[2696] | 1 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 2 | ! Adjoint of SDIRK - Singly-Diagonally-Implicit Runge-Kutta method ! |
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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, JacTR_SP_Vec |
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| 23 | USE KPP_ROOT_LinearAlgebra, ONLY: KppDecomp, KppSolve, & |
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| 24 | KppSolveTR, 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 | SUBROUTINE INTEGRATE_ADJ( NADJ, Y, Lambda, TIN, TOUT, & |
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| 38 | ATOL_adj, RTOL_adj, & |
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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 | USE KPP_ROOT_Parameters |
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| 42 | USE KPP_ROOT_Global |
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| 43 | IMPLICIT NONE |
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| 44 | |
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| 45 | !~~~> Y - Concentrations |
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| 46 | KPP_REAL :: Y(NVAR) |
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| 47 | !~~~> NADJ - No. of cost functionals for which adjoints |
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| 48 | ! are evaluated simultaneously |
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| 49 | ! If single cost functional is considered (like in |
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| 50 | ! most applications) simply set NADJ = 1 |
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| 51 | INTEGER :: NADJ |
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| 52 | !~~~> Lambda - Sensitivities w.r.t. concentrations |
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| 53 | ! Note: Lambda (1:NVAR,j) contains sensitivities of |
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| 54 | ! the j-th cost functional w.r.t. Y(1:NVAR), j=1...NADJ |
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| 55 | KPP_REAL :: Lambda(NVAR,NADJ) |
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| 56 | !~~~> Tolerances for adjoint calculations |
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| 57 | ! (used for full continuous adjoint, and for controlling |
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| 58 | ! iterations when used to solve the discrete adjoint) |
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| 59 | KPP_REAL, INTENT(IN) :: ATOL_adj(NVAR,NADJ), RTOL_adj(NVAR,NADJ) |
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| 60 | KPP_REAL, INTENT(IN) :: TIN ! Start Time |
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| 61 | KPP_REAL, INTENT(IN) :: TOUT ! End Time |
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| 62 | ! Optional input parameters and statistics |
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| 63 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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| 64 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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| 65 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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| 66 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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| 67 | INTEGER, INTENT(OUT), OPTIONAL :: Ierr_U |
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| 68 | |
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| 69 | INTEGER, SAVE :: Ntotal = 0 |
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| 70 | KPP_REAL :: RCNTRL(20), RSTATUS(20), T1, T2 |
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| 71 | INTEGER :: ICNTRL(20), ISTATUS(20), Ierr |
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| 72 | |
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| 73 | ICNTRL(:) = 0 |
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| 74 | RCNTRL(:) = 0.0_dp |
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| 75 | ISTATUS(:) = 0 |
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| 76 | RSTATUS(:) = 0.0_dp |
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| 77 | |
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| 78 | !~~~> fine-tune the integrator: |
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| 79 | ICNTRL(5) = 8 ! Max no. of Newton iterations |
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| 80 | ICNTRL(7) = 1 ! Adjoint solution by: 0=Newton, 1=direct |
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| 81 | ICNTRL(8) = 1 ! Save fwd LU factorization: 0 = do *not* save, 1 = save |
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| 82 | |
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| 83 | ! If optional parameters are given, and if they are >0, |
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| 84 | ! then they overwrite default settings. |
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| 85 | IF (PRESENT(ICNTRL_U)) THEN |
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| 86 | WHERE(ICNTRL_U(:) > 0) ICNTRL(:) = ICNTRL_U(:) |
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| 87 | END IF |
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| 88 | IF (PRESENT(RCNTRL_U)) THEN |
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| 89 | WHERE(RCNTRL_U(:) > 0) RCNTRL(:) = RCNTRL_U(:) |
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| 90 | END IF |
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| 91 | |
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| 92 | |
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| 93 | T1 = TIN; T2 = TOUT |
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| 94 | CALL SDIRKADJ( NVAR, NADJ, T1, T2, Y, Lambda, & |
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| 95 | RTOL, ATOL, ATOL_adj, RTOL_adj, & |
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| 96 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, Ierr ) |
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| 97 | |
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| 98 | !~~~> Debug option: number of steps |
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| 99 | ! Ntotal = Ntotal + ISTATUS(Nstp) |
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| 100 | ! WRITE(6,777) ISTATUS(Nstp),Ntotal,VAR(ind_O3),VAR(ind_NO2) |
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| 101 | ! 777 FORMAT('NSTEPS=',I5,' (',I5,') O3=',E24.14,' NO2=',E24.14) |
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| 102 | |
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| 103 | IF (Ierr < 0) THEN |
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| 104 | PRINT *,'SDIRK: Unsuccessful exit at T=',TIN,' (Ierr=',Ierr,')' |
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| 105 | ENDIF |
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| 106 | |
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| 107 | ! if optional parameters are given for output they to return information |
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| 108 | IF (PRESENT(ISTATUS_U)) ISTATUS_U(:) = ISTATUS(:) |
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| 109 | IF (PRESENT(RSTATUS_U)) RSTATUS_U(:) = RSTATUS(:) |
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| 110 | IF (PRESENT(Ierr_U)) Ierr_U = Ierr |
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| 111 | |
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| 112 | END SUBROUTINE INTEGRATE_ADJ |
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| 113 | |
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| 114 | |
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| 115 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 116 | SUBROUTINE SDIRKADJ(N, NADJ, Tinitial, Tfinal, Y, Lambda, & |
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| 117 | RelTol, AbsTol, RelTol_adj, AbsTol_adj, & |
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| 118 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, Ierr) |
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| 119 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 120 | ! |
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| 121 | ! Solves the system y'=F(t,y) using a Singly-Diagonally-Implicit |
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| 122 | ! Runge-Kutta (SDIRK) method. |
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| 123 | ! |
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| 124 | ! This implementation is based on the book and the code Sdirk4: |
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| 125 | ! |
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| 126 | ! E. Hairer and G. Wanner |
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| 127 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
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| 128 | ! Springer series in computational mathematics, Springer-Verlag, 1996. |
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| 129 | ! This code is based on the SDIRK4 routine in the above book. |
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| 130 | ! |
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| 131 | ! Methods: |
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| 132 | ! * Sdirk 2a, 2b: L-stable, 2 stages, order 2 |
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| 133 | ! * Sdirk 3a: L-stable, 3 stages, order 2, adjoint-invariant |
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| 134 | ! * Sdirk 4a, 4b: L-stable, 5 stages, order 4 |
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| 135 | ! |
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| 136 | ! (C) Adrian Sandu, July 2005 |
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| 137 | ! Virginia Polytechnic Institute and State University |
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| 138 | ! Contact: sandu@cs.vt.edu |
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| 139 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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| 140 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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| 141 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 142 | ! |
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| 143 | !~~~> INPUT ARGUMENTS: |
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| 144 | ! |
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| 145 | !- Y(NVAR) = vector of initial conditions (at T=Tinitial) |
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| 146 | !- [Tinitial,Tfinal] = time range of integration |
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| 147 | ! (if Tinitial>Tfinal the integration is performed backwards in time) |
