666666666666666667d0 |
---|
| 1192 | rkB(2) = -1.020833333333333333333333333333333d0 |
---|
| 1193 | rkB(3) = 7.812500000000000000000000000000000d0 |
---|
| 1194 | rkB(4) = -7.083333333333333333333333333333333d0 |
---|
| 1195 | rkB(5) = 0.250000000000000000000000000000000d0 |
---|
| 1196 | |
---|
| 1197 | rkBhat(1)= 1.069791666666666666666666666666667d0 |
---|
| 1198 | rkBhat(2)= -0.894270833333333333333333333333333d0 |
---|
| 1199 | rkBhat(3)= 7.695312500000000000000000000000000d0 |
---|
| 1200 | rkBhat(4)= -7.083333333333333333333333333333333d0 |
---|
| 1201 | rkBhat(5)= 0.212500000000000000000000000000000d0 |
---|
| 1202 | |
---|
| 1203 | rkC(1) = 0.25d0 |
---|
| 1204 | rkC(2) = 0.75d0 |
---|
| 1205 | rkC(3) = 0.55d0 |
---|
| 1206 | rkC(4) = 0.50d0 |
---|
| 1207 | rkC(5) = 1.00d0 |
---|
| 1208 | |
---|
| 1209 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1210 | rkD(1) = 0.0d0 |
---|
| 1211 | rkD(2) = 0.0d0 |
---|
| 1212 | rkD(3) = 0.0d0 |
---|
| 1213 | rkD(4) = 0.0d0 |
---|
| 1214 | rkD(5) = 1.0d0 |
---|
| 1215 | |
---|
| 1216 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1217 | rkE(1) = 0.5750d0 |
---|
| 1218 | rkE(2) = 0.2125d0 |
---|
| 1219 | rkE(3) = -4.6875d0 |
---|
| 1220 | rkE(4) = 4.2500d0 |
---|
| 1221 | rkE(5) = 0.1500d0 |
---|
| 1222 | |
---|
| 1223 | ! Local order of Err estimate |
---|
| 1224 | rkElo = 4 |
---|
| 1225 | |
---|
| 1226 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1227 | rkTheta(2,1) = 2.d0 |
---|
| 1228 | rkTheta(3,1) = 1.680000000000000000000000000000000d0 |
---|
| 1229 | rkTheta(3,2) = -.1600000000000000000000000000000000d0 |
---|
| 1230 | rkTheta(4,1) = 1.308823529411764705882352941176471d0 |
---|
| 1231 | rkTheta(4,2) = -.1838235294117647058823529411764706d0 |
---|
| 1232 | rkTheta(4,3) = 0.1102941176470588235294117647058824d0 |
---|
| 1233 | rkTheta(5,1) = -3.083333333333333333333333333333333d0 |
---|
| 1234 | rkTheta(5,2) = -4.291666666666666666666666666666667d0 |
---|
| 1235 | rkTheta(5,3) = 34.37500000000000000000000000000000d0 |
---|
| 1236 | rkTheta(5,4) = -28.33333333333333333333333333333333d0 |
---|
| 1237 | |
---|
| 1238 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1239 | rkAlpha(2,1) = 3. |
---|
| 1240 | rkAlpha(3,1) = .8800000000000000000000000000000000d0 |
---|
| 1241 | rkAlpha(3,2) = .4400000000000000000000000000000000d0 |
---|
| 1242 | rkAlpha(4,1) = .1666666666666666666666666666666667d0 |
---|
| 1243 | rkAlpha(4,2) = -.8333333333333333333333333333333333d-1 |
---|
| 1244 | rkAlpha(4,3) = .9469696969696969696969696969696970d0 |
---|
| 1245 | rkAlpha(5,1) = -6.d0 |
---|
| 1246 | rkAlpha(5,2) = 9.d0 |
---|
| 1247 | rkAlpha(5,3) = -56.81818181818181818181818181818182d0 |
---|
| 1248 | rkAlpha(5,4) = 54.d0 |
---|
| 1249 | |
---|
| 1250 | END SUBROUTINE Sdirk4b |
---|
| 1251 | |
---|
| 1252 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1253 | SUBROUTINE Sdirk2a |
---|
| 1254 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1255 | sdMethod = S2A |
---|
| 1256 | ! Number of stages |
---|
| 1257 | rkS = 2 |
---|
| 1258 | |
---|
| 1259 | ! Method coefficients |
---|
| 1260 | rkGamma = .2928932188134524755991556378951510d0 |
---|
| 1261 | |
---|
| 1262 | rkA(1,1) = .2928932188134524755991556378951510d0 |
---|
| 1263 | rkA(2,1) = .7071067811865475244008443621048490d0 |
---|
| 1264 | rkA(2,2) = .2928932188134524755991556378951510d0 |
---|
| 1265 | |
---|
| 1266 | rkB(1) = .7071067811865475244008443621048490d0 |
---|
| 1267 | rkB(2) = .2928932188134524755991556378951510d0 |
---|
| 1268 | |
---|
| 1269 | rkBhat(1)= .6666666666666666666666666666666667d0 |
---|
| 1270 | rkBhat(2)= .3333333333333333333333333333333333d0 |
---|
| 1271 | |
---|
| 1272 | rkC(1) = 0.292893218813452475599155637895151d0 |
---|
| 1273 | rkC(2) = 1.0d0 |
