1 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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2 | ! Second Order Adjoint of SDIRK - Singly-Diagonally-Implicit Runge-Kutta ! |
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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 2007 ! |
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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 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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13 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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14 | |
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15 | MODULE KPP_ROOT_Integrator |
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16 | |
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17 | USE KPP_ROOT_Precision |
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18 | USE KPP_ROOT_Global, ONLY: FIX, RCONST, TIME |
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19 | USE KPP_ROOT_Parameters, ONLY: NVAR, NSPEC, NFIX, LU_NONZERO, NHESS |
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20 | USE KPP_ROOT_JacobianSP, ONLY: LU_DIAG |
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21 | USE KPP_ROOT_Jacobian, ONLY: Jac_SP_Vec, JacTR_SP_Vec |
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22 | USE KPP_ROOT_LinearAlgebra, ONLY: KppDecomp, KppSolve, & |
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23 | KppSolveTR, Set2zero, WLAMCH, WCOPY, WAXPY, WSCAL, WADD |
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24 | USE KPP_ROOT_Hessian |
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25 | USE KPP_ROOT_Util |
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26 | |
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27 | IMPLICIT NONE |
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28 | PUBLIC |
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29 | SAVE |
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30 | |
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31 | !~~~> Statistics on the work performed by the SDIRK method |
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32 | INTEGER, PARAMETER :: Nfun=1, Njac=2, Nstp=3, Nacc=4, & |
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33 | Nrej=5, Ndec=6, Nsol=7, Nsng=8, & |
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34 | Ntexit=1, Nhexit=2, Nhnew=3 |
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35 | |
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36 | CONTAINS |
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37 | |
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38 | SUBROUTINE INTEGRATE_SOA( NSOA, Y, Y_tlm, Lambda, Sigma, & |
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39 | TIN, TOUT, ATOL_adj, RTOL_adj, & |
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40 | ICNTRL_U, RCNTRL_U, ISTATUS_U, RSTATUS_U, Ierr_U ) |
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41 | |
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42 | USE KPP_ROOT_Parameters |
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43 | USE KPP_ROOT_Global |
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44 | IMPLICIT NONE |
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45 | |
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46 | !~~~> Y - Concentrations |
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47 | KPP_REAL :: Y(NVAR) |
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48 | !~~~> NSOA - No. of vectors U_j for which |
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49 | ! Hessian*U_j is computed |
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50 | INTEGER :: NSOA |
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51 | !~~~> Y_tlm - Forward sensitivities |
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52 | ! Initially Y_tlm(1:NVAR,j) = U_j |
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53 | KPP_REAL :: Y_tlm(NVAR,NSOA) |
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54 | !~~~> ADJ - No. of cost functionals (always 1) |
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55 | INTEGER, PARAMETER :: NADJ = 1 |
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56 | !~~~> Lambda - Sensitivities w.r.t. concentrations |
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57 | ! Note: Lambda (1:NVAR,j) contains sensitivities of |
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58 | ! the j-th cost functional w.r.t. Y(1:NVAR), j=1...NADJ |
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59 | KPP_REAL :: Lambda(NVAR,NADJ) |
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60 | !~~~> Sigma - Second order adjoint sensitivities |
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61 | ! Note: Sigma(1:NVAR,j) = Hessian*U_j |
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62 | KPP_REAL :: Sigma(NVAR,NSOA) |
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63 | !~~~> Tolerances for adjoint calculations |
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64 | ! (used for full continuous adjoint, and for controlling |
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65 | ! iterations when used to solve the discrete adjoint) |
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66 | KPP_REAL, INTENT(IN) :: ATOL_adj(NVAR,NADJ), RTOL_adj(NVAR,NADJ) |
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67 | KPP_REAL, INTENT(IN) :: TIN ! Start Time |
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68 | KPP_REAL, INTENT(IN) :: TOUT ! End Time |
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69 | ! Optional input parameters and statistics |
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70 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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71 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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72 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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73 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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74 | INTEGER, INTENT(OUT), OPTIONAL :: Ierr_U |
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75 | |
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76 | INTEGER, SAVE :: Ntotal = 0 |
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77 | KPP_REAL :: RCNTRL(20), RSTATUS(20), T1, T2 |
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78 | INTEGER :: ICNTRL(20), ISTATUS(20), Ierr |
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79 | |
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80 | ICNTRL(:) = 0 |
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81 | RCNTRL(:) = 0.0_dp |
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82 | ISTATUS(:) = 0 |
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83 | RSTATUS(:) = 0.0_dp |
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84 | |
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85 | !~~~> fine-tune the integrator: |
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86 | ICNTRL(5) = 8 ! Max no. of Newton iterations |
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87 | ICNTRL(7) = 1 ! Adjoint solution by: 0=Newton, 1=direct |
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88 | ICNTRL(8) = 1 ! Save fwd LU factorization: 0 = do *not* save, 1 = save |
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89 | |
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90 | ! If optional parameters are given, and if they are >0, |
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91 | ! then they overwrite default settings. |
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92 | IF (PRESENT(ICNTRL_U)) THEN |
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93 | WHERE(ICNTRL_U(:) > 0) ICNTRL(:) = ICNTRL_U(:) |
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94 | END IF |
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95 | IF (PRESENT(RCNTRL_U)) THEN |
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96 | WHERE(RCNTRL_U(:) > 0) RCNTRL(:) = RCNTRL_U(:) |
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97 | END IF |
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98 | |
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99 | |
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100 | T1 = TIN; T2 = TOUT |
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101 | CALL SDIRK_SOA(NVAR, NSOA, T1, T2, Y, Y_tlm, Lambda, Sigma, & |
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102 | RTOL, ATOL, ATOL_adj, RTOL_adj, & |
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103 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, Ierr ) |
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104 | |
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105 | !~~~> Debug option: number of steps |
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106 | ! Ntotal = Ntotal + ISTATUS(Nstp) |
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107 | ! WRITE(6,777) ISTATUS(Nstp),Ntotal,VAR(ind_O3),VAR(ind_NO2) |
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108 | ! 777 FORMAT('NSTEPS=',I5,' (',I5,') O3=',E24.14,' NO2=',E24.14) |
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109 | |
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110 | IF (Ierr < 0) THEN |
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111 | PRINT *,'SDIRK: Unsuccessful exit at T=',TIN,' (Ierr=',Ierr,')' |
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112 | ENDIF |
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113 | |
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114 | ! if optional parameters are given for output they to return information |
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115 | IF (PRESENT(ISTATUS_U)) ISTATUS_U(:) = ISTATUS(:) |
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116 | IF (PRESENT(RSTATUS_U)) RSTATUS_U(:) = RSTATUS(:) |
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117 | IF (PRESENT(Ierr_U)) Ierr_U = Ierr |
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118 | |
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119 | END SUBROUTINE INTEGRATE_SOA |
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120 | |
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121 | |
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122 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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123 | SUBROUTINE SDIRK_SOA(N, NSOA, Tinitial, Tfinal, & |
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124 | Y, Y_tlm, Lambda, Sigma, & |
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125 | RelTol, AbsTol, RelTol_adj, AbsTol_adj, & |
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126 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, Ierr) |