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| 148 | !- RelTol, AbsTol = user precribed accuracy |
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| 149 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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| 150 | ! returns Ydot = Y' = F(T,Y) |
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| 151 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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| 152 | ! returns Jcb = dF/dY |
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| 153 | !- ICNTRL(1:20) = integer inputs parameters |
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| 154 | !- RCNTRL(1:20) = real inputs parameters |
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| 155 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 156 | ! |
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| 157 | !~~~> OUTPUT ARGUMENTS: |
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| 158 | ! |
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| 159 | !- Y(NVAR) -> vector of final states (at T->Tfinal) |
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| 160 | !- ISTATUS(1:20) -> integer output parameters |
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| 161 | !- RSTATUS(1:20) -> real output parameters |
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| 162 | !- Ierr -> job status upon return |
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| 163 | ! success (positive value) or |
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| 164 | ! failure (negative value) |
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| 165 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 166 | ! |
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| 167 | !~~~> INPUT PARAMETERS: |
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| 168 | ! |
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| 169 | ! Note: For input parameters equal to zero the default values of the |
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| 170 | ! corresponding variables are used. |
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| 171 | ! |
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| 172 | ! Note: For input parameters equal to zero the default values of the |
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| 173 | ! corresponding variables are used. |
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| 174 | !~~~> |
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| 175 | ! ICNTRL(1) = not used |
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| 176 | ! |
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| 177 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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| 178 | ! = 1: AbsTol, RelTol are scalars |
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| 179 | ! |
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| 180 | ! ICNTRL(3) = Method |
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| 181 | ! |
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| 182 | ! ICNTRL(4) -> maximum number of integration steps |
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| 183 | ! For ICNTRL(4)=0 the default value of 1500 is used |
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| 184 | ! Note: use a conservative estimate, since the checkpoint |
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| 185 | ! buffers are allocated to hold Max_no_steps |
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| 186 | ! |
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| 187 | ! ICNTRL(5) -> maximum number of Newton iterations |
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| 188 | ! For ICNTRL(5)=0 the default value of 8 is used |
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| 189 | ! |
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| 190 | ! ICNTRL(6) -> starting values of Newton iterations: |
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| 191 | ! ICNTRL(6)=0 : starting values are interpolated (the default) |
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| 192 | ! ICNTRL(6)=1 : starting values are zero |
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| 193 | ! |
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| 194 | ! ICNTRL(7) -> method to solve ADJ equations: |
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| 195 | ! ICNTRL(7)=0 : modified Newton re-using LU (the default) |
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| 196 | ! ICNTRL(7)=1 : direct solution (additional one LU factorization per stage) |
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| 197 | ! |
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| 198 | ! ICNTRL(8) -> checkpointing the LU factorization at each step: |
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| 199 | ! ICNTRL(8)=0 : do *not* save LU factorization (the default) |
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| 200 | ! ICNTRL(8)=1 : save LU factorization |
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| 201 | ! Note: if ICNTRL(7)=1 the LU factorization is *not* saved |
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| 202 | ! |
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| 203 | !~~~> Real parameters |
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| 204 | ! |
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| 205 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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| 206 | ! It is strongly recommended to keep Hmin = ZERO |
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| 207 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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| 208 | ! RCNTRL(3) -> Hstart, starting value for the integration step size |
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| 209 | ! |
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| 210 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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| 211 | ! RCNTRL(5) -> FacMax, upper bound on step increase factor (default=6) |
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| 212 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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| 213 | ! (default=0.1) |
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| 214 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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| 215 | ! than the predicted value (default=0.9) |
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| 216 | ! RCNTRL(8) -> ThetaMin. If Newton convergence rate smaller |
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| 217 | ! than ThetaMin the Jacobian is not recomputed; |
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| 218 | ! (default=0.001) |
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| 219 | ! RCNTRL(9) -> NewtonTol, stopping criterion for Newton's method |
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| 220 | ! (default=0.03) |
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| 221 | ! RCNTRL(10) -> Qmin |
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| 222 | ! RCNTRL(11) -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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| 223 | ! step size is kept constant and the LU factorization |
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| 224 | ! reused (default Qmin=1, Qmax=1.2) |
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| 225 | ! |
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| 226 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 227 | ! |
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| 228 | !~~~> OUTPUT PARAMETERS: |
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| 229 | ! |
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| 230 | ! Note: each call to Rosenbrock adds the current no. of fcn calls |
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| 231 | ! to previous value of ISTATUS(1), and similar for the other params. |
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| 232 | ! Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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| 233 | ! |
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| 234 | ! ISTATUS(1) = No. of function calls |
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| 235 | ! ISTATUS(2) = No. of jacobian calls |
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| 236 | ! ISTATUS(3) = No. of steps |
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| 237 | ! ISTATUS(4) = No. of accepted steps |
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| 238 | ! ISTATUS(5) = No. of rejected steps (except at the beginning) |
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| 239 | ! ISTATUS(6) = No. of LU decompositions |
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| 240 | ! ISTATUS(7) = No. of forward/backward substitutions |
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| 241 | ! ISTATUS(8) = No. of singular matrix decompositions |
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| 242 | ! |
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| 243 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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| 244 | ! computed Y upon return |
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| 245 | ! RSTATUS(2) -> Hexit,last accepted step before return |
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| 246 | ! RSTATUS(3) -> Hnew, last predicted step before return |
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| 247 | ! For multiple restarts, use Hnew as Hstart in the following run |
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| 248 | ! |
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| 249 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 250 | IMPLICIT NONE |
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| 251 | |
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| 252 | ! Arguments |
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| 253 | INTEGER, INTENT(IN) :: N, NADJ, ICNTRL(20) |
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| 254 | KPP_REAL, INTENT(INOUT) :: Y(NVAR), Lambda(NVAR,NADJ) |
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| 255 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal, & |
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| 256 | RelTol(NVAR), AbsTol(NVAR), RCNTRL(20), & |
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| 257 | RelTol_adj(NVAR,NADJ), AbsTol_adj(NVAR,NADJ) |
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| 258 | INTEGER, INTENT(OUT) :: Ierr |