---|
| 1274 | |
---|
| 1275 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1276 | rkD(1) = 0.0d0 |
---|
| 1277 | rkD(2) = 1.0d0 |
---|
| 1278 | |
---|
| 1279 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1280 | rkE(1) = 0.4714045207910316829338962414032326d0 |
---|
| 1281 | rkE(2) = -0.1380711874576983496005629080698993d0 |
---|
| 1282 | |
---|
| 1283 | ! Local order of Err estimate |
---|
| 1284 | rkElo = 2 |
---|
| 1285 | |
---|
| 1286 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1287 | rkTheta(2,1) = 2.414213562373095048801688724209698d0 |
---|
| 1288 | |
---|
| 1289 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1290 | rkAlpha(2,1) = 3.414213562373095048801688724209698d0 |
---|
| 1291 | |
---|
| 1292 | END SUBROUTINE Sdirk2a |
---|
| 1293 | |
---|
| 1294 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1295 | SUBROUTINE Sdirk2b |
---|
| 1296 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1297 | sdMethod = S2B |
---|
| 1298 | ! Number of stages |
---|
| 1299 | rkS = 2 |
---|
| 1300 | |
---|
| 1301 | ! Method coefficients |
---|
| 1302 | rkGamma = 1.707106781186547524400844362104849d0 |
---|
| 1303 | |
---|
| 1304 | rkA(1,1) = 1.707106781186547524400844362104849d0 |
---|
| 1305 | rkA(2,1) = -.707106781186547524400844362104849d0 |
---|
| 1306 | rkA(2,2) = 1.707106781186547524400844362104849d0 |
---|
| 1307 | |
---|
| 1308 | rkB(1) = -.707106781186547524400844362104849d0 |
---|
| 1309 | rkB(2) = 1.707106781186547524400844362104849d0 |
---|
| 1310 | |
---|
| 1311 | rkBhat(1)= .6666666666666666666666666666666667d0 |
---|
| 1312 | rkBhat(2)= .3333333333333333333333333333333333d0 |
---|
| 1313 | |
---|
| 1314 | rkC(1) = 1.707106781186547524400844362104849d0 |
---|
| 1315 | rkC(2) = 1.0d0 |
---|
| 1316 | |
---|
| 1317 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1318 | rkD(1) = 0.0d0 |
---|
| 1319 | rkD(2) = 1.0d0 |
---|
| 1320 | |
---|
| 1321 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1322 | rkE(1) = -.4714045207910316829338962414032326d0 |
---|
| 1323 | rkE(2) = .8047378541243650162672295747365659d0 |
---|
| 1324 | |
---|
| 1325 | ! Local order of Err estimate |
---|
| 1326 | rkElo = 2 |
---|
| 1327 | |
---|
| 1328 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1329 | rkTheta(2,1) = -.414213562373095048801688724209698d0 |
---|
| 1330 | |
---|
| 1331 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1332 | rkAlpha(2,1) = .5857864376269049511983112757903019d0 |
---|
| 1333 | |
---|
| 1334 | END SUBROUTINE Sdirk2b |
---|
| 1335 | |
---|
| 1336 | |
---|
| 1337 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1338 | SUBROUTINE Sdirk3a |
---|
| 1339 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1340 | sdMethod = S3A |
---|
| 1341 | ! Number of stages |
---|
| 1342 | rkS = 3 |
---|
| 1343 | |
---|
| 1344 | ! Method coefficients |
---|
| 1345 | rkGamma = .2113248654051871177454256097490213d0 |
---|
| 1346 | |
---|
| 1347 | rkA(1,1) = .2113248654051871177454256097490213d0 |
---|
| 1348 | rkA(2,1) = .2113248654051871177454256097490213d0 |
---|
| 1349 | rkA(2,2) = .2113248654051871177454256097490213d0 |
---|
| 1350 | rkA(3,1) = .2113248654051871177454256097490213d0 |
---|
| 1351 | rkA(3,2) = .5773502691896257645091487805019573d0 |
---|
| 1352 | rkA(3,3) = .2113248654051871177454256097490213d0 |
---|
| 1353 | |
---|
| 1354 | rkB(1) = .2113248654051871177454256097490213d0 |
---|
| 1355 | rkB(2) = .5773502691896257645091487805019573d0 |
---|
| 1356 | rkB(3) = .2113248654051871177454256097490213d0 |
---|
| 1357 | |
---|
| 1358 | rkBhat(1)= .2113248654051871177454256097490213d0 |
---|
| 1359 | rkBhat(2)= .6477918909913548037576239837516312d0 |
---|
| 1360 | rkBhat(3)= .1408832436034580784969504064993475d0 |
---|
| 1361 | |
---|