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127 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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128 | |
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129 | |
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130 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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131 | ! |
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132 | ! Solves the system y'=F(t,y) using a Singly-Diagonally-Implicit |
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133 | ! Runge-Kutta (SDIRK) method. |
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134 | ! |
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135 | ! This implementation is based on the book and the code Sdirk4: |
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136 | ! |
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137 | ! E. Hairer and G. Wanner |
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138 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
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139 | ! Springer series in computational mathematics, Springer-Verlag, 1996. |
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140 | ! This code is based on the SDIRK4 routine in the above book. |
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141 | ! |
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142 | ! Methods: |
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143 | ! * Sdirk 2a, 2b: L-stable, 2 stages, order 2 |
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144 | ! * Sdirk 3a: L-stable, 3 stages, order 2, adjoint-invariant |
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145 | ! * Sdirk 4a, 4b: L-stable, 5 stages, order 4 |
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146 | ! |
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147 | ! (C) Adrian Sandu, July 2005 |
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148 | ! Virginia Polytechnic Institute and State University |
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149 | ! Contact: sandu@cs.vt.edu |
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150 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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151 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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152 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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153 | ! |
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154 | !~~~> INPUT ARGUMENTS: |
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155 | ! |
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156 | !- Y(NVAR) = vector of initial conditions (at T=Tinitial) |
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157 | !- [Tinitial,Tfinal] = time range of integration |
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158 | ! (if Tinitial>Tfinal the integration is performed backwards in time) |
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159 | !- RelTol, AbsTol = user precribed accuracy |
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160 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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161 | ! returns Ydot = Y' = F(T,Y) |
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162 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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163 | ! returns Jcb = dF/dY |
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164 | !- ICNTRL(1:20) = integer inputs parameters |
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165 | !- RCNTRL(1:20) = real inputs parameters |
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166 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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167 | ! |
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168 | !~~~> OUTPUT ARGUMENTS: |
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169 | ! |
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170 | !- Y(NVAR) -> vector of final states (at T->Tfinal) |
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171 | !- ISTATUS(1:20) -> integer output parameters |
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172 | !- RSTATUS(1:20) -> real output parameters |
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173 | !- Ierr -> job status upon return |
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174 | ! success (positive value) or |
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175 | ! failure (negative value) |
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176 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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177 | ! |
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178 | !~~~> INPUT PARAMETERS: |
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179 | ! |
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180 | ! Note: For input parameters equal to zero the default values of the |
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181 | ! corresponding variables are used. |
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182 | ! |
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183 | ! Note: For input parameters equal to zero the default values of the |
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184 | ! corresponding variables are used. |
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185 | !~~~> |
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186 | ! ICNTRL(1) = not used |
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187 | ! |
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188 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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189 | ! = 1: AbsTol, RelTol are scalars |
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190 | ! |
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191 | ! ICNTRL(3) = Method |
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192 | ! |
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193 | ! ICNTRL(4) -> maximum number of integration steps |
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194 | ! For ICNTRL(4)=0 the default value of 100000 is used |
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195 | ! |
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196 | ! ICNTRL(5) -> maximum number of Newton iterations |
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197 | ! For ICNTRL(5)=0 the default value of 8 is used |
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198 | ! |
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199 | ! ICNTRL(6) -> starting values of Newton iterations: |
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200 | ! ICNTRL(6)=0 : starting values are interpolated (the default) |
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201 | ! ICNTRL(6)=1 : starting values are zero |
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202 | ! |
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203 | ! ICNTRL(7) -> method to solve TLM equations: |
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204 | ! ICNTRL(7)=0 : modified Newton re-using LU (the default) |
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205 | ! ICNTRL(7)=1 : direct solution (additional one LU factorization per stage) |
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206 | ! |
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207 | ! ICNTRL(9) -> switch for TLM Newton iteration error estimation strategy |
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208 | ! ICNTRL(9) = 0: base number of iterations as forward solution |
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209 | ! ICNTRL(9) = 1: use RTOL_tlm and ATOL_tlm to calculate |
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210 | ! error estimation for TLM at Newton stages |
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211 | ! |
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212 | ! ICNTRL(12) -> switch for TLM truncation error control |
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213 | ! ICNTRL(12) = 0: TLM error is not used |
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214 | ! ICNTRL(12) = 1: TLM error is computed and used |
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215 | ! |
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216 | ! |
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217 | !~~~> Real parameters |
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218 | ! |
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219 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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220 | ! It is strongly recommended to keep Hmin = ZERO |
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221 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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222 | ! RCNTRL(3) -> Hstart, starting value for the integration step size |
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223 | ! |
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224 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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225 | ! RCNTRL(5) -> FacMax, upper bound on step increase factor (default=6) |
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226 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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227 | ! (default=0.1) |
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228 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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229 | ! than the predicted value (default=0.9) |
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230 | ! RCNTRL(8) -> ThetaMin. If Newton convergence rate smaller |
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231 | ! than ThetaMin the Jacobian is not recomputed; |
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232 | ! (default=0.001) |
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233 | ! RCNTRL(9) -> NewtonTol, stopping criterion for Newton's method |
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234 | ! (default=0.03) |
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235 | ! RCNTRL(10) -> Qmin |
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236 | ! RCNTRL(11) -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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237 | ! step size is kept constant and the LU factorization |
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238 | ! reused (default Qmin=1, Qmax=1.2) |
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239 | ! |
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240 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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241 | ! |