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| 259 | INTEGER, INTENT(INOUT) :: ISTATUS(20) |
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| 260 | KPP_REAL, INTENT(OUT) :: RSTATUS(20) |
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| 261 | |
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| 262 | !~~~> SDIRK method coefficients, up to 5 stages |
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| 263 | INTEGER, PARAMETER :: Smax = 5 |
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| 264 | INTEGER, PARAMETER :: S2A=1, S2B=2, S3A=3, S4A=4, S4B=5 |
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| 265 | KPP_REAL :: rkGamma, rkA(Smax,Smax), rkB(Smax), rkC(Smax), & |
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| 266 | rkD(Smax), rkE(Smax), rkBhat(Smax), rkELO, & |
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| 267 | rkAlpha(Smax,Smax), rkTheta(Smax,Smax) |
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| 268 | INTEGER :: sdMethod, rkS ! The number of stages |
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| 269 | |
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| 270 | !~~~> Checkpoints in memory buffers |
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| 271 | INTEGER :: stack_ptr = 0 ! last written entry in checkpoint |
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| 272 | KPP_REAL, DIMENSION(:), POINTER :: chk_H, chk_T |
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| 273 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_Y |
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| 274 | KPP_REAL, DIMENSION(:,:,:), POINTER :: chk_Z |
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| 275 | INTEGER, DIMENSION(:,:), POINTER :: chk_P |
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| 276 | #ifdef FULL_ALGEBRA |
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| 277 | KPP_REAL, DIMENSION(:,:,:), POINTER :: chk_J |
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| 278 | #else |
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| 279 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_J |
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| 280 | #endif |
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| 281 | ! Local variables |
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| 282 | KPP_REAL :: Hmin, Hmax, Hstart, Roundoff, & |
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| 283 | FacMin, Facmax, FacSafe, FacRej, & |
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| 284 | ThetaMin, NewtonTol, Qmin, Qmax |
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| 285 | LOGICAL :: SaveLU, DirectADJ |
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| 286 | INTEGER :: ITOL, NewtonMaxit, Max_no_steps, i |
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| 287 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
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| 288 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
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| 289 | |
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| 290 | |
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| 291 | !~~~> Initialize statistics |
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| 292 | ISTATUS(1:20) = 0 |
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| 293 | RSTATUS(1:20) = ZERO |
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| 294 | Ierr = 0 |
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| 295 | |
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| 296 | !~~~> For Scalar tolerances (ICNTRL(2).NE.0) the code uses AbsTol(1) and RelTol(1) |
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| 297 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:NVAR) and RelTol(1:NVAR) |
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| 298 | IF (ICNTRL(2) == 0) THEN |
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| 299 | ITOL = 1 |
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| 300 | ELSE |
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| 301 | ITOL = 0 |
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| 302 | END IF |
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| 303 | |
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| 304 | !~~~> ICNTRL(3) - method selection |
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| 305 | SELECT CASE (ICNTRL(3)) |
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| 306 | CASE (0,1) |
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| 307 | CALL Sdirk2a |
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| 308 | CASE (2) |
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| 309 | CALL Sdirk2b |
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| 310 | CASE (3) |
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| 311 | CALL Sdirk3a |
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| 312 | CASE (4) |
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| 313 | CALL Sdirk4a |
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| 314 | CASE (5) |
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| 315 | CALL Sdirk4b |
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| 316 | CASE DEFAULT |
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| 317 | CALL Sdirk2a |
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| 318 | END SELECT |
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| 319 | |
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| 320 | !~~~> The maximum number of time steps admitted |
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| 321 | IF (ICNTRL(4) == 0) THEN |
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| 322 | Max_no_steps = 200000 |
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| 323 | ELSEIF (ICNTRL(4) > 0) THEN |
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| 324 | Max_no_steps = ICNTRL(4) |
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| 325 | ELSE |
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| 326 | PRINT * ,'User-selected ICNTRL(4)=',ICNTRL(4) |
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| 327 | CALL SDIRK_ErrorMsg(-1,Tinitial,ZERO,Ierr) |
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| 328 | END IF |
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| 329 | |
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| 330 | !~~~> The maximum number of Newton iterations admitted |
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| 331 | IF(ICNTRL(5) == 0)THEN |
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| 332 | NewtonMaxit=8 |
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| 333 | ELSE |
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| 334 | NewtonMaxit=ICNTRL(5) |
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| 335 | IF(NewtonMaxit <= 0)THEN |
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| 336 | PRINT * ,'User-selected ICNTRL(5)=',ICNTRL(5) |
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| 337 | CALL SDIRK_ErrorMsg(-2,Tinitial,ZERO,Ierr) |
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| 338 | END IF |
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| 339 | END IF |
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| 340 | |
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| 341 | !~~~> Solve ADJ equations directly or by Newton iterations |
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| 342 | DirectADJ = (ICNTRL(7) == 1) |
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| 343 | |
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| 344 | !~~~> Save or not the forward LU factorization |
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| 345 | SaveLU = (ICNTRL(8) /= 0) .AND. (.NOT.DirectADJ) |
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| 346 | |
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| 347 | !~~~> Unit roundoff (1+Roundoff>1) |
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| 348 | Roundoff = WLAMCH('E') |
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| 349 | |
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| 350 | !~~~> Lower bound on the step size: (positive value) |
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| 351 | IF (RCNTRL(1) == ZERO) THEN |
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| 352 | Hmin = ZERO |
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| 353 | ELSEIF (RCNTRL(1) > ZERO) THEN |
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| 354 | Hmin = RCNTRL(1) |
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| 355 | ELSE |
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| 356 | PRINT * , 'User-selected RCNTRL(1)=', RCNTRL(1) |
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| 357 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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| 358 | END IF |
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| 359 | |
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| 360 | !~~~> Upper bound on the step size: (positive value) |
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| 361 | IF (RCNTRL(2) == ZERO) THEN |
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| 362 | Hmax = ABS(Tfinal-Tinitial) |
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| 363 | ELSEIF (RCNTRL(2) > ZERO) THEN |
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| 364 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tfinal-Tinitial)) |
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| 365 | ELSE |
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| 366 | PRINT * , 'User-selected RCNTRL(2)=', RCNTRL(2) |
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| 367 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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| 368 | END IF |
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| 369 | |
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| 370 | !~~~> Starting step size: (positive value) |
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| 371 | IF (RCNTRL(3) == ZERO) THEN |
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| 372 | Hstart = MAX(Hmin,Roundoff) |
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| 373 | ELSEIF (RCNTRL(3) > ZERO) THEN |
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| 374 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tfinal-Tinitial)) |
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| 375 | ELSE |
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| 376 | PRINT * , 'User-selected Hstart: RCNTRL(3)=', RCNTRL(3) |
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| 377 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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| 378 | END IF |