| 1362 | rkC(1) = .2113248654051871177454256097490213d0 |
---|
| 1363 | rkC(2) = .4226497308103742354908512194980427d0 |
---|
| 1364 | rkC(3) = 1.d0 |
---|
| 1365 | |
---|
| 1366 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1367 | rkD(1) = 0.d0 |
---|
| 1368 | rkD(2) = 0.d0 |
---|
| 1369 | rkD(3) = 1.d0 |
---|
| 1370 | |
---|
| 1371 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1372 | rkE(1) = 0.9106836025229590978424821138352906d0 |
---|
| 1373 | rkE(2) = -1.244016935856292431175815447168624d0 |
---|
| 1374 | rkE(3) = 0.3333333333333333333333333333333333d0 |
---|
| 1375 | |
---|
| 1376 | ! Local order of Err estimate |
---|
| 1377 | rkElo = 2 |
---|
| 1378 | |
---|
| 1379 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1380 | rkTheta(2,1) = 1.0d0 |
---|
| 1381 | rkTheta(3,1) = -1.732050807568877293527446341505872d0 |
---|
| 1382 | rkTheta(3,2) = 2.732050807568877293527446341505872d0 |
---|
| 1383 | |
---|
| 1384 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1385 | rkAlpha(2,1) = 2.0d0 |
---|
| 1386 | rkAlpha(3,1) = -12.92820323027550917410978536602349d0 |
---|
| 1387 | rkAlpha(3,2) = 8.83012701892219323381861585376468d0 |
---|
| 1388 | |
---|
| 1389 | END SUBROUTINE Sdirk3a |
---|
| 1390 | |
---|
| 1391 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1392 | END SUBROUTINE SdirkTLM ! AND ALL ITS INTERNAL PROCEDURES |
---|
| 1393 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1394 | |
---|
| 1395 | |
---|
| 1396 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1397 | SUBROUTINE FUN_CHEM( T, Y, P ) |
---|
| 1398 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1399 | |
---|
| 1400 | USE KPP_ROOT_Parameters, ONLY: NVAR |
---|
| 1401 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
| 1402 | USE KPP_ROOT_Function, ONLY: Fun |
---|
| 1403 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
| 1404 | |
---|
| 1405 | KPP_REAL :: T, Told |
---|
| 1406 | KPP_REAL :: Y(NVAR), P(NVAR) |
---|
| 1407 | |
---|
| 1408 | Told = TIME |
---|
| 1409 | TIME = T |
---|
| 1410 | CALL Update_SUN() |
---|
| 1411 | CALL Update_RCONST() |
---|
| 1412 | |
---|
| 1413 | CALL Fun( Y, FIX, RCONST, P ) |
---|
| 1414 | |
---|
| 1415 | TIME = Told |
---|
| 1416 | |
---|
| 1417 | END SUBROUTINE FUN_CHEM |
---|
| 1418 | |
---|
| 1419 | |
---|
| 1420 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1421 | SUBROUTINE JAC_CHEM( T, Y, JV ) |
---|
| 1422 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1423 | |
---|
| 1424 | |
---|
| 1425 | USE KPP_ROOT_Parameters, ONLY: NVAR, LU_NONZERO |
---|
| 1426 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
| 1427 | USE KPP_ROOT_Jacobian, ONLY: Jac_SP,LU_IROW,LU_ICOL |
---|
| 1428 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
| 1429 | |
---|
| 1430 | KPP_REAL :: T, Told |
---|
| 1431 | KPP_REAL :: Y(NVAR) |
---|
| 1432 | #ifdef FULL_ALGEBRA |
---|
| 1433 | KPP_REAL :: JS(LU_NONZERO), JV(NVAR,NVAR) |
---|
| 1434 | INTEGER :: i, j |
---|
| 1435 | #else |
---|
| 1436 | KPP_REAL :: JV(LU_NONZERO) |
---|
| 1437 | #endif |
---|
| 1438 | |
---|
| 1439 | Told = TIME |
---|
| 1440 | TIME = T |
---|
| 1441 | CALL Update_SUN() |
---|
| 1442 | CALL Update_RCONST() |
---|
| 1443 | |
---|
| 1444 | #ifdef FULL_ALGEBRA |
---|
| 1445 | CALL Jac_SP(Y, FIX, RCONST, JS) |
---|
| 1446 | DO j=1,NVAR |
---|
| 1447 | DO i=1,NVAR |
---|
| 1448 | JV(i,j) = 0.0D0 |
---|
| 1449 | END DO |
---|
| 1450 | END DO |
---|
| 1451 | DO i=1,LU_NONZERO |
---|
| 1452 | JV(LU_IROW(i),LU_ICOL(i)) = JS(i) |
---|
| 1453 | END DO |
---|
| 1454 | #else |
---|
| 1455 | CALL Jac_SP(Y, FIX, RCONST, JV) |
---|
| 1456 | #endif |
---|
| 1457 | TIME = Told |
---|
| 1458 | |
---|
| 1459 | END SUBROUTINE JAC_CHEM |
---|
| 1460 | |
---|
| 1461 | END MODULE KPP_ROOT_Integrator |
---|