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242 | !~~~> OUTPUT PARAMETERS: |
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243 | ! |
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244 | ! Note: each call to Rosenbrock adds the current no. of fcn calls |
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245 | ! to previous value of ISTATUS(1), and similar for the other params. |
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246 | ! Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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247 | ! |
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248 | ! ISTATUS(1) = No. of function calls |
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249 | ! ISTATUS(2) = No. of jacobian calls |
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250 | ! ISTATUS(3) = No. of steps |
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251 | ! ISTATUS(4) = No. of accepted steps |
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252 | ! ISTATUS(5) = No. of rejected steps (except at the beginning) |
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253 | ! ISTATUS(6) = No. of LU decompositions |
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254 | ! ISTATUS(7) = No. of forward/backward substitutions |
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255 | ! ISTATUS(8) = No. of singular matrix decompositions |
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256 | ! |
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257 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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258 | ! computed Y upon return |
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259 | ! RSTATUS(2) -> Hexit,last accepted step before return |
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260 | ! RSTATUS(3) -> Hnew, last predicted step before return |
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261 | ! For multiple restarts, use Hnew as Hstart in the following run |
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262 | ! |
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263 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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264 | IMPLICIT NONE |
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265 | |
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266 | |
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267 | ! Arguments |
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268 | INTEGER, PARAMETER :: NADJ = 1 |
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269 | INTEGER, INTENT(IN) :: N, NSOA |
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270 | KPP_REAL, INTENT(INOUT) :: Y(NVAR), Y_tlm(NVAR,NSOA) |
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271 | KPP_REAL, INTENT(INOUT) :: Lambda(NVAR,NADJ) |
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272 | KPP_REAL, INTENT(INOUT) :: Sigma(NVAR,NSOA) |
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273 | INTEGER, INTENT(IN) :: ICNTRL(20) |
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274 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal, & |
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275 | RelTol(N), AbsTol(N), RCNTRL(20), & |
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276 | RelTol_adj(N,NSOA), AbsTol_adj(N,NSOA) |
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277 | INTEGER, INTENT(OUT) :: Ierr |
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278 | INTEGER, INTENT(INOUT) :: ISTATUS(20) |
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279 | KPP_REAL, INTENT(OUT) :: RSTATUS(20) |
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280 | |
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281 | !~~~> SDIRK method coefficients, up to 5 stages |
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282 | INTEGER, PARAMETER :: Smax = 5 |
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283 | INTEGER, PARAMETER :: S2A=1, S2B=2, S3A=3, S4A=4, S4B=5 |
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284 | KPP_REAL :: rkGamma, rkA(Smax,Smax), rkB(Smax), rkC(Smax), & |
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285 | rkD(Smax), rkE(Smax), rkBhat(Smax), rkELO, & |
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286 | rkAlpha(Smax,Smax), rkTheta(Smax,Smax) |
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287 | INTEGER :: sdMethod, rkS ! The number of stages |
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288 | |
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289 | !~~~> Checkpoints in memory buffers |
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290 | INTEGER :: stack_ptr = 0 ! last written entry in checkpoint |
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291 | KPP_REAL, DIMENSION(:), POINTER :: chk_H, chk_T |
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292 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_Y |
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293 | KPP_REAL, DIMENSION(:,:,:), POINTER :: chk_Z |
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294 | KPP_REAL, DIMENSION(:,:,:), POINTER :: chk_Y_tlm |
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295 | KPP_REAL, DIMENSION(:,:,:,:), POINTER :: chk_Z_tlm |
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296 | INTEGER, DIMENSION(:,:), POINTER :: chk_P |
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297 | #ifdef FULL_ALGEBRA |
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298 | KPP_REAL, DIMENSION(:,:,:), POINTER :: chk_J |
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299 | #else |
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300 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_J |
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301 | #endif |
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302 | |
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303 | !~~~> Local variables |
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304 | KPP_REAL :: Hmin, Hmax, Hstart, Roundoff, & |
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305 | FacMin, Facmax, FacSafe, FacRej, & |
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306 | ThetaMin, NewtonTol, Qmin, Qmax |
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307 | LOGICAL :: SaveLU, DirectADJ |
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308 | INTEGER :: ITOL, NewtonMaxit, Max_no_steps, i |
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309 | LOGICAL :: StartNewton, DirectTLM, TLMNewtonEst, TLMtruncErr |
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310 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
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311 | |
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312 | |
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313 | Ierr = 0 |
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314 | ISTATUS(1:20) = 0 |
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315 | RSTATUS(1:20) = ZERO |
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316 | |
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317 | !~~~> For Scalar tolerances (ICNTRL(2).NE.0) the code uses AbsTol(1) and RelTol(1) |
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318 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:NVAR) and RelTol(1:NVAR) |
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319 | IF (ICNTRL(2) == 0) THEN |
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320 | ITOL = 1 |
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321 | ELSE |
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322 | ITOL = 0 |
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323 | END IF |
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324 | |
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325 | !~~~> ICNTRL(3) - method selection |
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326 | SELECT CASE (ICNTRL(3)) |
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327 | CASE (0,1) |
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328 | CALL Sdirk2a |
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329 | CASE (2) |
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330 | CALL Sdirk2b |
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331 | CASE (3) |
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332 | CALL Sdirk3a |
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333 | CASE (4) |
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334 | CALL Sdirk4a |
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335 | CASE (5) |
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336 | CALL Sdirk4b |
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337 | CASE DEFAULT |
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338 | CALL Sdirk2a |
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339 | END SELECT |
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340 | |
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341 | !~~~> The maximum number of time steps admitted |
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342 | IF (ICNTRL(4) == 0) THEN |
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343 | Max_no_steps = 200000 |
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344 | ELSEIF (ICNTRL(4) > 0) THEN |
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345 | Max_no_steps=ICNTRL(4) |
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346 | ELSE |
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347 | PRINT * ,'User-selected ICNTRL(4)=',ICNTRL(4) |
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348 | CALL SDIRK_ErrorMsg(-1,Tinitial,ZERO,Ierr) |
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349 | END IF |
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350 | !~~~> The maximum number of Newton iterations admitted |
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351 | IF(ICNTRL(5) == 0)THEN |
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352 | NewtonMaxit=8 |
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353 | ELSE |
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354 | NewtonMaxit=ICNTRL(5) |
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355 | IF(NewtonMaxit <= 0)THEN |
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356 | PRINT * ,'User-selected ICNTRL(5)=',ICNTRL(5) |
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357 | CALL SDIRK_ErrorMsg(-2,Tinitial,ZERO,Ierr) |
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358 | END IF |
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359 | END IF |
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360 | !~~~> StartNewton: Use extrapolation for starting values of Newton iterations |
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361 | IF (ICNTRL(6) == 0) THEN |
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362 | StartNewton = .TRUE. |