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| 379 | |
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| 380 | !~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax |
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| 381 | IF (RCNTRL(4) == ZERO) THEN |
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| 382 | FacMin = 0.2_dp |
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| 383 | ELSEIF (RCNTRL(4) > ZERO) THEN |
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| 384 | FacMin = RCNTRL(4) |
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| 385 | ELSE |
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| 386 | PRINT * , 'User-selected FacMin: RCNTRL(4)=', RCNTRL(4) |
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| 387 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
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| 388 | END IF |
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| 389 | IF (RCNTRL(5) == ZERO) THEN |
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| 390 | FacMax = 10.0_dp |
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| 391 | ELSEIF (RCNTRL(5) > ZERO) THEN |
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| 392 | FacMax = RCNTRL(5) |
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| 393 | ELSE |
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| 394 | PRINT * , 'User-selected FacMax: RCNTRL(5)=', RCNTRL(5) |
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| 395 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
| 396 | END IF |
---|
| 397 | !~~~> FacRej: Factor to decrease step after 2 succesive rejections |
---|
| 398 | IF (RCNTRL(6) == ZERO) THEN |
---|
| 399 | FacRej = 0.1_dp |
---|
| 400 | ELSEIF (RCNTRL(6) > ZERO) THEN |
---|
| 401 | FacRej = RCNTRL(6) |
---|
| 402 | ELSE |
---|
| 403 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
---|
| 404 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
| 405 | END IF |
---|
| 406 | !~~~> FacSafe: Safety Factor in the computation of new step size |
---|
| 407 | IF (RCNTRL(7) == ZERO) THEN |
---|
| 408 | FacSafe = 0.9_dp |
---|
| 409 | ELSEIF (RCNTRL(7) > ZERO) THEN |
---|
| 410 | FacSafe = RCNTRL(7) |
---|
| 411 | ELSE |
---|
| 412 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
---|
| 413 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
| 414 | END IF |
---|
| 415 | |
---|
| 416 | !~~~> ThetaMin: decides whether the Jacobian should be recomputed |
---|
| 417 | IF(RCNTRL(8) == 0.D0)THEN |
---|
| 418 | ThetaMin = 1.0d-3 |
---|
| 419 | ELSE |
---|
| 420 | ThetaMin = RCNTRL(8) |
---|
| 421 | END IF |
---|
| 422 | |
---|
| 423 | !~~~> Stopping criterion for Newton's method |
---|
| 424 | IF(RCNTRL(9) == ZERO)THEN |
---|
| 425 | NewtonTol = 3.0d-2 |
---|
| 426 | ELSE |
---|
| 427 | NewtonTol = RCNTRL(9) |
---|
| 428 | END IF |
---|
| 429 | |
---|
| 430 | !~~~> Qmin, Qmax: IF Qmin < Hnew/Hold < Qmax, STEP SIZE = CONST. |
---|
| 431 | IF(RCNTRL(10) == ZERO)THEN |
---|
| 432 | Qmin=ONE |
---|
| 433 | ELSE |
---|
| 434 | Qmin=RCNTRL(10) |
---|
| 435 | END IF |
---|
| 436 | IF(RCNTRL(11) == ZERO)THEN |
---|
| 437 | Qmax=1.2D0 |
---|
| 438 | ELSE |
---|
| 439 | Qmax=RCNTRL(11) |
---|
| 440 | END IF |
---|
| 441 | |
---|
| 442 | !~~~> Check if tolerances are reasonable |
---|
| 443 | IF (ITOL == 0) THEN |
---|
| 444 | IF (AbsTol(1) <= ZERO .OR. RelTol(1) <= 10.D0*Roundoff) THEN |
---|
| 445 | PRINT * , ' Scalar AbsTol = ',AbsTol(1) |
---|
| 446 | PRINT * , ' Scalar RelTol = ',RelTol(1) |
---|
| 447 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr) |
---|
| 448 | END IF |
---|
| 449 | ELSE |
---|
| 450 | DO i=1,N |
---|
| 451 | IF (AbsTol(i) <= 0.D0.OR.RelTol(i) <= 10.D0*Roundoff) THEN |
---|
| 452 | PRINT * , ' AbsTol(',i,') = ',AbsTol(i) |
---|
| 453 | PRINT * , ' RelTol(',i,') = ',RelTol(i) |
---|
| 454 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr) |
---|
| 455 | END IF |
---|
| 456 | END DO |
---|
| 457 | END IF |
---|
| 458 | |
---|
| 459 | IF (Ierr < 0) RETURN |
---|
| 460 | |
---|
| 461 | !~~~> Allocate memory buffers |
---|
| 462 | CALL SDIRK_AllocBuffers |
---|
| 463 | |
---|
| 464 | !~~~> Call forward integration |
---|
| 465 | CALL SDIRK_FwdInt( N, Tinitial, Tfinal, Y, Ierr ) |
---|
| 466 | |
---|
| 467 | !~~~> Call adjoint integration |
---|
| 468 | CALL SDIRK_DadjInt( N, NADJ, Lambda, Ierr ) |
---|
| 469 | |
---|
| 470 | !~~~> Free memory buffers |
---|
| 471 | CALL SDIRK_FreeBuffers |
---|
| 472 | |
---|
| 473 | |
---|
| 474 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 475 | CONTAINS ! Procedures internal to SDIRKADJ |
---|
| 476 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 477 | |
---|
| 478 | |
---|
| 479 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 480 | SUBROUTINE SDIRK_FwdInt( N,Tinitial,Tfinal,Y,Ierr ) |
---|
| 481 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 482 | |
---|
| 483 | USE KPP_ROOT_Parameters |
---|
| 484 | IMPLICIT NONE |
---|
| 485 | |
---|
| 486 | !~~~> Arguments: |
---|
| 487 | INTEGER :: N |
---|
| 488 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
---|
| 489 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal |
---|
| 490 | INTEGER, INTENT(OUT) :: Ierr |
---|
| 491 | |
---|
| 492 | !~~~> Local variables: |
---|
| 493 | KPP_REAL :: Z(NVAR,Smax), G(NVAR), TMP(NVAR), & |
---|
| 494 | NewtonRate, SCAL(NVAR), RHS(NVAR), & |
---|
| 495 | T, H, Theta, Hratio, NewtonPredictedErr, & |
---|
| 496 | Qnewton, Err, Fac, Hnew,Tdirection, & |
---|
| 497 | NewtonIncrement, NewtonIncrementOld |
---|
| 498 | INTEGER :: j, ISING, istage, NewtonIter, IP(NVAR) |
---|
| 499 | LOGICAL :: Reject, FirstStep, SkipJac, SkipLU, NewtonDone |
---|
| 500 | |
---|
| 501 | #ifdef FULL_ALGEBRA |
---|
| 502 | KPP_REAL, DIMENSION(NVAR,NVAR) :: FJAC, E |
---|
| 503 | #else |
---|
| 504 | KPP_REAL, DIMENSION(LU_NONZERO):: FJAC, E |
---|
| 505 | #endif |
---|
| 506 | |
---|
| 507 | |
---|
| 508 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 509 | !~~~> Initializations |
---|
| 510 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 511 | |
---|
| 512 | T = Tinitial |
---|
| 513 | Tdirection = SIGN(ONE,Tfinal-Tinitial) |
---|
| 514 | H = MAX(ABS(Hmin),ABS(Hstart)) |
---|
| 515 | IF (ABS(H) <= 10.D0*Roundoff) H=1.0D-6 |
---|
| 516 | H=MIN(ABS(H),Hmax) |
---|
| 517 | H=SIGN(H,Tdirection) |
---|
| 518 | SkipLU =.FALSE. |
---|
| 519 | SkipJac = .FALSE. |
---|
| 520 | Reject=.FALSE. |
---|
| 521 | FirstStep=.TRUE. |
---|
| 522 | |
---|
| 523 | CALL SDIRK_ErrorScale(ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 524 | |
---|
| 525 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 526 | !~~~> Time loop begins |
---|
| 527 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 528 | Tloop: DO WHILE ( (Tfinal-T)*Tdirection - Roundoff > ZERO ) |
---|
| 529 | |
---|
| 530 | |
---|
| 531 | !~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition |
---|
| 532 | IF ( .NOT.SkipLU ) THEN ! This time around skip the Jac update and LU |
---|
| 533 | CALL SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
| 534 | SkipJac, SkipLU, E, IP, Reject, ISING ) |
---|
| 535 | IF (ISING /= 0) THEN |
---|
| 536 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
| 537 | END IF |
---|
| 538 | END IF |
---|
| 539 | |
---|
| 540 | IF (ISTATUS(Nstp) > Max_no_steps) THEN |
---|
| 541 | CALL SDIRK_ErrorMsg(-6,T,H,Ierr); RETURN |
---|
| 542 | END IF |
---|
| 543 | IF ( (T+0.1d0*H == T) .OR. (ABS(H) <= Roundoff) ) THEN |
---|
| 544 | CALL SDIRK_ErrorMsg(-7,T,H,Ierr); RETURN |
---|
| 545 | END IF |
---|
| 546 | |
---|
| 547 | stages:DO istage = 1, rkS |
---|
| 548 | |
---|
| 549 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 550 | !~~~> Simplified Newton iterations |
---|
| 551 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 552 | |
---|
| 553 | !~~~> Starting values for Newton iterations |
---|
| 554 | CALL Set2zero(N,Z(1,istage)) |
---|
| 555 | |
---|
| 556 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
| 557 | CALL Set2zero(N,G) |
---|
| 558 | IF (istage > 1) THEN |
---|
| 559 | DO j = 1, istage-1 |
---|
| 560 | ! Gj(:) = sum_j Theta(i,j)*Zj(:) = H * sum_j A(i,j)*Fun(Zj(:)) |
---|
| 561 | CALL WAXPY(N,rkTheta(istage,j),Z(1,j),1,G,1) |
---|
| 562 | ! Zi(:) = sum_j Alpha(i,j)*Zj(:) |
---|
| 563 | CALL WAXPY(N,rkAlpha(istage,j),Z(1,j),1,Z(1,istage),1) |
---|
| 564 | END DO |
---|
| 565 | END IF |
---|
| 566 | |
---|
| 567 | !~~~> Initializations for Newton iteration |
---|
| 568 | NewtonDone = .FALSE. |
---|
| 569 | Fac = 0.5d0 ! Step reduction factor if too many iterations |
---|
| 570 | |
---|
| 571 | NewtonLoop:DO NewtonIter = 1, NewtonMaxit |
---|
| 572 | |
---|
| 573 | !~~~> Prepare the loop-dependent part of the right-hand side |
---|
| 574 | CALL WADD(N,Y,Z(1,istage),TMP) ! TMP <- Y + Zi |
---|
| 575 | CALL FUN_CHEM(T+rkC(istage)*H,TMP,RHS) ! RHS <- Fun(Y+Zi) |
---|
| 576 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 577 | ! RHS(1:N) = G(1:N) - Z(1:N,istage) + (H*rkGamma)*RHS(1:N) |
---|
| 578 | CALL WSCAL(N, H*rkGamma, RHS, 1) |
---|
| 579 | CALL WAXPY (N, -ONE, Z(1,istage), 1, RHS, 1) |
---|
| 580 | CALL WAXPY (N, ONE, G,1, RHS,1) |
---|
| 581 | |
---|
| 582 | !~~~> Solve the linear system |
---|
| 583 | CALL SDIRK_Solve ( 'N', H, N, E, IP, ISING, RHS ) |
---|
| 584 | |
---|
| 585 | !~~~> Check convergence of Newton iterations |
---|
| 586 | CALL SDIRK_ErrorNorm(N, RHS, SCAL, NewtonIncrement) |
---|
| 587 | IF ( NewtonIter == 1 ) THEN |
---|
| 588 | Theta = ABS(ThetaMin) |
---|
| 589 | NewtonRate = 2.0d0 |
---|
| 590 | ELSE |
---|
| 591 | Theta = NewtonIncrement/NewtonIncrementOld |
---|
| 592 | IF (Theta < 0.99d0) THEN |
---|
| 593 | NewtonRate = Theta/(ONE-Theta) |
---|
| 594 | ! Predict error at the end of Newton process |
---|
| 595 | NewtonPredictedErr = NewtonIncrement & |
---|
| 596 | *Theta**(NewtonMaxit-NewtonIter)/(ONE-Theta) |
---|
| 597 | IF (NewtonPredictedErr >= NewtonTol) THEN |
---|
| 598 | ! Non-convergence of Newton: predicted error too large |
---|
| 599 | Qnewton = MIN(10.0d0,NewtonPredictedErr/NewtonTol) |
---|
| 600 | Fac = 0.8d0*Qnewton**(-ONE/(1+NewtonMaxit-NewtonIter)) |
---|
| 601 | EXIT NewtonLoop |
---|
| 602 | END IF |
---|
| 603 | ELSE ! Non-convergence of Newton: Theta too large |
---|
| 604 | EXIT NewtonLoop |
---|
| 605 | END IF |
---|
| 606 | END IF |
---|
| 607 | NewtonIncrementOld = NewtonIncrement |
---|
| 608 | ! Update solution: Z(:) <-- Z(:)+RHS(:) |
---|
| 609 | CALL WAXPY(N,ONE,RHS,1,Z(1,istage),1) |
---|
| 610 | |
---|
| 611 | ! Check error in Newton iterations |
---|
| 612 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
| 613 | IF (NewtonDone) EXIT NewtonLoop |
---|
| 614 | |
---|
| 615 | END DO NewtonLoop |
---|
| 616 | |
---|
| 617 | IF (.NOT.NewtonDone) THEN |
---|
| 618 | !CALL RK_ErrorMsg(-12,T,H,Ierr); |
---|
| 619 | H = Fac*H; Reject=.TRUE. |