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363 | ELSE |
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364 | StartNewton = .FALSE. |
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365 | END IF |
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366 | |
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367 | !~~~> Solve ADJ equations directly or by Newton iterations |
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368 | DirectADJ = (ICNTRL(7) == 1) |
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369 | |
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370 | !~~~> Save or not the forward LU factorization |
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371 | SaveLU = (ICNTRL(8) /= 0) .AND. (.NOT.DirectADJ) |
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372 | |
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373 | !~~~> Newton iteration error control selection |
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374 | IF (ICNTRL(9) == 0) THEN |
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375 | TLMNewtonEst = .FALSE. |
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376 | ELSE |
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377 | TLMNewtonEst = .TRUE. |
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378 | END IF |
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379 | !~~~> TLM truncation error control selection |
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380 | IF (ICNTRL(12) == 0) THEN |
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381 | TLMtruncErr = .FALSE. |
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382 | ELSE |
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383 | TLMtruncErr = .TRUE. |
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384 | END IF |
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385 | |
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386 | !~~~> Unit roundoff (1+Roundoff>1) |
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387 | Roundoff = WLAMCH('E') |
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388 | |
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389 | !~~~> Lower bound on the step size: (positive value) |
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390 | IF (RCNTRL(1) == ZERO) THEN |
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391 | Hmin = ZERO |
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392 | ELSEIF (RCNTRL(1) > ZERO) THEN |
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393 | Hmin = RCNTRL(1) |
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394 | ELSE |
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395 | PRINT * , 'User-selected RCNTRL(1)=', RCNTRL(1) |
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396 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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397 | END IF |
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398 | |
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399 | !~~~> Upper bound on the step size: (positive value) |
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400 | IF (RCNTRL(2) == ZERO) THEN |
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401 | Hmax = ABS(Tfinal-Tinitial) |
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402 | ELSEIF (RCNTRL(2) > ZERO) THEN |
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403 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tfinal-Tinitial)) |
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404 | ELSE |
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405 | PRINT * , 'User-selected RCNTRL(2)=', RCNTRL(2) |
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406 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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407 | END IF |
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408 | |
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409 | !~~~> Starting step size: (positive value) |
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410 | IF (RCNTRL(3) == ZERO) THEN |
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411 | Hstart = MAX(Hmin,Roundoff) |
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412 | ELSEIF (RCNTRL(3) > ZERO) THEN |
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413 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tfinal-Tinitial)) |
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414 | ELSE |
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415 | PRINT * , 'User-selected Hstart: RCNTRL(3)=', RCNTRL(3) |
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416 | CALL SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr) |
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417 | END IF |
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418 | |
---|
419 | !~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax |
---|
420 | IF (RCNTRL(4) == ZERO) THEN |
---|
421 | FacMin = 0.2_dp |
---|
422 | ELSEIF (RCNTRL(4) > ZERO) THEN |
---|
423 | FacMin = RCNTRL(4) |
---|
424 | ELSE |
---|
425 | PRINT * , 'User-selected FacMin: RCNTRL(4)=', RCNTRL(4) |
---|
426 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
427 | END IF |
---|
428 | IF (RCNTRL(5) == ZERO) THEN |
---|
429 | FacMax = 10.0_dp |
---|
430 | ELSEIF (RCNTRL(5) > ZERO) THEN |
---|
431 | FacMax = RCNTRL(5) |
---|
432 | ELSE |
---|
433 | PRINT * , 'User-selected FacMax: RCNTRL(5)=', RCNTRL(5) |
---|
434 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
435 | END IF |
---|
436 | !~~~> FacRej: Factor to decrease step after 2 succesive rejections |
---|
437 | IF (RCNTRL(6) == ZERO) THEN |
---|
438 | FacRej = 0.1_dp |
---|
439 | ELSEIF (RCNTRL(6) > ZERO) THEN |
---|
440 | FacRej = RCNTRL(6) |
---|
441 | ELSE |
---|
442 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
---|
443 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
444 | END IF |
---|
445 | !~~~> FacSafe: Safety Factor in the computation of new step size |
---|
446 | IF (RCNTRL(7) == ZERO) THEN |
---|
447 | FacSafe = 0.9_dp |
---|
448 | ELSEIF (RCNTRL(7) > ZERO) THEN |
---|
449 | FacSafe = RCNTRL(7) |
---|
450 | ELSE |
---|
451 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
---|
452 | CALL SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr) |
---|
453 | END IF |
---|
454 | |
---|
455 | !~~~> ThetaMin: decides whether the Jacobian should be recomputed |
---|
456 | IF(RCNTRL(8) == 0.D0)THEN |
---|
457 | ThetaMin = 1.0d-3 |
---|
458 | ELSE |
---|
459 | ThetaMin = RCNTRL(8) |
---|
460 | END IF |
---|
461 | |
---|
462 | !~~~> Stopping criterion for Newton's method |
---|
463 | IF(RCNTRL(9) == ZERO)THEN |
---|
464 | NewtonTol = 3.0d-2 |
---|
465 | ELSE |
---|
466 | NewtonTol = RCNTRL(9) |
---|
467 | END IF |
---|
468 | |
---|
469 | !~~~> Qmin, Qmax: IF Qmin < Hnew/Hold < Qmax, STEP SIZE = CONST. |
---|
470 | IF(RCNTRL(10) == ZERO)THEN |
---|
471 | Qmin=ONE |
---|
472 | ELSE |
---|
473 | Qmin=RCNTRL(10) |
---|
474 | END IF |
---|
475 | IF(RCNTRL(11) == ZERO)THEN |
---|
476 | Qmax=1.2D0 |
---|
477 | ELSE |
---|
478 | Qmax=RCNTRL(11) |
---|
479 | END IF |
---|
480 | |
---|
481 | !~~~> Check if tolerances are reasonable |
---|
482 | IF (ITOL == 0) THEN |
---|
483 | IF (AbsTol(1) <= ZERO .OR. RelTol(1) <= 10.D0*Roundoff) THEN |
---|
484 | PRINT * , ' Scalar AbsTol = ',AbsTol(1) |
---|
485 | PRINT * , ' Scalar RelTol = ',RelTol(1) |
---|
486 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr) |
---|
487 | END IF |
---|
488 | ELSE |
---|
489 | DO i=1,N |
---|
490 | IF (AbsTol(i) <= 0.D0.OR.RelTol(i) <= 10.D0*Roundoff) THEN |
---|
491 | PRINT * , ' AbsTol(',i,') = ',AbsTol(i) |
---|
492 | PRINT * , ' RelTol(',i,') = ',RelTol(i) |
---|
493 | CALL SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr) |
---|
494 | END IF |
---|
495 | END DO |
---|
496 | END IF |
---|
497 | |
---|
498 | IF (Ierr < 0) RETURN |
---|
499 | |
---|
500 | !~~~> Allocate memory buffers |
---|
501 | CALL SDIRK_AllocBuffers |
---|
502 | |
---|
503 | !~~~> Call forward integration |
---|
504 | CALL SDIRK_FwdTlmInt( N, NSOA, Tinitial, Tfinal, Y, Y_tlm, Ierr ) |
---|
505 | |
---|
506 | !~~~> Call adjoint integration |
---|
507 | CALL SDIRK_SoaInt( N, NSOA, Lambda, Sigma, Ierr ) |
---|
508 | |
---|
509 | !~~~> Free memory buffers |
---|
510 | CALL SDIRK_FreeBuffers |
---|
511 | |
---|
512 | |
---|
513 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
514 | CONTAINS ! Procedures internal to SDIRK_SOA |
---|
515 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
516 | |
---|
517 | |
---|
518 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
519 | SUBROUTINE SDIRK_FwdTlmInt( N,NTLM,Tinitial,Tfinal,Y,Y_tlm,Ierr ) |
---|
520 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
521 | |
---|
522 | USE KPP_ROOT_Parameters |
---|
523 | IMPLICIT NONE |
---|
524 | |
---|
525 | !~~~> Arguments: |
---|
526 | INTEGER, INTENT(IN) :: N, NTLM |
---|
527 | KPP_REAL, INTENT(INOUT) :: Y(N), Y_tlm(N,NTLM) |
---|
528 | KPP_REAL, INTENT(IN) :: Tinitial, Tfinal |
---|
529 | INTEGER, INTENT(OUT) :: Ierr |
---|
530 | |
---|
531 | !~~~> Local variables: |
---|
532 | KPP_REAL :: Z(NVAR,rkS), G(NVAR), TMP(NVAR), & |
---|
533 | NewtonRate, SCAL(NVAR), DZ(NVAR), & |
---|
534 | T, H, Theta, Hratio, NewtonPredictedErr, & |
---|
535 | Qnewton, Err, Fac, Hnew, Tdirection, & |
---|
536 | NewtonIncrement, NewtonIncrementOld, & |
---|
537 | SCAL_tlm(NVAR), Yerr(N), Yerr_tlm(N,NTLM), ThetaTLM |
---|
538 | KPP_REAL :: Z_tlm(NVAR,rkS,NTLM) |
---|
539 | INTEGER :: itlm, j, IER, istage, NewtonIter, saveNiter, NewtonIterTLM |
---|
540 | INTEGER :: IP(NVAR), IP_tlm(NVAR) |
---|
541 | LOGICAL :: Reject, FirstStep, SkipJac, SkipLU, NewtonDone |
---|
542 | |
---|
543 | #ifdef FULL_ALGEBRA |
---|
544 | KPP_REAL, DIMENSION(NVAR,NVAR) :: FJAC, E, Jac, E_tlm |
---|
545 | #else |
---|
546 | KPP_REAL, DIMENSION(LU_NONZERO) :: FJAC, E, Jac, E_tlm |
---|
547 | #endif |
---|
548 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
549 | |
---|
550 | |
---|
551 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
552 | !~~~> Initializations |
---|
553 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
554 | |
---|
555 | T = Tinitial |
---|
556 | Tdirection = SIGN(ONE,Tfinal-Tinitial) |
---|
557 | H = MAX(ABS(Hmin),ABS(Hstart)) |
---|
558 | IF (ABS(H) <= 10.D0*Roundoff) H=1.0D-6 |
---|
559 | H=MIN(ABS(H),Hmax) |
---|
560 | H=SIGN(H,Tdirection) |
---|
561 | SkipLU = .FALSE. |
---|
562 | SkipJac = .FALSE. |
---|
563 | Reject = .FALSE. |
---|
564 | FirstStep=.TRUE. |
---|
565 | |
---|
566 | CALL SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL) |
---|
567 | |
---|
568 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
569 | !~~~> Time loop begins |
---|
570 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
571 | Tloop: DO WHILE ( (Tfinal-T)*Tdirection - Roundoff > ZERO ) |
---|
572 | |
---|
573 | |
---|
574 | !~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition |
---|
575 | IF ( .NOT.SkipLU ) THEN ! This time around skip the Jac update and LU |