---|
| 620 | SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
| 621 | CYCLE Tloop |
---|
| 622 | END IF |
---|
| 623 | |
---|
| 624 | !~~~> End of implified Newton iterations |
---|
| 625 | |
---|
| 626 | |
---|
| 627 | END DO stages |
---|
| 628 | |
---|
| 629 | |
---|
| 630 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 631 | !~~~> Error estimation |
---|
| 632 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 633 | ISTATUS(Nstp) = ISTATUS(Nstp) + 1 |
---|
| 634 | CALL Set2zero(N,TMP) |
---|
| 635 | DO i = 1,rkS |
---|
| 636 | IF (rkE(i)/=ZERO) CALL WAXPY(N,rkE(i),Z(1,i),1,TMP,1) |
---|
| 637 | END DO |
---|
| 638 | |
---|
| 639 | CALL SDIRK_Solve( 'N', H, N, E, IP, ISING, TMP ) |
---|
| 640 | CALL SDIRK_ErrorNorm(N, TMP, SCAL, Err) |
---|
| 641 | |
---|
| 642 | !~~~> Computation of new step size Hnew |
---|
| 643 | Fac = FacSafe*(Err)**(-ONE/rkELO) |
---|
| 644 | Fac = MAX(FacMin,MIN(FacMax,Fac)) |
---|
| 645 | Hnew = H*Fac |
---|
| 646 | |
---|
| 647 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 648 | !~~~> Accept/Reject step |
---|
| 649 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 650 | accept: IF ( Err < ONE ) THEN !~~~> Step is accepted |
---|
| 651 | |
---|
| 652 | FirstStep=.FALSE. |
---|
| 653 | ISTATUS(Nacc) = ISTATUS(Nacc) + 1 |
---|
| 654 | |
---|
| 655 | !~~~> Checkpoint solution |
---|
| 656 | CALL SDIRK_Push( T, H, Y, Z, E, IP ) |
---|
| 657 | |
---|
| 658 | !~~~> Update time and solution |
---|
| 659 | T = T + H |
---|
| 660 | ! Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) |
---|
| 661 | DO i = 1,rkS |
---|
| 662 | IF (rkD(i)/=ZERO) CALL WAXPY(N,rkD(i),Z(1,i),1,Y,1) |
---|
| 663 | END DO |
---|
| 664 | |
---|
| 665 | !~~~> Update scaling coefficients |
---|
| 666 | CALL SDIRK_ErrorScale(ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 667 | |
---|
| 668 | !~~~> Next time step |
---|
| 669 | Hnew = Tdirection*MIN(ABS(Hnew),Hmax) |
---|
| 670 | ! Last T and H |
---|
| 671 | RSTATUS(Ntexit) = T |
---|
| 672 | RSTATUS(Nhexit) = H |
---|
| 673 | RSTATUS(Nhnew) = Hnew |
---|
| 674 | ! No step increase after a rejection |
---|
| 675 | IF (Reject) Hnew = Tdirection*MIN(ABS(Hnew),ABS(H)) |
---|
| 676 | Reject = .FALSE. |
---|
| 677 | IF ((T+Hnew/Qmin-Tfinal)*Tdirection > ZERO) THEN |
---|
| 678 | H = Tfinal-T |
---|
| 679 | ELSE |
---|
| 680 | Hratio=Hnew/H |
---|
| 681 | ! If step not changed too much keep Jacobian and reuse LU |
---|
| 682 | SkipLU = ( (Theta <= ThetaMin) .AND. (Hratio >= Qmin) & |
---|
| 683 | .AND. (Hratio <= Qmax) ) |
---|
| 684 | IF (.NOT.SkipLU) H = Hnew |
---|
| 685 | END IF |
---|
| 686 | ! If convergence is fast enough, do not update Jacobian |
---|
| 687 | ! SkipJac = (Theta <= ThetaMin) |
---|
| 688 | SkipJac = .FALSE. |
---|
| 689 | |
---|
| 690 | ELSE accept !~~~> Step is rejected |
---|
| 691 | |
---|
| 692 | IF (FirstStep .OR. Reject) THEN |
---|
| 693 | H = FacRej*H |
---|
| 694 | ELSE |
---|
| 695 | H = Hnew |
---|
| 696 | END IF |
---|
| 697 | Reject = .TRUE. |
---|
| 698 | SkipJac = .TRUE. |
---|
| 699 | SkipLU = .FALSE. |
---|
| 700 | IF (ISTATUS(Nacc) >= 1) ISTATUS(Nrej) = ISTATUS(Nrej) + 1 |
---|
| 701 | |
---|
| 702 | END IF accept |
---|
| 703 | |
---|
| 704 | END DO Tloop |
---|
| 705 | |
---|
| 706 | ! Successful return |
---|
| 707 | Ierr = 1 |
---|
| 708 | |
---|
| 709 | END SUBROUTINE SDIRK_FwdInt |
---|
| 710 | |
---|
| 711 | |
---|
| 712 | |
---|
| 713 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 714 | SUBROUTINE SDIRK_DadjInt( N, NADJ, Lambda, Ierr ) |
---|
| 715 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 716 | |
---|
| 717 | USE KPP_ROOT_Parameters |
---|
| 718 | IMPLICIT NONE |
---|
| 719 | |
---|
| 720 | !~~~> Arguments: |
---|
| 721 | INTEGER, INTENT(IN) :: N, NADJ |
---|
| 722 | KPP_REAL, INTENT(INOUT) :: Lambda(NVAR,NADJ) |
---|
| 723 | INTEGER, INTENT(OUT) :: Ierr |
---|
| 724 | |
---|
| 725 | !~~~> Local variables: |
---|
| 726 | KPP_REAL :: Y(NVAR) |
---|
| 727 | KPP_REAL :: Z(NVAR,Smax), U(NVAR,NADJ,Smax), & |
---|
| 728 | TMP(NVAR), G(NVAR), & |
---|
| 729 | NewtonRate, SCAL(NVAR), DU(NVAR), & |
---|
| 730 | T, H, Theta, NewtonPredictedErr, & |
---|
| 731 | NewtonIncrement, NewtonIncrementOld |
---|
| 732 | INTEGER :: j, ISING, istage, iadj, NewtonIter, & |
---|
| 733 | IP(NVAR), IP_adj(NVAR) |
---|
| 734 | LOGICAL :: Reject, SkipJac, SkipLU, NewtonDone |
---|
| 735 | |
---|
| 736 | #ifdef FULL_ALGEBRA |
---|
| 737 | KPP_REAL, DIMENSION(NVAR,NVAR) :: E, Jac, E_adj |
---|
| 738 | #else |
---|
| 739 | KPP_REAL, DIMENSION(LU_NONZERO):: E, Jac, E_adj |
---|
| 740 | #endif |
---|
| 741 | |
---|
| 742 | |
---|
| 743 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 744 | !~~~> Time loop begins |
---|
| 745 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 746 | Tloop: DO WHILE ( stack_ptr > 0 ) |
---|
| 747 | |
---|
| 748 | !~~~> Recover checkpoints for stage values and vectors |
---|
| 749 | CALL SDIRK_Pop( T, H, Y, Z, E, IP ) |
---|
| 750 | |
---|
| 751 | !~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition |
---|
| 752 | IF (.NOT.SaveLU) THEN |
---|
| 753 | SkipJac = .FALSE.; SkipLU = .FALSE. |
---|
| 754 | CALL SDIRK_PrepareMatrix ( H, T, Y, Jac, & |
---|
| 755 | SkipJac, SkipLU, E, IP, Reject, ISING ) |
---|
| 756 | IF (ISING /= 0) THEN |
---|
| 757 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
| 758 | END IF |
---|
| 759 | END IF |
---|
| 760 | |
---|
| 761 | stages:DO istage = rkS, 1, -1 |
---|
| 762 | |
---|
| 763 | !~~~> Jacobian of the current stage solution |
---|
| 764 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
| 765 | CALL JAC_CHEM(T+rkC(istage)*H,TMP,Jac) |
---|
| 766 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 767 | |
---|
| 768 | IF (DirectADJ) THEN |
---|
| 769 | #ifdef FULL_ALGEBRA |
---|
| 770 | E_adj(1:N,1:N) = -Jac(1:N,1:N) |
---|
| 771 | DO j=1,N |
---|
| 772 | E_adj(j,j) = E_adj(j,j) + ONE/(H*rkGamma) |
---|
| 773 | END DO |
---|
| 774 | CALL DGETRF( N, N, E_adj, N, IP_adj, ISING ) |
---|
| 775 | #else |
---|
| 776 | E_adj(1:LU_NONZERO) = -Jac(1:LU_NONZERO) |
---|
| 777 | DO i = 1,NVAR |
---|
| 778 | j = LU_DIAG(i); E_adj(j) = E_adj(j) + ONE/(H*rkGamma) |
---|
| 779 | END DO |
---|
| 780 | CALL KppDecomp ( E_adj, ISING) |
---|
| 781 | #endif |
---|
| 782 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
| 783 | IF (ISING /= 0) THEN |
---|
| 784 | PRINT*,'At stage ',istage,' the matrix used in adjoint', & |
---|
| 785 | ' computation is singular' |
---|
| 786 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
| 787 | END IF |
---|
| 788 | END IF |
---|
| 789 | |
---|
| 790 | adj: DO iadj = 1, NADJ |
---|
| 791 | |
---|
| 792 | !~~~> Update scaling coefficients |
---|
| 793 | CALL SDIRK_ErrorScale(ITOL, AbsTol_adj(1:NVAR,iadj), & |
---|
| 794 | RelTol_adj(1:NVAR,iadj), Lambda(1:NVAR,iadj), SCAL) |
---|
| 795 | |
---|
| 796 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
| 797 | ! G(:) = H*Jac^T*( B(i)*Lambda + sum_j A(j,i)*Uj(:) ) |
---|
| 798 | G(1:N) = rkB(istage)*Lambda(1:N,iadj) |
---|
| 799 | IF (istage < rkS) THEN |
---|
| 800 | DO j = istage+1, rkS |
---|
| 801 | CALL WAXPY(N,rkA(j,istage),U(1,iadj,j),1,G,1) |
---|
| 802 | END DO |
---|
| 803 | END IF |
---|
| 804 | #ifdef FULL_ALGEBRA |
---|
| 805 | TMP = MATMUL(TRANSPOSE(Jac),G) ! DZ <- Jac(Y+Z)*Y_tlm |
---|
| 806 | #else |
---|
| 807 | CALL JacTR_SP_Vec ( Jac, G, TMP ) |
---|
| 808 | #endif |
---|
| 809 | G(1:N) = H*TMP(1:N) |
---|
| 810 | |
---|
| 811 | DirADJ:IF (DirectADJ) THEN |
---|
| 812 | |
---|
| 813 | CALL SDIRK_Solve ( 'T', H, N, E_adj, IP_adj, ISING, G ) |
---|
| 814 | U(1:N,iadj,istage) = G(1:N) |
---|
| 815 | |
---|
| 816 | ELSE DirADJ |
---|
| 817 | |
---|
| 818 | !~~~> Initializations for Newton iteration |
---|
| 819 | CALL Set2zero(N,U(1,iadj,istage)) |
---|
| 820 | NewtonDone = .FALSE. |
---|
| 821 | |
---|
| 822 | NewtonLoop:DO NewtonIter = 1, NewtonMaxit |
---|
| 823 | |
---|
| 824 | !~~~> Prepare the loop-dependent part of the right-hand side |
---|
| 825 | #ifdef FULL_ALGEBRA |
---|
| 826 | TMP = MATMUL(TRANSPOSE(Jac),U(1:N,iadj,istage)) |
---|
| 827 | #else |
---|
| 828 | CALL JacTR_SP_Vec ( Jac, U(1:N,iadj,istage), TMP ) |
---|
| 829 | #endif |
---|
| 830 | DU(1:N) = U(1:N,iadj,istage) - (H*rkGamma)*TMP(1:N) - G(1:N) |
---|
| 831 | |
---|
| 832 | !~~~> Solve the linear system |
---|
| 833 | CALL SDIRK_Solve ( 'T', H, N, E, IP, ISING, DU ) |
---|
| 834 | |
---|
| 835 | !~~~> Check convergence of Newton iterations |
---|
| 836 | |
---|
| 837 | CALL SDIRK_ErrorNorm(N, DU, SCAL, NewtonIncrement) |
---|
| 838 | IF ( NewtonIter == 1 ) THEN |
---|
| 839 | Theta = ABS(ThetaMin) |
---|
| 840 | NewtonRate = 2.0d0 |
---|
| 841 | ELSE |
---|
| 842 | Theta = NewtonIncrement/NewtonIncrementOld |
---|
| 843 | IF (Theta < 0.99d0) THEN |
---|
| 844 | NewtonRate = Theta/(ONE-Theta) |
---|
| 845 | ! Predict error at the end of Newton process |
---|
| 846 | NewtonPredictedErr = NewtonIncrement & |
---|
| 847 | *Theta**(NewtonMaxit-NewtonIter)/(ONE-Theta) |
---|
| 848 | ! Non-convergence of Newton: predicted error too large |
---|
| 849 | IF (NewtonPredictedErr >= NewtonTol) EXIT NewtonLoop |
---|
| 850 | ELSE ! Non-convergence of Newton: Theta too large |
---|
| 851 | EXIT NewtonLoop |
---|
| 852 | END IF |
---|
| 853 | END IF |
---|
| 854 | NewtonIncrementOld = NewtonIncrement |
---|
| 855 | ! Update solution |
---|
| 856 | U(1:N,iadj,istage) = U(1:N,iadj,istage) - DU(1:N) |
---|
| 857 | |
---|
| 858 | ! Check error in Newton iterations |
---|
| 859 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
| 860 | ! AbsTol is often inappropriate for adjoints - |
---|
| 861 | ! we do at least 4 Newton iterations to ensure convergence |
---|
| 862 | ! of all adjoint components |
---|
| 863 | IF ((NewtonIter>=4) .AND. NewtonDone) EXIT NewtonLoop |
---|
| 864 | |
---|
| 865 | END DO NewtonLoop |
---|
| 866 | |
---|
| 867 | !~~~> If Newton iterations fail employ the direct solution |
---|
| 868 | IF (.NOT.NewtonDone) THEN |
---|
| 869 | PRINT*,'Problems with Newton Adjoint!!!' |
---|
| 870 | #ifdef FULL_ALGEBRA |
---|
| 871 | E_adj(1:N,1:N) = -Jac(1:N,1:N) |
---|
| 872 | DO j=1,N |
---|
| 873 | E_adj(j,j) = E_adj(j,j) + ONE/(H*rkGamma) |
---|
| 874 | END DO |
---|
| 875 | CALL DGETRF( N, N, E_adj, N, IP_adj, ISING ) |
---|
| 876 | #else |
---|
| 877 | E_adj(1:LU_NONZERO) = -Jac(1:LU_NONZERO) |
---|
| 878 | DO i = 1,NVAR |
---|
| 879 | j = LU_DIAG(i); E_adj(j) = E_adj(j) + ONE/(H*rkGamma) |
---|
| 880 | END DO |
---|
| 881 | CALL KppDecomp ( E_adj, ISING) |
---|
| 882 | #endif |
---|
| 883 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
| 884 | IF (ISING /= 0) THEN |
---|
| 885 | PRINT*,'At stage ',istage,' the matrix used in adjoint', & |
---|
| 886 | ' computation is singular' |
---|
| 887 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