---|
576 | CALL SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
577 | SkipJac, SkipLU, E, IP, Reject, IER ) |
---|
578 | IF (IER /= 0) THEN |
---|
579 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
580 | END IF |
---|
581 | END IF |
---|
582 | |
---|
583 | IF (ISTATUS(Nstp) > Max_no_steps) THEN |
---|
584 | CALL SDIRK_ErrorMsg(-6,T,H,Ierr); RETURN |
---|
585 | END IF |
---|
586 | IF ( (T+0.1d0*H == T) .OR. (ABS(H) <= Roundoff) ) THEN |
---|
587 | CALL SDIRK_ErrorMsg(-7,T,H,Ierr); RETURN |
---|
588 | END IF |
---|
589 | |
---|
590 | stages:DO istage = 1, rkS |
---|
591 | |
---|
592 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
593 | !~~~> Simplified Newton iterations |
---|
594 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
595 | |
---|
596 | !~~~> Starting values for Newton iterations |
---|
597 | CALL Set2zero(N,Z(1,istage)) |
---|
598 | |
---|
599 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
600 | CALL Set2zero(N,G) |
---|
601 | IF (istage > 1) THEN |
---|
602 | DO j = 1, istage-1 |
---|
603 | ! Gj(:) = sum_j Theta(i,j)*Zj(:) = H * sum_j A(i,j)*Fun(Zj(:)) |
---|
604 | CALL WAXPY(N,rkTheta(istage,j),Z(1,j),1,G,1) |
---|
605 | ! Zi(:) = sum_j Alpha(i,j)*Zj(:) |
---|
606 | IF (StartNewton) THEN |
---|
607 | CALL WAXPY(N,rkAlpha(istage,j),Z(1,j),1,Z(1,istage),1) |
---|
608 | END IF |
---|
609 | END DO |
---|
610 | END IF |
---|
611 | |
---|
612 | !~~~> Initializations for Newton iteration |
---|
613 | NewtonDone = .FALSE. |
---|
614 | Fac = 0.5d0 ! Step reduction factor if too many iterations |
---|
615 | |
---|
616 | NewtonLoop:DO NewtonIter = 1, NewtonMaxit |
---|
617 | |
---|
618 | !~~~> Prepare the loop-dependent part of the right-hand side |
---|
619 | CALL WADD(N,Y,Z(1,istage),TMP) ! TMP <- Y + Zi |
---|
620 | CALL FUN_CHEM(T+rkC(istage)*H,TMP,DZ) ! DZ <- Fun(Y+Zi) |
---|
621 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
622 | ! DZ(1:N) = G(1:N) - Z(1:N,istage) + (H*rkGamma)*DZ(1:N) |
---|
623 | CALL WSCAL(N, H*rkGamma, DZ, 1) |
---|
624 | CALL WAXPY (N, -ONE, Z(1,istage), 1, DZ, 1) |
---|
625 | CALL WAXPY (N, ONE, G,1, DZ,1) |
---|
626 | |
---|
627 | !~~~> Solve the linear system |
---|
628 | CALL SDIRK_Solve ( 'N', H, N, E, IP, IER, DZ ) |
---|
629 | |
---|
630 | !~~~> Check convergence of Newton iterations |
---|
631 | CALL SDIRK_ErrorNorm(N, DZ, SCAL, NewtonIncrement) |
---|
632 | IF ( NewtonIter == 1 ) THEN |
---|
633 | Theta = ABS(ThetaMin) |
---|
634 | NewtonRate = 2.0d0 |
---|
635 | ELSE |
---|
636 | Theta = NewtonIncrement/NewtonIncrementOld |
---|
637 | IF (Theta < 0.99d0) THEN |
---|
638 | NewtonRate = Theta/(ONE-Theta) |
---|
639 | ! Predict error at the end of Newton process |
---|
640 | NewtonPredictedErr = NewtonIncrement & |
---|
641 | *Theta**(NewtonMaxit-NewtonIter)/(ONE-Theta) |
---|
642 | IF (NewtonPredictedErr >= NewtonTol) THEN |
---|
643 | ! Non-convergence of Newton: predicted error too large |
---|
644 | Qnewton = MIN(10.0d0,NewtonPredictedErr/NewtonTol) |
---|
645 | Fac = 0.8d0*Qnewton**(-ONE/(1+NewtonMaxit-NewtonIter)) |
---|
646 | EXIT NewtonLoop |
---|
647 | END IF |
---|
648 | ELSE ! Non-convergence of Newton: Theta too large |
---|
649 | EXIT NewtonLoop |
---|
650 | END IF |
---|
651 | END IF |
---|
652 | NewtonIncrementOld = NewtonIncrement |
---|
653 | ! Update solution: Z(:) <-- Z(:)+DZ(:) |
---|
654 | CALL WAXPY(N,ONE,DZ,1,Z(1,istage),1) |
---|
655 | |
---|
656 | ! Check error in Newton iterations |
---|
657 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
658 | IF (NewtonDone) THEN |
---|
659 | ! Tune error in TLM variables by defining the minimal number of Newton iterations. |
---|
660 | saveNiter = NewtonIter+1 |
---|
661 | EXIT NewtonLoop |
---|
662 | END IF |
---|
663 | |
---|
664 | END DO NewtonLoop |
---|
665 | |
---|
666 | IF (.NOT.NewtonDone) THEN |
---|
667 | !CALL RK_ErrorMsg(-12,T,H,Ierr); |
---|
668 | H = Fac*H; Reject=.TRUE. |
---|
669 | SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
670 | CYCLE Tloop |
---|
671 | END IF |
---|
672 | |
---|
673 | !~~~> End of simplified Newton iterations for forward variables |
---|
674 | |
---|
675 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
676 | !~~~> Solve for TLM variables |
---|
677 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
678 | |
---|
679 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
680 | SkipJac = .FALSE. |
---|
681 | CALL SDIRK_PrepareMatrix ( H, T+rkC(istage)*H, TMP, Jac, & |
---|
682 | SkipJac, SkipLU, E_tlm, IP_tlm, Reject, IER ) |
---|
683 | IF (IER /= 0) CYCLE TLoop |
---|
684 | |
---|
685 | TlmL: DO itlm = 1, NTLM |
---|
686 | G(1:N) = Y_tlm(1:N,itlm) |
---|
687 | IF (istage > 1) THEN |
---|
688 | ! Gj(:) = sum_j Theta(i,j)*Zj_tlm(:) |
---|
689 | ! = H * sum_j A(i,j)*Jac(Zj(:))*(Yj_tlm+Zj_tlm) |
---|
690 | DO j = 1, istage-1 |
---|
691 | CALL WAXPY(N,rkTheta(istage,j),Z_tlm(1,j,itlm),1,G,1) |
---|
692 | END DO |
---|
693 | END IF |
---|
694 | CALL SDIRK_Solve ( 'N', H, N, E_tlm, IP_tlm, IER, G ) |
---|
695 | Z_tlm(1:N,istage,itlm) = G(1:N) - Y_tlm(1:N,itlm) |
---|
696 | END DO TlmL |
---|
697 | |
---|
698 | |
---|
699 | END DO stages |
---|
700 | |
---|
701 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
702 | !~~~> Error estimation |
---|
703 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
704 | ISTATUS(Nstp) = ISTATUS(Nstp) + 1 |
---|
705 | CALL Set2zero(N,Yerr) |
---|
706 | DO i = 1,rkS |
---|
707 | IF (rkE(i)/=ZERO) CALL WAXPY(N,rkE(i),Z(1,i),1,Yerr,1) |
---|
708 | END DO |
---|
709 | |
---|
710 | CALL SDIRK_Solve ( 'N', H, N, E, IP, IER, Yerr ) |
---|
711 | CALL SDIRK_ErrorNorm(N, Yerr, SCAL, Err) |
---|
712 | |
---|
713 | !~~~> Computation of new step size Hnew |
---|
714 | Fac = FacSafe*(Err)**(-ONE/rkELO) |
---|
715 | Fac = MAX(FacMin,MIN(FacMax,Fac)) |
---|
716 | Hnew = H*Fac |
---|
717 | |
---|
718 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
719 | !~~~> Accept/Reject step |
---|
720 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
721 | accept: IF ( Err < ONE ) THEN !~~~> Step is accepted |
---|
722 | |
---|
723 | FirstStep=.FALSE. |
---|
724 | ISTATUS(Nacc) = ISTATUS(Nacc) + 1 |
---|
725 | |
---|
726 | !~~~> Checkpoint (old) solution |
---|
727 | CALL SDIRK_Push( T, H, Y, Z, Y_tlm, Z_tlm, E, IP ) |
---|
728 | |
---|
729 | !~~~> Update time and solution |
---|
730 | T = T + H |
---|
731 | ! Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) |
---|
732 | DO i = 1,rkS |
---|
733 | IF (rkD(i)/=ZERO) THEN |
---|
734 | CALL WAXPY(N,rkD(i),Z(1,i),1,Y,1) |
---|
735 | DO itlm = 1, NTLM |
---|
736 | CALL WAXPY(N,rkD(i),Z_tlm(1,i,itlm),1,Y_tlm(1,itlm),1) |
---|
737 | END DO |
---|
738 | END IF |
---|
739 | END DO |
---|
740 | |
---|
741 | !~~~> Update scaling coefficients |
---|
742 | CALL SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL) |
---|
743 | |
---|
744 | !~~~> Next time step |
---|
745 | Hnew = Tdirection*MIN(ABS(Hnew),Hmax) |
---|
746 | ! Last T and H |
---|
747 | RSTATUS(Ntexit) = T |
---|
748 | RSTATUS(Nhexit) = H |
---|
749 | RSTATUS(Nhnew) = Hnew |
---|
750 | ! No step increase after a rejection |
---|
751 | IF (Reject) Hnew = Tdirection*MIN(ABS(Hnew),ABS(H)) |
---|
752 | Reject = .FALSE. |
---|
753 | IF ((T+Hnew/Qmin-Tfinal)*Tdirection > ZERO) THEN |
---|
754 | H = Tfinal-T |
---|
755 | ELSE |
---|
756 | Hratio=Hnew/H |
---|
757 | ! If step not changed too much keep Jacobian and reuse LU |
---|
758 | SkipLU = ( (Theta <= ThetaMin) .AND. (Hratio >= Qmin) & |
---|
759 | .AND. (Hratio <= Qmax) ) |
---|
760 | ! For TLM: do not skip LU (decrease TLM error) |
---|
761 | SkipLU = .FALSE. |
---|
762 | IF (.NOT.SkipLU) H = Hnew |
---|
763 | END IF |
---|
764 | ! If convergence is fast enough, do not update Jacobian |
---|
765 | ! SkipJac = (Theta <= ThetaMin) |
---|
766 | SkipJac = .FALSE. |
---|
767 | |
---|
768 | ELSE accept !~~~> Step is rejected |
---|
769 | |
---|
770 | IF (FirstStep .OR. Reject) THEN |
---|
771 | H = FacRej*H |
---|
772 | ELSE |
---|
773 | H = Hnew |
---|
774 | END IF |
---|
775 | Reject = .TRUE. |
---|
776 | SkipJac = .TRUE. |
---|
777 | SkipLU = .FALSE. |
---|
778 | IF (ISTATUS(Nacc) >= 1) ISTATUS(Nrej) = ISTATUS(Nrej) + 1 |
---|
779 | |
---|
780 | END IF accept |
---|
781 | |
---|
782 | END DO Tloop |
---|
783 | |
---|
784 | ! Successful return |
---|
785 | Ierr = 1 |
---|
786 | |
---|
787 | END SUBROUTINE SDIRK_FwdTlmInt |
---|
788 | |
---|
789 | |
---|
790 | |
---|
791 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
792 | SUBROUTINE SDIRK_SoaInt( N, NSOA, Lambda, Sigma, Ierr ) |
---|
793 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
794 | |
---|
795 | USE KPP_ROOT_Parameters |
---|
796 | IMPLICIT NONE |
---|
797 | |
---|
798 | INTEGER, PARAMETER :: NADJ = 1 |
---|
799 | !~~~> Arguments: |
---|
800 | INTEGER, INTENT(IN) :: N, NSOA |
---|
801 | KPP_REAL, INTENT(INOUT) :: Lambda(NVAR,NADJ) |
---|
802 | KPP_REAL, INTENT(INOUT) :: Sigma(NVAR,NSOA) |
---|
803 | INTEGER, INTENT(OUT) :: Ierr |
---|
804 | |
---|
805 | !~~~> Local variables: |
---|
806 | KPP_REAL :: Y(NVAR) |
---|
807 | KPP_REAL :: Z(NVAR,Smax), U(NVAR,Smax), & |
---|
808 | TMP(NVAR), G1(NVAR), & |
---|
809 | NewtonRate, SCAL(NVAR), DU(NVAR), & |
---|
810 | T, H, Theta, NewtonPredictedErr, & |
---|
811 | NewtonIncrement, NewtonIncrementOld |
---|
812 | KPP_REAL :: Y_tlm(NVAR,NSOA), Z_tlm(NVAR,Smax,NSOA), & |
---|
813 | G2(NVAR,NSOA), Hess0(NHESS), TMP2(NVAR) |
---|
814 | KPP_REAL :: W(NVAR,Smax,NSOA), TMP_tlm(NVAR) |
---|
815 | INTEGER :: j, IER, istage, iadj, isoa, NewtonIter, & |
---|
816 | IP(NVAR), IP_adj(NVAR) |
---|
817 | LOGICAL :: Reject, SkipJac, SkipLU, NewtonDone |
---|
818 | |
---|
819 | #ifdef FULL_ALGEBRA |
---|
820 | KPP_REAL, DIMENSION(NVAR,NVAR) :: E, Jac, E_adj |
---|
821 | #else |
---|
822 | KPP_REAL, DIMENSION(LU_NONZERO):: E, Jac, E_adj |
---|
823 | #endif |
---|
824 | |
---|
825 | |
---|
826 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
827 | !~~~> Time loop begins |
---|
828 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
829 | Tloop: DO WHILE ( stack_ptr > 0 ) |
---|
830 | |
---|
831 | !~~~> Recover checkpoints for stage values and vectors |
---|
832 | CALL SDIRK_Pop( T, H, Y, Z, Y_tlm, Z_tlm, E, IP ) |
---|
833 | |
---|
834 | !~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition |
---|
835 | ! IF (.NOT.SaveLU) THEN |
---|
836 | ! SkipJac = .FALSE.; SkipLU = .FALSE. |
---|
837 | ! CALL SDIRK_PrepareMatrix ( H, T, Y, Jac, & |
---|
838 | ! SkipJac, SkipLU, E, IP, Reject, IER ) |
---|
839 | ! IF (IER /= 0) THEN |
---|
840 | ! CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
841 | ! END IF |
---|
842 | ! END IF |
---|
843 | |
---|
844 | stages:DO istage = rkS, 1, -1 |
---|
845 | |
---|
846 | !~~~> Jacobian at the current stage solution |
---|
847 | TMP(1:N) = Y(1:N) + Z(1:N,istage) |
---|
848 | CALL JAC_CHEM(T+rkC(istage)*H,TMP,Jac) |
---|
849 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
850 | |
---|
851 | !~~~> Hessian at the current stage solution |
---|