| 888 | END IF |
---|
| 889 | CALL SDIRK_Solve ( 'T', H, N, E_adj, IP_adj, ISING, G ) |
---|
| 890 | U(1:N,iadj,istage) = G(1:N) |
---|
| 891 | |
---|
| 892 | END IF |
---|
| 893 | |
---|
| 894 | !~~~> End of simplified Newton iterations |
---|
| 895 | |
---|
| 896 | END IF DirADJ |
---|
| 897 | |
---|
| 898 | END DO adj |
---|
| 899 | |
---|
| 900 | END DO stages |
---|
| 901 | |
---|
| 902 | !~~~> Update adjoint solution |
---|
| 903 | ! Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) |
---|
| 904 | DO istage = 1,rkS |
---|
| 905 | DO iadj = 1,NADJ |
---|
| 906 | Lambda(1:N,iadj) = Lambda(1:N,iadj) + U(1:N,iadj,istage) |
---|
| 907 | !CALL WAXPY(N,ONE,U(1:N,iadj,istage),1,Lambda(1,iadj),1) |
---|
| 908 | END DO |
---|
| 909 | END DO |
---|
| 910 | |
---|
| 911 | END DO Tloop |
---|
| 912 | |
---|
| 913 | ! Successful return |
---|
| 914 | Ierr = 1 |
---|
| 915 | |
---|
| 916 | END SUBROUTINE SDIRK_DadjInt |
---|
| 917 | |
---|
| 918 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 919 | SUBROUTINE SDIRK_AllocBuffers |
---|
| 920 | !~~~> Allocate buffer space for checkpointing |
---|
| 921 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 922 | INTEGER :: i |
---|
| 923 | |
---|
| 924 | ALLOCATE( chk_H(Max_no_steps), STAT=i ) |
---|
| 925 | IF (i/=0) THEN |
---|
| 926 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
| 927 | END IF |
---|
| 928 | ALLOCATE( chk_T(Max_no_steps), STAT=i ) |
---|
| 929 | IF (i/=0) THEN |
---|
| 930 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
| 931 | END IF |
---|
| 932 | ALLOCATE( chk_Y(NVAR,Max_no_steps), STAT=i ) |
---|
| 933 | IF (i/=0) THEN |
---|
| 934 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
| 935 | END IF |
---|
| 936 | ALLOCATE( chk_Z(NVAR,rkS,Max_no_steps), STAT=i ) |
---|
| 937 | IF (i/=0) THEN |
---|
| 938 | PRINT*,'Failed allocation of buffer K'; STOP |
---|
| 939 | END IF |
---|
| 940 | IF (SaveLU) THEN |
---|
| 941 | #ifdef FULL_ALGEBRA |
---|
| 942 | ALLOCATE( chk_J(NVAR,NVAR,Max_no_steps), STAT=i ) |
---|
| 943 | #else |
---|
| 944 | ALLOCATE( chk_J(LU_NONZERO,Max_no_steps), STAT=i ) |
---|
| 945 | #endif |
---|
| 946 | IF (i/=0) THEN |
---|
| 947 | PRINT*,'Failed allocation of buffer J'; STOP |
---|
| 948 | END IF |
---|
| 949 | ALLOCATE( chk_P(NVAR,Max_no_steps), STAT=i ) |
---|
| 950 | IF (i/=0) THEN |
---|
| 951 | PRINT*,'Failed allocation of buffer P'; STOP |
---|
| 952 | END IF |
---|
| 953 | END IF |
---|
| 954 | |
---|
| 955 | END SUBROUTINE SDIRK_AllocBuffers |
---|
| 956 | |
---|
| 957 | |
---|
| 958 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 959 | SUBROUTINE SDIRK_FreeBuffers |
---|
| 960 | !~~~> Dallocate buffer space for discrete adjoint |
---|
| 961 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 962 | INTEGER :: i |
---|
| 963 | |
---|
| 964 | DEALLOCATE( chk_H, STAT=i ) |
---|
| 965 | IF (i/=0) THEN |
---|
| 966 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
| 967 | END IF |
---|
| 968 | DEALLOCATE( chk_T, STAT=i ) |
---|
| 969 | IF (i/=0) THEN |
---|
| 970 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
| 971 | END IF |
---|
| 972 | DEALLOCATE( chk_Y, STAT=i ) |
---|
| 973 | IF (i/=0) THEN |
---|
| 974 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
| 975 | END IF |
---|
| 976 | DEALLOCATE( chk_Z, STAT=i ) |
---|
| 977 | IF (i/=0) THEN |
---|
| 978 | PRINT*,'Failed deallocation of buffer K'; STOP |
---|
| 979 | END IF |
---|
| 980 | IF (SaveLU) THEN |
---|
| 981 | DEALLOCATE( chk_J, STAT=i ) |
---|
| 982 | IF (i/=0) THEN |
---|
| 983 | PRINT*,'Failed deallocation of buffer J'; STOP |
---|
| 984 | END IF |
---|
| 985 | DEALLOCATE( chk_P, STAT=i ) |
---|
| 986 | IF (i/=0) THEN |
---|
| 987 | PRINT*,'Failed deallocation of buffer P'; STOP |
---|
| 988 | END IF |
---|
| 989 | END IF |
---|
| 990 | |
---|
| 991 | END SUBROUTINE SDIRK_FreeBuffers |
---|
| 992 | |
---|
| 993 | |
---|
| 994 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 995 | SUBROUTINE SDIRK_Push( T, H, Y, Z, E, P ) |
---|
| 996 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 997 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
| 998 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 999 | |
---|
| 1000 | KPP_REAL :: T, H, Y(NVAR), Z(NVAR,Smax) |
---|
| 1001 | INTEGER :: P(NVAR) |
---|
| 1002 | #ifdef FULL_ALGEBRA |
---|
| 1003 | KPP_REAL :: E(NVAR,NVAR) |
---|
| 1004 | #else |
---|
| 1005 | KPP_REAL :: E(LU_NONZERO) |
---|
| 1006 | #endif |
---|
| 1007 | |
---|
| 1008 | stack_ptr = stack_ptr + 1 |
---|
| 1009 | IF ( stack_ptr > Max_no_steps ) THEN |
---|
| 1010 | PRINT*,'Push failed: buffer overflow' |
---|
| 1011 | STOP |
---|
| 1012 | END IF |
---|
| 1013 | chk_H( stack_ptr ) = H |
---|
| 1014 | chk_T( stack_ptr ) = T |
---|
| 1015 | chk_Y(1:NVAR,stack_ptr) = Y(1:NVAR) |
---|
| 1016 | chk_Z(1:NVAR,1:rkS,stack_ptr) = Z(1:NVAR,1:rkS) |
---|
| 1017 | IF (SaveLU) THEN |
---|
| 1018 | #ifdef FULL_ALGEBRA |
---|
| 1019 | chk_J(1:NVAR,1:NVAR,stack_ptr) = E(1:NVAR,1:NVAR) |
---|
| 1020 | chk_P(1:NVAR,stack_ptr) = P(1:NVAR) |
---|
| 1021 | #else |
---|
| 1022 | chk_J(1:LU_NONZERO,stack_ptr) = E(1:LU_NONZERO) |
---|
| 1023 | #endif |
---|
| 1024 | END IF |
---|
| 1025 | |
---|
| 1026 | END SUBROUTINE SDIRK_Push |
---|
| 1027 | |
---|
| 1028 | |
---|
| 1029 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1030 | SUBROUTINE SDIRK_Pop( T, H, Y, Z, E, P ) |
---|
| 1031 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1032 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
| 1033 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1034 | |
---|
| 1035 | KPP_REAL :: T, H, Y(NVAR), Z(NVAR,Smax) |
---|
| 1036 | INTEGER :: P(NVAR) |
---|
| 1037 | #ifdef FULL_ALGEBRA |
---|
| 1038 | KPP_REAL :: E(NVAR,NVAR) |
---|
| 1039 | #else |
---|
| 1040 | KPP_REAL :: E(LU_NONZERO) |
---|
| 1041 | #endif |
---|
| 1042 | |
---|
| 1043 | IF ( stack_ptr <= 0 ) THEN |
---|
| 1044 | PRINT*,'Pop failed: empty buffer' |
---|
| 1045 | STOP |
---|
| 1046 | END IF |
---|
| 1047 | H = chk_H( stack_ptr ) |
---|
| 1048 | T = chk_T( stack_ptr ) |
---|
| 1049 | Y(1:NVAR) = chk_Y(1:NVAR,stack_ptr) |
---|
| 1050 | Z(1:NVAR,1:rkS) = chk_Z(1:NVAR,1:rkS,stack_ptr) |
---|
| 1051 | IF (SaveLU) THEN |
---|
| 1052 | #ifdef FULL_ALGEBRA |
---|
| 1053 | E(1:NVAR,1:NVAR) = chk_J(1:NVAR,1:NVAR,stack_ptr) |
---|
| 1054 | P(1:NVAR) = chk_P(1:NVAR,stack_ptr) |
---|
| 1055 | #else |
---|
| 1056 | E(1:LU_NONZERO) = chk_J(1:LU_NONZERO,stack_ptr) |
---|
| 1057 | #endif |
---|
| 1058 | END IF |
---|
| 1059 | |
---|
| 1060 | stack_ptr = stack_ptr - 1 |
---|
| 1061 | |
---|
| 1062 | END SUBROUTINE SDIRK_Pop |
---|
| 1063 | |
---|
| 1064 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1065 | SUBROUTINE SDIRK_ErrorScale(ITOL, AbsTol, RelTol, Y, SCAL) |
---|
| 1066 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1067 | IMPLICIT NONE |
---|
| 1068 | INTEGER :: i, ITOL |
---|
| 1069 | KPP_REAL :: AbsTol(NVAR), RelTol(NVAR), & |
---|
| 1070 | Y(NVAR), SCAL(NVAR) |
---|
| 1071 | IF (ITOL == 0) THEN |
---|
| 1072 | DO i=1,NVAR |
---|
| 1073 | SCAL(i) = ONE / ( AbsTol(1)+RelTol(1)*ABS(Y(i)) ) |
---|
| 1074 | END DO |
---|
| 1075 | ELSE |
---|
| 1076 | DO i=1,NVAR |
---|
| 1077 | SCAL(i) = ONE / ( AbsTol(i)+RelTol(i)*ABS(Y(i)) ) |
---|
| 1078 | END DO |
---|
| 1079 | END IF |
---|
| 1080 | END SUBROUTINE SDIRK_ErrorScale |
---|
| 1081 | |
---|
| 1082 | |
---|
| 1083 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1084 | SUBROUTINE SDIRK_ErrorNorm(N, Y, SCAL, Err) |
---|
| 1085 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1086 | ! |
---|
| 1087 | INTEGER :: i, N |
---|
| 1088 | KPP_REAL :: Y(N), SCAL(N), Err |
---|
| 1089 | Err = ZERO |
---|
| 1090 | DO i=1,N |
---|
| 1091 | Err = Err+(Y(i)*SCAL(i))**2 |
---|
| 1092 | END DO |
---|
| 1093 | Err = MAX( SQRT(Err/DBLE(N)), 1.0d-10 ) |
---|
| 1094 | ! |
---|
| 1095 | END SUBROUTINE SDIRK_ErrorNorm |
---|
| 1096 | |
---|
| 1097 | |
---|
| 1098 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1099 | SUBROUTINE SDIRK_ErrorMsg(Code,T,H,Ierr) |
---|
| 1100 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1101 | ! Handles all error messages |
---|
| 1102 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1103 | KPP_REAL, INTENT(IN) :: T, H |
---|
| 1104 | INTEGER, INTENT(IN) :: Code |
---|
| 1105 | INTEGER, INTENT(OUT) :: Ierr |
---|
| 1106 | |
---|
| 1107 | Ierr = Code |
---|
| 1108 | PRINT * , & |
---|
| 1109 | 'Forced exit from SDIRK due to the following error:' |
---|
| 1110 | |
---|
| 1111 | SELECT CASE (Code) |
---|
| 1112 | CASE (-1) |
---|
| 1113 | PRINT * , '--> Improper value for maximal no of steps' |
---|
| 1114 | CASE (-2) |
---|
| 1115 | PRINT * , '--> Improper value for maximal no of Newton iterations' |
---|
| 1116 | CASE (-3) |
---|
| 1117 | PRINT * , '--> Hmin/Hmax/Hstart must be positive' |
---|
| 1118 | CASE (-4) |
---|
| 1119 | PRINT * , '--> FacMin/FacMax/FacRej must be positive' |
---|
| 1120 | CASE (-5) |
---|
| 1121 | PRINT * , '--> Improper tolerance values' |
---|
| 1122 | CASE (-6) |
---|
| 1123 | PRINT * , '--> No of steps exceeds maximum bound', max_no_steps |
---|
| 1124 | CASE (-7) |
---|
| 1125 | PRINT * , '--> Step size too small: T + 10*H = T', & |
---|
| 1126 | ' or H < Roundoff' |
---|
| 1127 | CASE (-8) |
---|
| 1128 | PRINT * , '--> Matrix is repeatedly singular' |
---|
| 1129 | CASE DEFAULT |
---|
| 1130 | PRINT *, 'Unknown Error code: ', Code |
---|
| 1131 | END SELECT |
---|
| 1132 | |
---|
| 1133 | PRINT *, "T=", T, "and H=", H |
---|
| 1134 | |
---|
| 1135 | END SUBROUTINE SDIRK_ErrorMsg |
---|
| 1136 | |
---|
| 1137 | |
---|
| 1138 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1139 | SUBROUTINE SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
| 1140 | SkipJac, SkipLU, E, IP, Reject, ISING ) |
---|
| 1141 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1142 | !~~~> Compute the matrix E = 1/(H*GAMMA)*Jac, and its decomposition |
---|
| 1143 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1144 | |
---|
| 1145 | IMPLICIT NONE |
---|
| 1146 | |
---|
| 1147 | KPP_REAL, INTENT(INOUT) :: H |
---|
| 1148 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
---|
| 1149 | LOGICAL, INTENT(INOUT) :: SkipJac,SkipLU,Reject |
---|
| 1150 | INTEGER, INTENT(OUT) :: ISING, IP(NVAR) |
---|
| 1151 | #ifdef FULL_ALGEBRA |
---|
| 1152 | KPP_REAL, INTENT(INOUT) :: FJAC(NVAR,NVAR) |
---|
| 1153 | KPP_REAL, INTENT(OUT) :: E(NVAR,NVAR) |
---|
| 1154 | #else |
---|
| 1155 | KPP_REAL, INTENT(INOUT) :: FJAC(LU_NONZERO) |
---|
| 1156 | KPP_REAL, INTENT(OUT) :: E(LU_NONZERO) |
---|
| 1157 | #endif |
---|
| 1158 | KPP_REAL :: HGammaInv |
---|
| 1159 | INTEGER :: i, j, ConsecutiveSng |
---|
| 1160 | |
---|
| 1161 | ConsecutiveSng = 0 |
---|
| 1162 | ISING = 1 |
---|
| 1163 | |
---|
| 1164 | Hloop: DO WHILE (ISING /= 0) |
---|
| 1165 | |
---|
| 1166 | HGammaInv = ONE/(H*rkGamma) |
---|
| 1167 | |
---|
| 1168 | !~~~> Compute the Jacobian |
---|
| 1169 | ! IF (SkipJac) THEN |
---|
| 1170 | ! SkipJac = .FALSE. |
---|
| 1171 | ! ELSE |
---|
| 1172 | IF (.NOT. SkipJac) THEN |
---|
| 1173 | CALL JAC_CHEM( T, Y, FJAC ) |
---|
| 1174 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1175 | END IF |
---|
| 1176 | |
---|
| 1177 | #ifdef FULL_ALGEBRA |
---|
| 1178 | DO j=1,NVAR |
---|
| 1179 | DO i=1,NVAR |
---|
| 1180 | E(i,j) = -FJAC(i,j) |
---|
| 1181 | END DO |
---|
| 1182 | E(j,j) = E(j,j)+HGammaInv |
---|
| 1183 | END DO |
---|
| 1184 | CALL DGETRF( NVAR, NVAR, E, NVAR, IP, ISING ) |
---|
| 1185 | #else |
---|
| 1186 | DO i = 1,LU_NONZERO |
---|
| 1187 | E(i) = -FJAC(i) |
---|
| 1188 | END DO |
---|
| 1189 | DO i = 1,NVAR |
---|
| 1190 | j = LU_DIAG(i); E(j) = E(j) + HGammaInv |
---|
| 1191 | END DO |
---|
| 1192 | CALL KppDecomp ( E, ISING) |
---|
| 1193 | IP(1) = 1 |
---|
| 1194 | #endif |
---|
| 1195 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
| 1196 | |
---|
| 1197 | IF (ISING /= 0) THEN |
---|
| 1198 | WRITE (6,*) ' MATRIX IS SINGULAR, ISING=',ISING,' T=',T,' H=',H |
---|
| 1199 | ISTATUS(Nsng) = ISTATUS(Nsng) + 1; ConsecutiveSng = ConsecutiveSng + 1 |
---|
| 1200 | IF (ConsecutiveSng >= 6) RETURN ! Failure |
---|
| 1201 | H = 0.5d0*H |
---|
| 1202 | SkipJac = .FALSE. |
---|
| 1203 | SkipLU = .FALSE. |
---|
| 1204 | Reject = .TRUE. |
---|
| 1205 | END IF |
---|
| 1206 | |
---|
| 1207 | END DO Hloop |
---|
| 1208 | |
---|
| 1209 | END SUBROUTINE SDIRK_PrepareMatrix |
---|
| 1210 | |
---|
| 1211 | |
---|
| 1212 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1213 | SUBROUTINE SDIRK_Solve ( Transp, H, N, E, IP, ISING, RHS ) |
---|
| 1214 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1215 | !~~~> Solves the system (H*Gamma-Jac)*x = R |
---|
| 1216 | ! using the LU decomposition of E = I - 1/(H*Gamma)*Jac |
---|
| 1217 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1218 | IMPLICIT NONE |
---|
| 1219 | INTEGER, INTENT(IN) :: N, IP(N), ISING |
---|
| 1220 | CHARACTER, INTENT(IN) :: Transp |
---|
| 1221 | KPP_REAL, INTENT(IN) :: H |
---|
| 1222 | #ifdef FULL_ALGEBRA |
---|
| 1223 | KPP_REAL, INTENT(IN) :: E(NVAR,NVAR) |
---|
| 1224 | #else |
---|
| 1225 | KPP_REAL, INTENT(IN) :: E(LU_NONZERO) |
---|
| 1226 | #endif |
---|
| 1227 | KPP_REAL, INTENT(INOUT) :: RHS(N) |
---|
| 1228 | KPP_REAL :: HGammaInv |
---|
| 1229 | |
---|
| 1230 | HGammaInv = ONE/(H*rkGamma) |
---|
| 1231 | CALL WSCAL(N,HGammaInv,RHS,1) |
---|
| 1232 | SELECT CASE (TRANSP) |
---|
| 1233 | CASE ('N') |
---|
| 1234 | #ifdef FULL_ALGEBRA |
---|
| 1235 | CALL DGETRS( 'N', N, 1, E, N, IP, RHS, N, ISING ) |
---|
| 1236 | #else |
---|
| 1237 | CALL KppSolve(E, RHS) |
---|
| 1238 | #endif |
---|
| 1239 | CASE ('T') |
---|
| 1240 | #ifdef FULL_ALGEBRA |
---|
| 1241 | CALL DGETRS( 'T', N, 1, E, N, IP, RHS, N, ISING ) |
---|
| 1242 | #else |
---|
| 1243 | CALL KppSolveTR(E, RHS, RHS) |
---|
| 1244 | #endif |
---|
| 1245 | CASE DEFAULT |
---|
| 1246 | PRINT*,'Error in SDIRK_Solve. Unknown Transp argument:',Transp |
---|
| 1247 | STOP |
---|
| 1248 | END SELECT |
---|
| 1249 | ISTATUS(Nsol) = ISTATUS(Nsol) + 1 |
---|
| 1250 | |
---|
| 1251 | END SUBROUTINE SDIRK_Solve |
---|
| 1252 | |
---|
| 1253 | |
---|
| 1254 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1255 | SUBROUTINE Sdirk4a |
---|
| 1256 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1257 | sdMethod = S4A |
---|
| 1258 | ! Number of stages |
---|
| 1259 | rkS = 5 |
---|
| 1260 | |
---|
| 1261 | ! Method coefficients |
---|
| 1262 | rkGamma = .2666666666666666666666666666666667d0 |
---|
| 1263 | |
---|
| 1264 | rkA(1,1) = .2666666666666666666666666666666667d0 |
---|
| 1265 | rkA(2,1) = .5000000000000000000000000000000000d0 |
---|
| 1266 | rkA(2,2) = .2666666666666666666666666666666667d0 |
---|
| 1267 | rkA(3,1) = .3541539528432732316227461858529820d0 |
---|
| 1268 | rkA(3,2) = -.5415395284327323162274618585298197d-1 |
---|
| 1269 | rkA(3,3) = .2666666666666666666666666666666667d0 |
---|
| 1270 | rkA(4,1) = .8515494131138652076337791881433756d-1 |
---|
| 1271 | rkA(4,2) = -.6484332287891555171683963466229754d-1 |
---|
| 1272 | rkA(4,3) = .7915325296404206392428857585141242d-1 |
---|
| 1273 | rkA(4,4) = .2666666666666666666666666666666667d0 |
---|
| 1274 | rkA(5,1) = 2.100115700566932777970612055999074d0 |
---|
| 1275 | rkA(5,2) = -.7677800284445976813343102185062276d0 |
---|
| 1276 | rkA(5,3) = 2.399816361080026398094746205273880d0 |
---|
| 1277 | rkA(5,4) = -2.998818699869028161397714709433394d0 |
---|
| 1278 | rkA(5,5) = .2666666666666666666666666666666667d0 |
---|
| 1279 | |
---|
| 1280 | rkB(1) = 2.100115700566932777970612055999074d0 |
---|
| 1281 | rkB(2) = -.7677800284445976813343102185062276d0 |
---|
| 1282 | rkB(3) = 2.399816361080026398094746205273880d0 |
---|
| 1283 | rkB(4) = -2.998818699869028161397714709433394d0 |
---|
| 1284 | rkB(5) = .2666666666666666666666666666666667d0 |
---|
| 1285 | |
---|
| 1286 | rkBhat(1)= 2.885264204387193942183851612883390d0 |
---|
| 1287 | rkBhat(2)= -.1458793482962771337341223443218041d0 |
---|
| 1288 | rkBhat(3)= 2.390008682465139866479830743628554d0 |
---|
| 1289 | rkBhat(4)= -4.129393538556056674929560012190140d0 |
---|
| 1290 | rkBhat(5)= 0.d0 |
---|
| 1291 | |
---|
| 1292 | rkC(1) = .2666666666666666666666666666666667d0 |
---|
| 1293 | rkC(2) = .7666666666666666666666666666666667d0 |
---|
| 1294 | rkC(3) = .5666666666666666666666666666666667d0 |
---|
| 1295 | rkC(4) = .3661315380631796996374935266701191d0 |
---|
| 1296 | rkC(5) = 1.d0 |
---|
| 1297 | |
---|
| 1298 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1299 | rkD(1) = 0.d0 |
---|
| 1300 | rkD(2) = 0.d0 |
---|
| 1301 | rkD(3) = 0.d0 |
---|
| 1302 | rkD(4) = 0.d0 |
---|
| 1303 | rkD(5) = 1.d0 |
---|
| 1304 | |
---|
| 1305 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1306 | rkE(1) = -.6804000050475287124787034884002302d0 |
---|
| 1307 | rkE(2) = 1.558961944525217193393931795738823d0 |
---|
| 1308 | rkE(3) = -13.55893003128907927748632408763868d0 |
---|
| 1309 | rkE(4) = 15.48522576958521253098585004571302d0 |
---|
| 1310 | rkE(5) = 1.d0 |
---|
| 1311 | |
---|
| 1312 | ! Local order of Err estimate |
---|
| 1313 | rkElo = 4 |
---|
| 1314 | |
---|
| 1315 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1316 | rkTheta(2,1) = 1.875000000000000000000000000000000d0 |
---|
| 1317 | rkTheta(3,1) = 1.708847304091539528432732316227462d0 |
---|
| 1318 | rkTheta(3,2) = -.2030773231622746185852981969486824d0 |
---|
| 1319 | rkTheta(4,1) = .2680325578937783958847157206823118d0 |
---|
| 1320 | rkTheta(4,2) = -.1828840955527181631794050728644549d0 |
---|
| 1321 | rkTheta(4,3) = .2968246986151577397160821594427966d0 |
---|
| 1322 | rkTheta(5,1) = .9096171815241460655379433581446771d0 |
---|
| 1323 | rkTheta(5,2) = -3.108254967778352416114774430509465d0 |
---|
| 1324 | rkTheta(5,3) = 12.33727431701306195581826123274001d0 |
---|
| 1325 | rkTheta(5,4) = -11.24557012450885560524143016037523d0 |
---|
| 1326 | |
---|
| 1327 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1328 | rkAlpha(2,1) = 2.875000000000000000000000000000000d0 |
---|
| 1329 | rkAlpha(3,1) = .8500000000000000000000000000000000d0 |
---|
| 1330 | rkAlpha(3,2) = .4434782608695652173913043478260870d0 |
---|
| 1331 | rkAlpha(4,1) = .7352046091658870564637910527807370d0 |
---|
| 1332 | rkAlpha(4,2) = -.9525565003057343527941920657462074d-1 |
---|
| 1333 | rkAlpha(4,3) = .4290111305453813852259481840631738d0 |
---|
| 1334 | rkAlpha(5,1) = -16.10898993405067684831655675112808d0 |
---|
| 1335 | rkAlpha(5,2) = 6.559571569643355712998131800797873d0 |
---|
| 1336 | rkAlpha(5,3) = -15.90772144271326504260996815012482d0 |
---|
| 1337 | rkAlpha(5,4) = 25.34908987169226073668861694892683d0 |
---|
| 1338 | |
---|
| 1339 | !~~~> Coefficients for continuous solution |
---|
| 1340 | ! rkD(1,1)= 24.74416644927758d0 |
---|
| 1341 | ! rkD(1,2)= -4.325375951824688d0 |
---|
| 1342 | ! rkD(1,3)= 41.39683763286316d0 |
---|
| 1343 | ! rkD(1,4)= -61.04144619901784d0 |
---|
| 1344 | ! rkD(1,5)= -3.391332232917013d0 |
---|
| 1345 | ! rkD(2,1)= -51.98245719616925d0 |
---|
| 1346 | ! rkD(2,2)= 10.52501981094525d0 |
---|
| 1347 | ! rkD(2,3)= -154.2067922191855d0 |
---|
| 1348 | ! rkD(2,4)= 214.3082125319825d0 |
---|
| 1349 | ! rkD(2,5)= 14.71166018088679d0 |
---|
| 1350 | ! rkD(3,1)= 33.14347947522142d0 |
---|
| 1351 | ! rkD(3,2)= -19.72986789558523d0 |
---|
| 1352 | ! rkD(3,3)= 230.4878502285804d0 |
---|
| 1353 | ! rkD(3,4)= -287.6629744338197d0 |
---|
| 1354 | ! rkD(3,5)= -18.99932366302254d0 |
---|
| 1355 | ! rkD(4,1)= -5.905188728329743d0 |
---|
| 1356 | ! rkD(4,2)= 13.53022403646467d0 |
---|
| 1357 | ! rkD(4,3)= -117.6778956422581d0 |
---|
| 1358 | ! rkD(4,4)= 134.3962081008550d0 |
---|
| 1359 | ! rkD(4,5)= 8.678995715052762d0 |
---|
| 1360 | ! |
---|
| 1361 | ! DO i=1,4 ! CONTi <-- Sum_j rkD(i,j)*Zj |
---|
| 1362 | ! CALL Set2zero(N,CONT(1,i)) |
---|
| 1363 | ! DO j = 1,rkS |
---|
| 1364 | ! CALL WAXPY(N,rkD(i,j),Z(1,j),1,CONT(1,i),1) |
---|
| 1365 | ! END DO |
---|
| 1366 | ! END DO |
---|
| 1367 | |
---|
| 1368 | rkELO = 4.0d0 |
---|
| 1369 | |
---|
| 1370 | END SUBROUTINE Sdirk4a |
---|
| 1371 | |
---|
| 1372 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1373 | SUBROUTINE Sdirk4b |
---|
| 1374 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1375 | sdMethod = S4B |
---|
| 1376 | ! Number of stages |
---|
| 1377 | rkS = 5 |
---|
| 1378 | |
---|
| 1379 | ! Method coefficients |
---|
| 1380 | rkGamma = .25d0 |
---|
| 1381 | |
---|
| 1382 | rkA(1,1) = 0.25d0 |
---|
| 1383 | rkA(2,1) = 0.5d00 |
---|
| 1384 | rkA(2,2) = 0.25d0 |
---|
| 1385 | rkA(3,1) = 0.34d0 |
---|
| 1386 | rkA(3,2) =-0.40d-1 |
---|
| 1387 | rkA(3,3) = 0.25d0 |
---|
| 1388 | rkA(4,1) = 0.2727941176470588235294117647058824d0 |
---|
| 1389 | rkA(4,2) =-0.5036764705882352941176470588235294d-1 |
---|
| 1390 | rkA(4,3) = 0.2757352941176470588235294117647059d-1 |
---|
| 1391 | rkA(4,4) = 0.25d0 |
---|
| 1392 | rkA(5,1) = 1.041666666666666666666666666666667d0 |
---|
| 1393 | rkA(5,2) =-1.020833333333333333333333333333333d0 |
---|
| 1394 | rkA(5,3) = 7.812500000000000000000000000000000d0 |
---|
| 1395 | rkA(5,4) =-7.083333333333333333333333333333333d0 |
---|
| 1396 | rkA(5,5) = 0.25d0 |
---|
| 1397 | |
---|
| 1398 | rkB(1) = 1.041666666666666666666666666666667d0 |
---|
| 1399 | rkB(2) = -1.020833333333333333333333333333333d0 |
---|
| 1400 | rkB(3) = 7.812500000000000000000000000000000d0 |
---|
| 1401 | rkB(4) = -7.083333333333333333333333333333333d0 |
---|
| 1402 | rkB(5) = 0.250000000000000000000000000000000d0 |
---|
| 1403 | |
---|
| 1404 | rkBhat(1)= 1.069791666666666666666666666666667d0 |
---|
| 1405 | rkBhat(2)= -0.894270833333333333333333333333333d0 |
---|
| 1406 | rkBhat(3)= 7.695312500000000000000000000000000d0 |