852 | CALL HESS_CHEM(T+rkC(istage)*H,TMP,Hess0) |
---|
853 | |
---|
854 | #ifdef FULL_ALGEBRA |
---|
855 | E_adj(1:N,1:N) = -Jac(1:N,1:N) |
---|
856 | DO j=1,N |
---|
857 | E_adj(j,j) = E_adj(j,j) + ONE/(H*rkGamma) |
---|
858 | END DO |
---|
859 | CALL DGETRF( N, N, E_adj, N, IP_adj, IER ) |
---|
860 | #else |
---|
861 | E_adj(1:LU_NONZERO) = -Jac(1:LU_NONZERO) |
---|
862 | DO i = 1,NVAR |
---|
863 | j = LU_DIAG(i); E_adj(j) = E_adj(j) + ONE/(H*rkGamma) |
---|
864 | END DO |
---|
865 | CALL KppDecomp ( E_adj, IER) |
---|
866 | #endif |
---|
867 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
868 | IF (IER /= 0) THEN |
---|
869 | PRINT*,'At stage ',istage,' the matrix used in adjoint', & |
---|
870 | ' computation is singular' |
---|
871 | CALL SDIRK_ErrorMsg(-8,T,H,Ierr); RETURN |
---|
872 | END IF |
---|
873 | |
---|
874 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
875 | !~~~> G1(:) = H*( B(i)*Lambda + sum_j A(j,i)*Uj(:) ) |
---|
876 | G1(1:N) = rkB(istage)*Lambda(1:N,1) |
---|
877 | IF (istage < rkS) THEN |
---|
878 | DO j = istage+1, rkS |
---|
879 | CALL WAXPY(N,rkA(j,istage),U(1,j),1,G1,1) |
---|
880 | END DO |
---|
881 | END IF |
---|
882 | G1(1:N) = H*G1(1:N) |
---|
883 | TMP2(1:N) = G1(1:N) |
---|
884 | |
---|
885 | ! G1(:) = H*Jac^T*( B(i)*Lambda + sum_j A(j,i)*Uj(:) ) |
---|
886 | #ifdef FULL_ALGEBRA |
---|
887 | TMP = MATMUL(TRANSPOSE(Jac),G1) ! DZ <- Jac(Y+Z)*Y_tlm |
---|
888 | #else |
---|
889 | CALL JacTR_SP_Vec ( Jac, G1, TMP ) |
---|
890 | #endif |
---|
891 | G1(1:N) = TMP(1:N) |
---|
892 | |
---|
893 | !~~~> Compute FOA stage |
---|
894 | CALL SDIRK_Solve ( 'T', H, N, E_adj, IP_adj, IER, G1 ) |
---|
895 | U(1:N,istage) = G1(1:N) |
---|
896 | |
---|
897 | !~~~> Prepare the loop-independent part of the SOA right-hand side |
---|
898 | G1(1:N) = rkB(istage)*Lambda(1:N,1) |
---|
899 | IF (istage < rkS) THEN |
---|
900 | DO j = istage+1, rkS |
---|
901 | CALL WAXPY(N,rkA(j,istage),U(1,j),1,G1,1) |
---|
902 | END DO |
---|
903 | CALL WAXPY(N,rkGamma,U(1,istage),1,G1,1) |
---|
904 | END IF |
---|
905 | G1(1:N) = H*G1(1:N) |
---|
906 | |
---|
907 | !~~~> G2(:) = H*( B(i)*Sigma + sum_j A(j,i)*Wj(:) ) |
---|
908 | DO isoa = 1, NSOA |
---|
909 | |
---|
910 | G2(1:N,isoa) = rkB(istage)*Sigma(1:N,isoa) |
---|
911 | IF (istage < rkS) THEN |
---|
912 | DO j = istage+1, rkS |
---|
913 | G2(1:N,isoa) = G2(1:N,isoa) + rkA(j,istage)*W(1:N,j,isoa) |
---|
914 | END DO |
---|
915 | END IF |
---|
916 | G2(1:N,isoa) = H*G2(1:N,isoa) |
---|
917 | |
---|
918 | #ifdef FULL_ALGEBRA |
---|
919 | TMP = MATMUL(TRANSPOSE(Jac),G2(1,isoa)) ! DZ <- Jac(Y+Z)*Y_tlm |
---|
920 | #else |
---|
921 | CALL JacTR_SP_Vec ( Jac, G2(1,isoa), TMP ) |
---|
922 | #endif |
---|
923 | G2(1:N,isoa) = TMP(1:N) |
---|
924 | |
---|
925 | !~~~> Add [ Hess0 x Y_tlm(istage) ]^T * G1 |
---|
926 | TMP_tlm(1:N) = Y_tlm(1:N,isoa) + Z_tlm(1:N,istage,isoa) |
---|
927 | CALL HessTR_Vec ( Hess0, G1, TMP_tlm, TMP ) |
---|
928 | G2(1:N,isoa) = G2(1:N,isoa) + TMP(1:N) |
---|
929 | |
---|
930 | END DO ! isoa = 1, NSOA |
---|
931 | |
---|
932 | !~~~> Compute SOA stage |
---|
933 | DO isoa = 1, NSOA |
---|
934 | TMP(1:N) = G2(1:N,isoa) |
---|
935 | CALL SDIRK_Solve ( 'T', H, N, E_adj, IP_adj, IER, TMP ) |
---|
936 | W(1:N,istage,isoa) = TMP |
---|
937 | END DO ! isoa = 1, NSOA |
---|
938 | |
---|
939 | END DO stages |
---|
940 | |
---|
941 | !~~~> Update first order adjoint solution |
---|
942 | DO istage = 1,rkS |
---|
943 | Lambda(1:N,1) = Lambda(1:N,1) + U(1:N,istage) |
---|
944 | END DO |
---|
945 | |
---|
946 | !~~~> Update second order adjoint solution |
---|
947 | DO istage = 1,rkS |
---|
948 | DO isoa = 1,NSOA |
---|
949 | Sigma(1:N,isoa) = Sigma(1:N,isoa) + W(1:N,istage,isoa) |
---|
950 | END DO |
---|
951 | END DO |
---|
952 | |
---|
953 | END DO Tloop |
---|
954 | |
---|
955 | ! Successful return |
---|
956 | Ierr = 1 |
---|
957 | |
---|
958 | END SUBROUTINE SDIRK_SoaInt |
---|
959 | |
---|
960 | |
---|
961 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
962 | SUBROUTINE SDIRK_AllocBuffers |
---|
963 | !~~~> Allocate buffer space for checkpointing |
---|
964 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
965 | INTEGER :: i |
---|
966 | |
---|
967 | ALLOCATE( chk_H(Max_no_steps), STAT=i ) |
---|
968 | IF (i/=0) THEN |
---|
969 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
970 | END IF |
---|
971 | ALLOCATE( chk_T(Max_no_steps), STAT=i ) |
---|
972 | IF (i/=0) THEN |
---|
973 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
974 | END IF |
---|
975 | ALLOCATE( chk_Y(NVAR,Max_no_steps), STAT=i ) |
---|
976 | IF (i/=0) THEN |
---|
977 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
978 | END IF |
---|
979 | ALLOCATE( chk_Y_tlm(NVAR,NSOA,Max_no_steps), STAT=i ) |
---|
980 | IF (i/=0) THEN |
---|
981 | PRINT*,'Failed allocation of buffer Y_tlm'; STOP |
---|
982 | END IF |
---|
983 | ALLOCATE( chk_Z(NVAR,rkS,Max_no_steps), STAT=i ) |
---|
984 | IF (i/=0) THEN |
---|
985 | PRINT*,'Failed allocation of buffer Z'; STOP |
---|
986 | END IF |
---|
987 | ALLOCATE( chk_Z_tlm(NVAR,rkS,NSOA,Max_no_steps), STAT=i ) |
---|
988 | IF (i/=0) THEN |
---|
989 | PRINT*,'Failed allocation of buffer Z_tlm'; STOP |
---|
990 | END IF |
---|
991 | IF (SaveLU) THEN |
---|
992 | #ifdef FULL_ALGEBRA |
---|
993 | ALLOCATE( chk_J(NVAR,NVAR,Max_no_steps), STAT=i ) |
---|
994 | #else |
---|
995 | ALLOCATE( chk_J(LU_NONZERO,Max_no_steps), STAT=i ) |
---|
996 | #endif |
---|
997 | IF (i/=0) THEN |
---|
998 | PRINT*,'Failed allocation of buffer J'; STOP |
---|
999 | END IF |
---|
1000 | ALLOCATE( chk_P(NVAR,Max_no_steps), STAT=i ) |
---|
1001 | IF (i/=0) THEN |
---|
1002 | PRINT*,'Failed allocation of buffer P'; STOP |
---|
1003 | END IF |
---|
1004 | END IF |
---|
1005 | |
---|
1006 | END SUBROUTINE SDIRK_AllocBuffers |
---|
1007 | |
---|
1008 | |
---|
1009 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1010 | SUBROUTINE SDIRK_FreeBuffers |
---|
1011 | !~~~> Dallocate buffer space for discrete adjoint |
---|
1012 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1013 | INTEGER :: i |
---|
1014 | |
---|
1015 | DEALLOCATE( chk_H, STAT=i ) |
---|
1016 | IF (i/=0) THEN |
---|
1017 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
1018 | END IF |
---|
1019 | DEALLOCATE( chk_T, STAT=i ) |
---|
1020 | IF (i/=0) THEN |
---|
1021 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
1022 | END IF |
---|
1023 | DEALLOCATE( chk_Y, STAT=i ) |
---|
1024 | IF (i/=0) THEN |
---|
1025 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
1026 | END IF |
---|
1027 | DEALLOCATE( chk_Y_tlm, STAT=i ) |
---|
1028 | IF (i/=0) THEN |
---|
1029 | PRINT*,'Failed deallocation of buffer Y_tlm'; STOP |
---|
1030 | END IF |
---|
1031 | DEALLOCATE( chk_Z, STAT=i ) |
---|
1032 | IF (i/=0) THEN |
---|
1033 | PRINT*,'Failed deallocation of buffer Z'; STOP |
---|
1034 | END IF |
---|
1035 | DEALLOCATE( chk_Z_tlm, STAT=i ) |
---|
1036 | IF (i/=0) THEN |
---|
1037 | PRINT*,'Failed deallocation of buffer Z_tlm'; STOP |
---|
1038 | END IF |
---|
1039 | IF (SaveLU) THEN |
---|
1040 | DEALLOCATE( chk_J, STAT=i ) |
---|
1041 | IF (i/=0) THEN |
---|
1042 | PRINT*,'Failed deallocation of buffer J'; STOP |
---|
1043 | END IF |
---|
1044 | DEALLOCATE( chk_P, STAT=i ) |
---|
1045 | IF (i/=0) THEN |
---|
1046 | PRINT*,'Failed deallocation of buffer P'; STOP |
---|
1047 | END IF |
---|
1048 | END IF |
---|
1049 | |
---|
1050 | END SUBROUTINE SDIRK_FreeBuffers |
---|
1051 | |
---|
1052 | |
---|
1053 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1054 | SUBROUTINE SDIRK_Push( T, H, Y, Z, Y_tlm, Z_tlm, E, P ) |
---|
1055 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1056 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
1057 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1058 | |
---|
1059 | KPP_REAL :: T, H, Y(NVAR), Z(NVAR,rkS) |
---|
1060 | KPP_REAL :: Y_tlm(NVAR,NSOA), Z_tlm(NVAR,rkS,NSOA) |
---|
1061 | INTEGER :: P(NVAR) |
---|
1062 | #ifdef FULL_ALGEBRA |
---|
1063 | KPP_REAL :: E(NVAR,NVAR) |
---|
1064 | #else |
---|
1065 | KPP_REAL :: E(LU_NONZERO) |
---|
1066 | #endif |
---|
1067 | |
---|
1068 | stack_ptr = stack_ptr + 1 |
---|
1069 | IF ( stack_ptr > Max_no_steps ) THEN |
---|
1070 | PRINT*,'Push failed: buffer overflow' |
---|
1071 | STOP |
---|
1072 | END IF |
---|
1073 | chk_H( stack_ptr ) = H |
---|
1074 | chk_T( stack_ptr ) = T |
---|
1075 | chk_Y(1:NVAR,stack_ptr) = Y(1:NVAR) |
---|
1076 | chk_Z(1:NVAR,1:rkS,stack_ptr) = Z(1:NVAR,1:rkS) |
---|
1077 | chk_Y_tlm(1:NVAR,1:NSOA,stack_ptr) = Y_tlm(1:NVAR,1:NSOA) |
---|
1078 | chk_Z_tlm(1:NVAR,1:rkS,1:NSOA,stack_ptr) = Z_tlm(1:NVAR,1:rkS,1:NSOA) |
---|
1079 | IF (SaveLU) THEN |
---|
1080 | #ifdef FULL_ALGEBRA |
---|
1081 | chk_J(1:NVAR,1:NVAR,stack_ptr) = E(1:NVAR,1:NVAR) |
---|
1082 | chk_P(1:NVAR,stack_ptr) = P(1:NVAR) |
---|
1083 | #else |
---|
1084 | chk_J(1:LU_NONZERO,stack_ptr) = E(1:LU_NONZERO) |
---|
1085 | #endif |
---|
1086 | END IF |
---|
1087 | |
---|
1088 | END SUBROUTINE SDIRK_Push |
---|
1089 | |
---|
1090 | |
---|
1091 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1092 | SUBROUTINE SDIRK_Pop( T, H, Y, Z, Y_tlm, Z_tlm, E, P ) |
---|
1093 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1094 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
1095 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1096 | |
---|
1097 | KPP_REAL :: T, H, Y(NVAR), Z(NVAR,Smax) |
---|
1098 | KPP_REAL :: Y_tlm(NVAR,NSOA), Z_tlm(NVAR,Smax,NSOA) |
---|
1099 | INTEGER :: P(NVAR) |
---|
1100 | #ifdef FULL_ALGEBRA |
---|
1101 | KPP_REAL :: E(NVAR,NVAR) |
---|
1102 | #else |
---|
1103 | KPP_REAL :: E(LU_NONZERO) |
---|
1104 | #endif |
---|
1105 | |
---|
1106 | IF ( stack_ptr <= 0 ) THEN |
---|
1107 | PRINT*,'Pop failed: empty buffer' |
---|
1108 | STOP |
---|
1109 | END IF |
---|
1110 | H = chk_H( stack_ptr ) |
---|
1111 | T = chk_T( stack_ptr ) |
---|
1112 | Y(1:NVAR) = chk_Y(1:NVAR,stack_ptr) |
---|
1113 | Z(1:NVAR,1:rkS) = chk_Z(1:NVAR,1:rkS,stack_ptr) |
---|
1114 | Y_tlm(1:NVAR,1:NSOA) = chk_Y_tlm(1:NVAR,1:NSOA,stack_ptr) |
---|
1115 | Z_tlm(1:NVAR,1:rkS,1:NSOA) = chk_Z_tlm(1:NVAR,1:rkS,1:NSOA,stack_ptr) |
---|
1116 | IF (SaveLU) THEN |
---|
1117 | #ifdef FULL_ALGEBRA |
---|
1118 | E(1:NVAR,1:NVAR) = chk_J(1:NVAR,1:NVAR,stack_ptr) |
---|
1119 | P(1:NVAR) = chk_P(1:NVAR,stack_ptr) |
---|
1120 | #else |
---|
1121 | E(1:LU_NONZERO) = chk_J(1:LU_NONZERO,stack_ptr) |
---|
1122 | #endif |
---|
1123 | END IF |
---|
1124 | |
---|
1125 | stack_ptr = stack_ptr - 1 |
---|
1126 | |
---|
1127 | END SUBROUTINE SDIRK_Pop |
---|
1128 | |
---|
1129 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1130 | SUBROUTINE SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL) |
---|
1131 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1132 | IMPLICIT NONE |
---|
1133 | INTEGER :: i, N, ITOL |
---|
1134 | KPP_REAL :: AbsTol(N), RelTol(N), & |
---|
1135 | Y(N), SCAL(N) |
---|
1136 | IF (ITOL == 0) THEN |
---|
1137 | DO i=1,N |
---|
1138 | SCAL(i) = ONE / ( AbsTol(1)+RelTol(1)*ABS(Y(i)) ) |
---|