---|
| 1407 | rkBhat(4)= -7.083333333333333333333333333333333d0 |
---|
| 1408 | rkBhat(5)= 0.212500000000000000000000000000000d0 |
---|
| 1409 | |
---|
| 1410 | rkC(1) = 0.25d0 |
---|
| 1411 | rkC(2) = 0.75d0 |
---|
| 1412 | rkC(3) = 0.55d0 |
---|
| 1413 | rkC(4) = 0.50d0 |
---|
| 1414 | rkC(5) = 1.00d0 |
---|
| 1415 | |
---|
| 1416 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1417 | rkD(1) = 0.0d0 |
---|
| 1418 | rkD(2) = 0.0d0 |
---|
| 1419 | rkD(3) = 0.0d0 |
---|
| 1420 | rkD(4) = 0.0d0 |
---|
| 1421 | rkD(5) = 1.0d0 |
---|
| 1422 | |
---|
| 1423 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1424 | rkE(1) = 0.5750d0 |
---|
| 1425 | rkE(2) = 0.2125d0 |
---|
| 1426 | rkE(3) = -4.6875d0 |
---|
| 1427 | rkE(4) = 4.2500d0 |
---|
| 1428 | rkE(5) = 0.1500d0 |
---|
| 1429 | |
---|
| 1430 | ! Local order of Err estimate |
---|
| 1431 | rkElo = 4 |
---|
| 1432 | |
---|
| 1433 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1434 | rkTheta(2,1) = 2.d0 |
---|
| 1435 | rkTheta(3,1) = 1.680000000000000000000000000000000d0 |
---|
| 1436 | rkTheta(3,2) = -.1600000000000000000000000000000000d0 |
---|
| 1437 | rkTheta(4,1) = 1.308823529411764705882352941176471d0 |
---|
| 1438 | rkTheta(4,2) = -.1838235294117647058823529411764706d0 |
---|
| 1439 | rkTheta(4,3) = 0.1102941176470588235294117647058824d0 |
---|
| 1440 | rkTheta(5,1) = -3.083333333333333333333333333333333d0 |
---|
| 1441 | rkTheta(5,2) = -4.291666666666666666666666666666667d0 |
---|
| 1442 | rkTheta(5,3) = 34.37500000000000000000000000000000d0 |
---|
| 1443 | rkTheta(5,4) = -28.33333333333333333333333333333333d0 |
---|
| 1444 | |
---|
| 1445 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1446 | rkAlpha(2,1) = 3. |
---|
| 1447 | rkAlpha(3,1) = .8800000000000000000000000000000000d0 |
---|
| 1448 | rkAlpha(3,2) = .4400000000000000000000000000000000d0 |
---|
| 1449 | rkAlpha(4,1) = .1666666666666666666666666666666667d0 |
---|
| 1450 | rkAlpha(4,2) = -.8333333333333333333333333333333333d-1 |
---|
| 1451 | rkAlpha(4,3) = .9469696969696969696969696969696970d0 |
---|
| 1452 | rkAlpha(5,1) = -6.d0 |
---|
| 1453 | rkAlpha(5,2) = 9.d0 |
---|
| 1454 | rkAlpha(5,3) = -56.81818181818181818181818181818182d0 |
---|
| 1455 | rkAlpha(5,4) = 54.d0 |
---|
| 1456 | |
---|
| 1457 | END SUBROUTINE Sdirk4b |
---|
| 1458 | |
---|
| 1459 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1460 | SUBROUTINE Sdirk2a |
---|
| 1461 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1462 | sdMethod = S2A |
---|
| 1463 | ! Number of stages |
---|
| 1464 | rkS = 2 |
---|
| 1465 | |
---|
| 1466 | ! Method coefficients |
---|
| 1467 | rkGamma = .2928932188134524755991556378951510d0 |
---|
| 1468 | |
---|
| 1469 | rkA(1,1) = .2928932188134524755991556378951510d0 |
---|
| 1470 | rkA(2,1) = .7071067811865475244008443621048490d0 |
---|
| 1471 | rkA(2,2) = .2928932188134524755991556378951510d0 |
---|
| 1472 | |
---|
| 1473 | rkB(1) = .7071067811865475244008443621048490d0 |
---|
| 1474 | rkB(2) = .2928932188134524755991556378951510d0 |
---|
| 1475 | |
---|
| 1476 | rkBhat(1)= .6666666666666666666666666666666667d0 |
---|
| 1477 | rkBhat(2)= .3333333333333333333333333333333333d0 |
---|
| 1478 | |
---|
| 1479 | rkC(1) = 0.292893218813452475599155637895151d0 |
---|
| 1480 | rkC(2) = 1.0d0 |
---|
| 1481 | |
---|
| 1482 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1483 | rkD(1) = 0.0d0 |
---|
| 1484 | rkD(2) = 1.0d0 |
---|
| 1485 | |
---|
| 1486 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1487 | rkE(1) = 0.4714045207910316829338962414032326d0 |
---|
| 1488 | rkE(2) = -0.1380711874576983496005629080698993d0 |
---|
| 1489 | |
---|
| 1490 | ! Local order of Err estimate |
---|
| 1491 | rkElo = 2 |
---|
| 1492 | |
---|
| 1493 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1494 | rkTheta(2,1) = 2.414213562373095048801688724209698d0 |
---|
| 1495 | |
---|
| 1496 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1497 | rkAlpha(2,1) = 3.414213562373095048801688724209698d0 |
---|
| 1498 | |
---|
| 1499 | END SUBROUTINE Sdirk2a |
---|
| 1500 | |
---|
| 1501 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1502 | SUBROUTINE Sdirk2b |
---|
| 1503 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1504 | sdMethod = S2B |
---|
| 1505 | ! Number of stages |
---|
| 1506 | rkS = 2 |
---|
| 1507 | |
---|
| 1508 | ! Method coefficients |
---|
| 1509 | rkGamma = 1.707106781186547524400844362104849d0 |
---|
| 1510 | |
---|
| 1511 | rkA(1,1) = 1.707106781186547524400844362104849d0 |
---|
| 1512 | rkA(2,1) = -.707106781186547524400844362104849d0 |
---|
| 1513 | rkA(2,2) = 1.707106781186547524400844362104849d0 |
---|
| 1514 | |
---|
| 1515 | rkB(1) = -.707106781186547524400844362104849d0 |
---|
| 1516 | rkB(2) = 1.707106781186547524400844362104849d0 |
---|
| 1517 | |
---|
| 1518 | rkBhat(1)= .6666666666666666666666666666666667d0 |
---|
| 1519 | rkBhat(2)= .3333333333333333333333333333333333d0 |
---|
| 1520 | |
---|
| 1521 | rkC(1) = 1.707106781186547524400844362104849d0 |
---|
| 1522 | rkC(2) = 1.0d0 |
---|
| 1523 | |
---|
| 1524 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1525 | rkD(1) = 0.0d0 |
---|
| 1526 | rkD(2) = 1.0d0 |
---|
| 1527 | |
---|
| 1528 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1529 | rkE(1) = -.4714045207910316829338962414032326d0 |
---|
| 1530 | rkE(2) = .8047378541243650162672295747365659d0 |
---|
| 1531 | |
---|
| 1532 | ! Local order of Err estimate |
---|
| 1533 | rkElo = 2 |
---|
| 1534 | |
---|
| 1535 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1536 | rkTheta(2,1) = -.414213562373095048801688724209698d0 |
---|
| 1537 | |
---|
| 1538 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1539 | rkAlpha(2,1) = .5857864376269049511983112757903019d0 |
---|
| 1540 | |
---|
| 1541 | END SUBROUTINE Sdirk2b |
---|
| 1542 | |
---|
| 1543 | |
---|
| 1544 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1545 | SUBROUTINE Sdirk3a |
---|
| 1546 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1547 | sdMethod = S3A |
---|
| 1548 | ! Number of stages |
---|
| 1549 | rkS = 3 |
---|
| 1550 | |
---|
| 1551 | ! Method coefficients |
---|
| 1552 | rkGamma = .2113248654051871177454256097490213d0 |
---|
| 1553 | |
---|
| 1554 | rkA(1,1) = .2113248654051871177454256097490213d0 |
---|
| 1555 | rkA(2,1) = .2113248654051871177454256097490213d0 |
---|
| 1556 | rkA(2,2) = .2113248654051871177454256097490213d0 |
---|
| 1557 | rkA(3,1) = .2113248654051871177454256097490213d0 |
---|
| 1558 | rkA(3,2) = .5773502691896257645091487805019573d0 |
---|
| 1559 | rkA(3,3) = .2113248654051871177454256097490213d0 |
---|
| 1560 | |
---|
| 1561 | rkB(1) = .2113248654051871177454256097490213d0 |
---|
| 1562 | rkB(2) = .5773502691896257645091487805019573d0 |
---|
| 1563 | rkB(3) = .2113248654051871177454256097490213d0 |
---|
| 1564 | |
---|
| 1565 | rkBhat(1)= .2113248654051871177454256097490213d0 |
---|
| 1566 | rkBhat(2)= .6477918909913548037576239837516312d0 |
---|
| 1567 | rkBhat(3)= .1408832436034580784969504064993475d0 |
---|
| 1568 | |
---|
| 1569 | rkC(1) = .2113248654051871177454256097490213d0 |
---|
| 1570 | rkC(2) = .4226497308103742354908512194980427d0 |
---|
| 1571 | rkC(3) = 1.d0 |
---|
| 1572 | |
---|
| 1573 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
| 1574 | rkD(1) = 0.d0 |
---|
| 1575 | rkD(2) = 0.d0 |
---|
| 1576 | rkD(3) = 1.d0 |
---|
| 1577 | |
---|
| 1578 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
| 1579 | rkE(1) = 0.9106836025229590978424821138352906d0 |
---|
| 1580 | rkE(2) = -1.244016935856292431175815447168624d0 |
---|
| 1581 | rkE(3) = 0.3333333333333333333333333333333333d0 |
---|
| 1582 | |
---|
| 1583 | ! Local order of Err estimate |
---|
| 1584 | rkElo = 2 |
---|
| 1585 | |
---|
| 1586 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
| 1587 | rkTheta(2,1) = 1.0d0 |
---|
| 1588 | rkTheta(3,1) = -1.732050807568877293527446341505872d0 |
---|
| 1589 | rkTheta(3,2) = 2.732050807568877293527446341505872d0 |
---|
| 1590 | |
---|
| 1591 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
| 1592 | rkAlpha(2,1) = 2.0d0 |
---|
| 1593 | rkAlpha(3,1) = -12.92820323027550917410978536602349d0 |
---|
| 1594 | rkAlpha(3,2) = 8.83012701892219323381861585376468d0 |
---|
| 1595 | |
---|
| 1596 | END SUBROUTINE Sdirk3a |
---|
| 1597 | |
---|
| 1598 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1599 | END SUBROUTINE SDIRKADJ ! AND ALL ITS INTERNAL PROCEDURES |
---|
| 1600 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1601 | |
---|
| 1602 | |
---|
| 1603 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1604 | SUBROUTINE FUN_CHEM( T, Y, P ) |
---|
| 1605 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1606 | |
---|
| 1607 | USE KPP_ROOT_Parameters, ONLY: NVAR |
---|
| 1608 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
| 1609 | USE KPP_ROOT_Function, ONLY: Fun |
---|
| 1610 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
| 1611 | |
---|
| 1612 | KPP_REAL :: T, Told |
---|
| 1613 | KPP_REAL :: Y(NVAR), P(NVAR) |
---|
| 1614 | |
---|
| 1615 | Told = TIME |
---|
| 1616 | TIME = T |
---|
| 1617 | CALL Update_SUN() |
---|
| 1618 | CALL Update_RCONST() |
---|
| 1619 | |
---|
| 1620 | CALL Fun( Y, FIX, RCONST, P ) |
---|
| 1621 | |
---|
| 1622 | TIME = Told |
---|
| 1623 | |
---|
| 1624 | END SUBROUTINE FUN_CHEM |
---|
| 1625 | |
---|
| 1626 | |
---|
| 1627 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1628 | SUBROUTINE JAC_CHEM( T, Y, JV ) |
---|
| 1629 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1630 | |
---|
| 1631 | USE KPP_ROOT_Parameters, ONLY: NVAR, LU_NONZERO |
---|
| 1632 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
| 1633 | USE KPP_ROOT_Jacobian, ONLY: Jac_SP,LU_IROW,LU_ICOL |
---|
| 1634 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
| 1635 | |
---|
| 1636 | KPP_REAL :: T, Told |
---|
| 1637 | KPP_REAL :: Y(NVAR) |
---|
| 1638 | #ifdef FULL_ALGEBRA |
---|
| 1639 | KPP_REAL :: JS(LU_NONZERO), JV(NVAR,NVAR) |
---|
| 1640 | INTEGER :: i, j |
---|
| 1641 | #else |
---|
| 1642 | KPP_REAL :: JV(LU_NONZERO) |
---|
| 1643 | #endif |
---|
| 1644 | |
---|
| 1645 | Told = TIME |
---|
| 1646 | TIME = T |
---|
| 1647 | CALL Update_SUN() |
---|
| 1648 | CALL Update_RCONST() |
---|
| 1649 | |
---|
| 1650 | #ifdef FULL_ALGEBRA |
---|
| 1651 | CALL Jac_SP(Y, FIX, RCONST, JS) |
---|
| 1652 | DO j=1,NVAR |
---|
| 1653 | DO j=1,NVAR |
---|
| 1654 | JV(i,j) = 0.0d0 |
---|
| 1655 | END DO |
---|
| 1656 | END DO |
---|
| 1657 | DO i=1,LU_NONZERO |
---|
| 1658 | JV(LU_IROW(i),LU_ICOL(i)) = JS(i) |
---|
| 1659 | END DO |
---|
| 1660 | #else |
---|
| 1661 | CALL Jac_SP(Y, FIX, RCONST, JV) |
---|
| 1662 | #endif |
---|
| 1663 | TIME = Told |
---|
| 1664 | |
---|
| 1665 | END SUBROUTINE JAC_CHEM |
---|
| 1666 | |
---|
| 1667 | END MODULE KPP_ROOT_Integrator |
---|
| 1668 | |
---|
| 1669 | |
---|