1139 | END DO |
---|
1140 | ELSE |
---|
1141 | DO i=1,N |
---|
1142 | SCAL(i) = ONE / ( AbsTol(i)+RelTol(i)*ABS(Y(i)) ) |
---|
1143 | END DO |
---|
1144 | END IF |
---|
1145 | END SUBROUTINE SDIRK_ErrorScale |
---|
1146 | |
---|
1147 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1148 | SUBROUTINE SDIRK_ErrorNorm(N, Y, SCAL, Err) |
---|
1149 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1150 | ! |
---|
1151 | INTEGER :: i, N |
---|
1152 | KPP_REAL :: Y(N), SCAL(N), Err |
---|
1153 | Err = ZERO |
---|
1154 | DO i=1,N |
---|
1155 | Err = Err+(Y(i)*SCAL(i))**2 |
---|
1156 | END DO |
---|
1157 | Err = MAX( SQRT(Err/DBLE(N)), 1.0d-10 ) |
---|
1158 | ! |
---|
1159 | END SUBROUTINE SDIRK_ErrorNorm |
---|
1160 | |
---|
1161 | |
---|
1162 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1163 | SUBROUTINE SDIRK_ErrorMsg(Code,T,H,Ierr) |
---|
1164 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1165 | ! Handles all error messages |
---|
1166 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1167 | KPP_REAL, INTENT(IN) :: T, H |
---|
1168 | INTEGER, INTENT(IN) :: Code |
---|
1169 | INTEGER, INTENT(OUT) :: Ierr |
---|
1170 | |
---|
1171 | Ierr = Code |
---|
1172 | PRINT * , & |
---|
1173 | 'Forced exit from SDIRK due to the following error:' |
---|
1174 | |
---|
1175 | SELECT CASE (Code) |
---|
1176 | CASE (-1) |
---|
1177 | PRINT * , '--> Improper value for maximal no of steps' |
---|
1178 | CASE (-2) |
---|
1179 | PRINT * , '--> Improper value for maximal no of Newton iterations' |
---|
1180 | CASE (-3) |
---|
1181 | PRINT * , '--> Hmin/Hmax/Hstart must be positive' |
---|
1182 | CASE (-4) |
---|
1183 | PRINT * , '--> FacMin/FacMax/FacRej must be positive' |
---|
1184 | CASE (-5) |
---|
1185 | PRINT * , '--> Improper tolerance values' |
---|
1186 | CASE (-6) |
---|
1187 | PRINT * , '--> No of steps exceeds maximum bound', max_no_steps |
---|
1188 | CASE (-7) |
---|
1189 | PRINT * , '--> Step size too small: T + 10*H = T', & |
---|
1190 | ' or H < Roundoff' |
---|
1191 | CASE (-8) |
---|
1192 | PRINT * , '--> Matrix is repeatedly singular' |
---|
1193 | CASE DEFAULT |
---|
1194 | PRINT *, 'Unknown Error code: ', Code |
---|
1195 | END SELECT |
---|
1196 | |
---|
1197 | PRINT *, "T=", T, "and H=", H |
---|
1198 | |
---|
1199 | END SUBROUTINE SDIRK_ErrorMsg |
---|
1200 | |
---|
1201 | |
---|
1202 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1203 | SUBROUTINE SDIRK_PrepareMatrix ( H, T, Y, FJAC, & |
---|
1204 | SkipJac, SkipLU, E, IP, Reject, ISING ) |
---|
1205 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1206 | !~~~> Compute the matrix E = 1/(H*GAMMA)*Jac, and its decomposition |
---|
1207 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1208 | |
---|
1209 | IMPLICIT NONE |
---|
1210 | |
---|
1211 | KPP_REAL, INTENT(INOUT) :: H |
---|
1212 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
---|
1213 | LOGICAL, INTENT(INOUT) :: SkipJac,SkipLU,Reject |
---|
1214 | INTEGER, INTENT(OUT) :: ISING, IP(NVAR) |
---|
1215 | #ifdef FULL_ALGEBRA |
---|
1216 | KPP_REAL, INTENT(INOUT) :: FJAC(NVAR,NVAR) |
---|
1217 | KPP_REAL, INTENT(OUT) :: E(NVAR,NVAR) |
---|
1218 | #else |
---|
1219 | KPP_REAL, INTENT(INOUT) :: FJAC(LU_NONZERO) |
---|
1220 | KPP_REAL, INTENT(OUT) :: E(LU_NONZERO) |
---|
1221 | #endif |
---|
1222 | KPP_REAL :: HGammaInv |
---|
1223 | INTEGER :: i, j, ConsecutiveSng |
---|
1224 | |
---|
1225 | ConsecutiveSng = 0 |
---|
1226 | ISING = 1 |
---|
1227 | |
---|
1228 | Hloop: DO WHILE (ISING /= 0) |
---|
1229 | |
---|
1230 | HGammaInv = ONE/(H*rkGamma) |
---|
1231 | |
---|
1232 | !~~~> Compute the Jacobian |
---|
1233 | ! IF (SkipJac) THEN |
---|
1234 | ! SkipJac = .FALSE. |
---|
1235 | ! ELSE |
---|
1236 | IF (.NOT. SkipJac) THEN |
---|
1237 | CALL JAC_CHEM( T, Y, FJAC ) |
---|
1238 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
1239 | END IF |
---|
1240 | |
---|
1241 | #ifdef FULL_ALGEBRA |
---|
1242 | DO j=1,NVAR |
---|
1243 | DO i=1,NVAR |
---|
1244 | E(i,j) = -FJAC(i,j) |
---|
1245 | END DO |
---|
1246 | E(j,j) = E(j,j)+HGammaInv |
---|
1247 | END DO |
---|
1248 | CALL DGETRF( NVAR, NVAR, E, NVAR, IP, ISING ) |
---|
1249 | #else |
---|
1250 | DO i = 1,LU_NONZERO |
---|
1251 | E(i) = -FJAC(i) |
---|
1252 | END DO |
---|
1253 | DO i = 1,NVAR |
---|
1254 | j = LU_DIAG(i); E(j) = E(j) + HGammaInv |
---|
1255 | END DO |
---|
1256 | CALL KppDecomp ( E, ISING) |
---|
1257 | IP(1) = 1 |
---|
1258 | #endif |
---|
1259 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
1260 | |
---|
1261 | IF (ISING /= 0) THEN |
---|
1262 | WRITE (6,*) ' MATRIX IS SINGULAR, ISING=',ISING,' T=',T,' H=',H |
---|
1263 | ISTATUS(Nsng) = ISTATUS(Nsng) + 1; ConsecutiveSng = ConsecutiveSng + 1 |
---|
1264 | IF (ConsecutiveSng >= 6) RETURN ! Failure |
---|
1265 | H = 0.5d0*H |
---|
1266 | SkipJac = .FALSE. |
---|
1267 | SkipLU = .FALSE. |
---|
1268 | Reject = .TRUE. |
---|
1269 | END IF |
---|
1270 | |
---|
1271 | END DO Hloop |
---|
1272 | |
---|
1273 | END SUBROUTINE SDIRK_PrepareMatrix |
---|
1274 | |
---|
1275 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1276 | SUBROUTINE SDIRK_Solve ( Transp, H, N, E, IP, ISING, RHS ) |
---|
1277 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1278 | !~~~> Solves the system (H*Gamma-Jac)*x = R |
---|
1279 | ! using the LU decomposition of E = I - 1/(H*Gamma)*Jac |
---|
1280 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1281 | IMPLICIT NONE |
---|
1282 | INTEGER, INTENT(IN) :: N, IP(N), ISING |
---|
1283 | CHARACTER, INTENT(IN) :: Transp |
---|
1284 | KPP_REAL, INTENT(IN) :: H |
---|
1285 | #ifdef FULL_ALGEBRA |
---|
1286 | KPP_REAL, INTENT(IN) :: E(NVAR,NVAR) |
---|
1287 | #else |
---|
1288 | KPP_REAL, INTENT(IN) :: E(LU_NONZERO) |
---|
1289 | #endif |
---|
1290 | KPP_REAL, INTENT(INOUT) :: RHS(N) |
---|
1291 | KPP_REAL :: HGammaInv |
---|
1292 | |
---|
1293 | HGammaInv = ONE/(H*rkGamma) |
---|
1294 | CALL WSCAL(N,HGammaInv,RHS,1) |
---|
1295 | SELECT CASE (TRANSP) |
---|
1296 | CASE ('N') |
---|
1297 | #ifdef FULL_ALGEBRA |
---|
1298 | CALL DGETRS( 'N', N, 1, E, N, IP, RHS, N, ISING ) |
---|
1299 | #else |
---|
1300 | CALL KppSolve(E, RHS) |
---|
1301 | #endif |
---|
1302 | CASE ('T') |
---|
1303 | #ifdef FULL_ALGEBRA |
---|
1304 | CALL DGETRS( 'T', N, 1, E, N, IP, RHS, N, ISING ) |
---|
1305 | #else |
---|
1306 | CALL KppSolveTR(E, RHS, RHS) |
---|
1307 | #endif |
---|
1308 | CASE DEFAULT |
---|
1309 | PRINT*,'Error in SDIRK_Solve. Unknown Transp argument:',Transp |
---|
1310 | STOP |
---|
1311 | END SELECT |
---|
1312 | ISTATUS(Nsol) = ISTATUS(Nsol) + 1 |
---|
1313 | |
---|
1314 | END SUBROUTINE SDIRK_Solve |
---|
1315 | |
---|
1316 | |
---|
1317 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1318 | SUBROUTINE Sdirk4a |
---|
1319 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1320 | sdMethod = S4A |
---|
1321 | ! Number of stages |
---|
1322 | rkS = 5 |
---|
1323 | |
---|
1324 | ! Method coefficients |
---|
1325 | rkGamma = .2666666666666666666666666666666667d0 |
---|
1326 | |
---|
1327 | rkA(1,1) = .2666666666666666666666666666666667d0 |
---|
1328 | rkA(2,1) = .5000000000000000000000000000000000d0 |
---|
1329 | rkA(2,2) = .2666666666666666666666666666666667d0 |
---|
1330 | rkA(3,1) = .3541539528432732316227461858529820d0 |
---|
1331 | rkA(3,2) = -.5415395284327323162274618585298197d-1 |
---|
1332 | rkA(3,3) = .2666666666666666666666666666666667d0 |
---|
1333 | rkA(4,1) = .8515494131138652076337791881433756d-1 |
---|
1334 | rkA(4,2) = -.6484332287891555171683963466229754d-1 |
---|
1335 | rkA(4,3) = .7915325296404206392428857585141242d-1 |
---|
1336 | rkA(4,4) = .2666666666666666666666666666666667d0 |
---|
1337 | rkA(5,1) = 2.100115700566932777970612055999074d0 |
---|
1338 | rkA(5,2) = -.7677800284445976813343102185062276d0 |
---|
1339 | rkA(5,3) = 2.399816361080026398094746205273880d0 |
---|
1340 | rkA(5,4) = -2.998818699869028161397714709433394d0 |
---|
1341 | rkA(5,5) = .2666666666666666666666666666666667d0 |
---|
1342 | |
---|
1343 | rkB(1) = 2.100115700566932777970612055999074d0 |
---|
1344 | rkB(2) = -.7677800284445976813343102185062276d0 |
---|
1345 | rkB(3) = 2.399816361080026398094746205273880d0 |
---|
1346 | rkB(4) = -2.998818699869028161397714709433394d0 |
---|
1347 | rkB(5) = .2666666666666666666666666666666667d0 |
---|
1348 | |
---|
1349 | rkBhat(1)= 2.885264204387193942183851612883390d0 |
---|
1350 | rkBhat(2)= -.1458793482962771337341223443218041d0 |
---|
1351 | rkBhat(3)= 2.390008682465139866479830743628554d0 |
---|
1352 | rkBhat(4)= -4.129393538556056674929560012190140d0 |
---|
1353 | rkBhat(5)= 0.d0 |
---|
1354 | |
---|
1355 | rkC(1) = .2666666666666666666666666666666667d0 |
---|
1356 | rkC(2) = .7666666666666666666666666666666667d0 |
---|
1357 | rkC(3) = .5666666666666666666666666666666667d0 |
---|
1358 | rkC(4) = .3661315380631796996374935266701191d0 |
---|
1359 | rkC(5) = 1.d0 |
---|
1360 | |
---|
1361 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
1362 | rkD(1) = 0.d0 |
---|
1363 | rkD(2) = 0.d0 |
---|
1364 | rkD(3) = 0.d0 |
---|
1365 | rkD(4) = 0.d0 |
---|
1366 | rkD(5) = 1.d0 |
---|
1367 | |
---|
1368 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
1369 | rkE(1) = -.6804000050475287124787034884002302d0 |
---|
1370 | rkE(2) = 1.558961944525217193393931795738823d0 |
---|
1371 | rkE(3) = -13.55893003128907927748632408763868d0 |
---|
1372 | rkE(4) = 15.48522576958521253098585004571302d0 |
---|
1373 | rkE(5) = 1.d0 |
---|
1374 | |
---|
1375 | ! Local order of Err estimate |
---|
1376 | rkElo = 4 |
---|
1377 | |
---|
1378 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
1379 | rkTheta(2,1) = 1.875000000000000000000000000000000d0 |
---|
1380 | rkTheta(3,1) = 1.708847304091539528432732316227462d0 |
---|
1381 | rkTheta(3,2) = -.2030773231622746185852981969486824d0 |
---|
1382 | rkTheta(4,1) = .2680325578937783958847157206823118d0 |
---|
1383 | rkTheta(4,2) = -.1828840955527181631794050728644549d0 |
---|
1384 | rkTheta(4,3) = .2968246986151577397160821594427966d0 |
---|
1385 | rkTheta(5,1) = .9096171815241460655379433581446771d0 |
---|
1386 | rkTheta(5,2) = -3.108254967778352416114774430509465d0 |
---|
1387 | rkTheta(5,3) = 12.33727431701306195581826123274001d0 |
---|
1388 | rkTheta(5,4) = -11.24557012450885560524143016037523d0 |
---|
1389 | |
---|
1390 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
1391 | rkAlpha(2,1) = 2.875000000000000000000000000000000d0 |
---|
1392 | rkAlpha(3,1) = .8500000000000000000000000000000000d0 |
---|
1393 | rkAlpha(3,2) = .4434782608695652173913043478260870d0 |
---|
1394 | rkAlpha(4,1) = .7352046091658870564637910527807370d0 |
---|
1395 | rkAlpha(4,2) = -.9525565003057343527941920657462074d-1 |
---|
1396 | rkAlpha(4,3) = .4290111305453813852259481840631738d0 |
---|
1397 | rkAlpha(5,1) = -16.10898993405067684831655675112808d0 |
---|
1398 | rkAlpha(5,2) = 6.559571569643355712998131800797873d0 |
---|
1399 | rkAlpha(5,3) = -15.90772144271326504260996815012482d0 |
---|
1400 | rkAlpha(5,4) = 25.34908987169226073668861694892683d0 |
---|
1401 | |
---|
1402 | !~~~> Coefficients for continuous solution |
---|
1403 | ! rkD(1,1)= 24.74416644927758d0 |
---|
1404 | ! rkD(1,2)= -4.325375951824688d0 |
---|
1405 | ! rkD(1,3)= 41.39683763286316d0 |
---|
1406 | ! rkD(1,4)= -61.04144619901784d0 |
---|
1407 | ! rkD(1,5)= -3.391332232917013d0 |
---|
1408 | ! rkD(2,1)= -51.98245719616925d0 |
---|
1409 | ! rkD(2,2)= 10.52501981094525d0 |
---|
1410 | ! rkD(2,3)= -154.2067922191855d0 |
---|
1411 | ! rkD(2,4)= 214.3082125319825d0 |
---|
1412 | ! rkD(2,5)= 14.71166018088679d0 |
---|
1413 | ! rkD(3,1)= 33.14347947522142d0 |
---|
1414 | ! rkD(3,2)= -19.72986789558523d0 |
---|
1415 | ! rkD(3,3)= 230.4878502285804d0 |
---|
1416 | ! rkD(3,4)= -287.6629744338197d0 |
---|
1417 | ! rkD(3,5)= -18.99932366302254d0 |
---|
1418 | ! rkD(4,1)= -5.905188728329743d0 |
---|
1419 | ! rkD(4,2)= 13.53022403646467d0 |
---|
1420 | ! rkD(4,3)= -117.6778956422581d0 |
---|
1421 | ! rkD(4,4)= 134.3962081008550d0 |
---|
1422 | ! rkD(4,5)= 8.678995715052762d0 |
---|
1423 | ! |
---|
1424 | ! DO i=1,4 ! CONTi <-- Sum_j rkD(i,j)*Zj |
---|
1425 | ! CALL Set2zero(N,CONT(1,i)) |
---|
1426 | ! DO j = 1,rkS |
---|
1427 | ! CALL WAXPY(N,rkD(i,j),Z(1,j),1,CONT(1,i),1) |
---|
1428 | ! END DO |
---|
1429 | ! END DO |
---|
1430 | |
---|
1431 | rkELO = 4.0d0 |
---|
1432 | |
---|
1433 | END SUBROUTINE Sdirk4a |
---|
1434 | |
---|
1435 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1436 | SUBROUTINE Sdirk4b |
---|
1437 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1438 | sdMethod = S4B |
---|
1439 | ! Number of stages |
---|
1440 | rkS = 5 |
---|
1441 | |
---|
1442 | ! Method coefficients |
---|
1443 | rkGamma = .25d0 |
---|
1444 | |
---|
1445 | rkA(1,1) = 0.25d0 |
---|
1446 | rkA(2,1) = 0.5d00 |
---|
1447 | rkA(2,2) = 0.25d0 |
---|
1448 | rkA(3,1) = 0.34d0 |
---|
1449 | rkA(3,2) =-0.40d-1 |
---|
1450 | rkA(3,3) = 0.25d0 |
---|
1451 | rkA(4,1) = 0.2727941176470588235294117647058824d0 |
---|
1452 | rkA(4,2) =-0.5036764705882352941176470588235294d-1 |
---|
1453 | rkA(4,3) = 0.2757352941176470588235294117647059d-1 |
---|
1454 | rkA(4,4) = 0.25d0 |
---|
1455 | rkA(5,1) = 1.041666666666666666666666666666667d0 |
---|
1456 | rkA(5,2) =-1.020833333333333333333333333333333d0 |
---|
1457 | rkA(5,3) = 7.812500000000000000000000000000000d0 |
---|
1458 | rkA(5,4) =-7.083333333333333333333333333333333d0 |
---|
1459 | rkA(5,5) = 0.25d0 |
---|
1460 | |
---|
1461 | rkB(1) = 1.041666666666666666666666666666667d0 |
---|
1462 | rkB(2) = -1.020833333333333333333333333333333d0 |
---|
1463 | rkB(3) = 7.812500000000000000000000000000000d0 |
---|
1464 | rkB(4) = -7.083333333333333333333333333333333d0 |
---|
1465 | rkB(5) = 0.250000000000000000000000000000000d0 |
---|
1466 | |
---|
1467 | rkBhat(1)= 1.069791666666666666666666666666667d0 |
---|
1468 | rkBhat(2)= -0.894270833333333333333333333333333d0 |
---|
1469 | rkBhat(3)= 7.695312500000000000000000000000000d0 |
---|
1470 | rkBhat(4)= -7.083333333333333333333333333333333d0 |
---|
1471 | rkBhat(5)= 0.212500000000000000000000000000000d0 |
---|
1472 | |
---|
1473 | rkC(1) = 0.25d0 |
---|
1474 | rkC(2) = 0.75d0 |
---|
1475 | rkC(3) = 0.55d0 |
---|
1476 | rkC(4) = 0.50d0 |
---|
1477 | rkC(5) = 1.00d0 |
---|
1478 | |
---|
1479 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
1480 | rkD(1) = 0.0d0 |
---|
1481 | rkD(2) = 0.0d0 |
---|
1482 | rkD(3) = 0.0d0 |
---|
1483 | rkD(4) = 0.0d0 |
---|
1484 | rkD(5) = 1.0d0 |
---|
1485 | |
---|
1486 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
1487 | rkE(1) = 0.5750d0 |
---|
1488 | rkE(2) = 0.2125d0 |
---|
1489 | rkE(3) = -4.6875d0 |
---|
1490 | rkE(4) = 4.2500d0 |
---|
1491 | rkE(5) = 0.1500d0 |
---|
1492 | |
---|
1493 | ! Local order of Err estimate |
---|
1494 | rkElo = 4 |
---|
1495 | |
---|
1496 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
1497 | rkTheta(2,1) = 2.d0 |
---|
1498 | rkTheta(3,1) = 1.680000000000000000000000000000000d0 |
---|
1499 | rkTheta(3,2) = -.1600000000000000000000000000000000d0 |
---|
1500 | rkTheta(4,1) = 1.308823529411764705882352941176471d0 |
---|
1501 | rkTheta(4,2) = -.1838235294117647058823529411764706d0 |
---|
1502 | rkTheta(4,3) = 0.1102941176470588235294117647058824d0 |
---|
1503 | rkTheta(5,1) = -3.083333333333333333333333333333333d0 |
---|
1504 | rkTheta(5,2) = -4.291666666666666666666666666666667d0 |
---|
1505 | rkTheta(5,3) = 34.37500000000000000000000000000000d0 |
---|
1506 | rkTheta(5,4) = -28.33333333333333333333333333333333d0 |
---|
1507 | |
---|
1508 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
1509 | rkAlpha(2,1) = 3. |
---|
1510 | rkAlpha(3,1) = .8800000000000000000000000000000000d0 |
---|
1511 | rkAlpha(3,2) = .4400000000000000000000000000000000d0 |
---|
1512 | rkAlpha(4,1) = .1666666666666666666666666666666667d0 |
---|
1513 | rkAlpha(4,2) = -.8333333333333333333333333333333333d-1 |
---|
1514 | rkAlpha(4,3) = .9469696969696969696969696969696970d0 |
---|
1515 | rkAlpha(5,1) = -6.d0 |
---|
1516 | rkAlpha(5,2) = 9.d0 |
---|
1517 | rkAlpha(5,3) = -56.81818181818181818181818181818182d0 |
---|
1518 | rkAlpha(5,4) = 54.d0 |
---|
1519 | |
---|
1520 | END SUBROUTINE Sdirk4b |
---|
1521 | |
---|
1522 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1523 | SUBROUTINE Sdirk2a |
---|
1524 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1525 | sdMethod = S2A |
---|
1526 | ! Number of stages |
---|
1527 | rkS = 2 |
---|
1528 | |
---|
1529 | ! Method coefficients |
---|
1530 | rkGamma = .2928932188134524755991556378951510d0 |
---|
1531 | |
---|
1532 | rkA(1,1) = .2928932188134524755991556378951510d0 |
---|
1533 | rkA(2,1) = .7071067811865475244008443621048490d0 |
---|
1534 | rkA(2,2) = .2928932188134524755991556378951510d0 |
---|
1535 | |
---|
1536 | rkB(1) = .7071067811865475244008443621048490d0 |
---|
1537 | rkB(2) = .2928932188134524755991556378951510d0 |
---|
1538 | |
---|
1539 | rkBhat(1)= .6666666666666666666666666666666667d0 |
---|
1540 | rkBhat(2)= .3333333333333333333333333333333333d0 |
---|
1541 | |
---|
1542 | rkC(1) = 0.292893218813452475599155637895151d0 |
---|
1543 | rkC(2) = 1.0d0 |
---|
1544 | |
---|
1545 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
1546 | rkD(1) = 0.0d0 |
---|
1547 | rkD(2) = 1.0d0 |
---|
1548 | |
---|
1549 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
1550 | rkE(1) = 0.4714045207910316829338962414032326d0 |
---|
1551 | rkE(2) = -0.1380711874576983496005629080698993d0 |
---|
1552 | |
---|
1553 | ! Local order of Err estimate |
---|
1554 | rkElo = 2 |
---|
1555 | |
---|
1556 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
1557 | rkTheta(2,1) = 2.414213562373095048801688724209698d0 |
---|
1558 | |
---|
1559 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
1560 | rkAlpha(2,1) = 3.414213562373095048801688724209698d0 |
---|
1561 | |
---|
1562 | END SUBROUTINE Sdirk2a |
---|
1563 | |
---|
1564 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1565 | SUBROUTINE Sdirk2b |
---|
1566 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1567 | sdMethod = S2B |
---|
1568 | ! Number of stages |
---|
1569 | rkS = 2 |
---|
1570 | |
---|
1571 | ! Method coefficients |
---|
1572 | rkGamma = 1.707106781186547524400844362104849d0 |
---|
1573 | |
---|
1574 | rkA(1,1) = 1.707106781186547524400844362104849d0 |
---|
1575 | rkA(2,1) = -.707106781186547524400844362104849d0 |
---|
1576 | rkA(2,2) = 1.707106781186547524400844362104849d0 |
---|
1577 | |
---|
1578 | rkB(1) = -.707106781186547524400844362104849d0 |
---|
1579 | rkB(2) = 1.707106781186547524400844362104849d0 |
---|
1580 | |
---|
1581 | rkBhat(1)= .6666666666666666666666666666666667d0 |
---|
1582 | rkBhat(2)= .3333333333333333333333333333333333d0 |
---|
1583 | |
---|
1584 | rkC(1) = 1.707106781186547524400844362104849d0 |
---|
1585 | rkC(2) = 1.0d0 |
---|
1586 | |
---|
1587 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
1588 | rkD(1) = 0.0d0 |
---|
1589 | rkD(2) = 1.0d0 |
---|
1590 | |
---|
1591 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
1592 | rkE(1) = -.4714045207910316829338962414032326d0 |
---|
1593 | rkE(2) = .8047378541243650162672295747365659d0 |
---|
1594 | |
---|
1595 | ! Local order of Err estimate |
---|
1596 | rkElo = 2 |
---|
1597 | |
---|
1598 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
1599 | rkTheta(2,1) = -.414213562373095048801688724209698d0 |
---|
1600 | |
---|
1601 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
1602 | rkAlpha(2,1) = .5857864376269049511983112757903019d0 |
---|
1603 | |
---|
1604 | END SUBROUTINE Sdirk2b |
---|
1605 | |
---|
1606 | |
---|
1607 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1608 | SUBROUTINE Sdirk3a |
---|
1609 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1610 | sdMethod = S3A |
---|
1611 | ! Number of stages |
---|
1612 | rkS = 3 |
---|
1613 | |
---|
1614 | ! Method coefficients |
---|
1615 | rkGamma = .2113248654051871177454256097490213d0 |
---|
1616 | |
---|
1617 | rkA(1,1) = .2113248654051871177454256097490213d0 |
---|
1618 | rkA(2,1) = .2113248654051871177454256097490213d0 |
---|
1619 | rkA(2,2) = .2113248654051871177454256097490213d0 |
---|
1620 | rkA(3,1) = .2113248654051871177454256097490213d0 |
---|
1621 | rkA(3,2) = .5773502691896257645091487805019573d0 |
---|
1622 | rkA(3,3) = .2113248654051871177454256097490213d0 |
---|
1623 | |
---|
1624 | rkB(1) = .2113248654051871177454256097490213d0 |
---|
1625 | rkB(2) = .5773502691896257645091487805019573d0 |
---|
1626 | rkB(3) = .2113248654051871177454256097490213d0 |
---|
1627 | |
---|
1628 | rkBhat(1)= .2113248654051871177454256097490213d0 |
---|
1629 | rkBhat(2)= .6477918909913548037576239837516312d0 |
---|
1630 | rkBhat(3)= .1408832436034580784969504064993475d0 |
---|
1631 | |
---|
1632 | rkC(1) = .2113248654051871177454256097490213d0 |
---|
1633 | rkC(2) = .4226497308103742354908512194980427d0 |
---|
1634 | rkC(3) = 1.d0 |
---|
1635 | |
---|
1636 | ! Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} |
---|
1637 | rkD(1) = 0.d0 |
---|
1638 | rkD(2) = 0.d0 |
---|
1639 | rkD(3) = 1.d0 |
---|
1640 | |
---|
1641 | ! Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} |
---|
1642 | rkE(1) = 0.9106836025229590978424821138352906d0 |
---|
1643 | rkE(2) = -1.244016935856292431175815447168624d0 |
---|
1644 | rkE(3) = 0.3333333333333333333333333333333333d0 |
---|
1645 | |
---|
1646 | ! Local order of Err estimate |
---|
1647 | rkElo = 2 |
---|
1648 | |
---|
1649 | ! h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} |
---|
1650 | rkTheta(2,1) = 1.0d0 |
---|
1651 | rkTheta(3,1) = -1.732050807568877293527446341505872d0 |
---|
1652 | rkTheta(3,2) = 2.732050807568877293527446341505872d0 |
---|
1653 | |
---|
1654 | ! Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} |
---|
1655 | rkAlpha(2,1) = 2.0d0 |
---|
1656 | rkAlpha(3,1) = -12.92820323027550917410978536602349d0 |
---|
1657 | rkAlpha(3,2) = 8.83012701892219323381861585376468d0 |
---|
1658 | |
---|
1659 | END SUBROUTINE Sdirk3a |
---|
1660 | |
---|
1661 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1662 | END SUBROUTINE SDIRK_SOA ! AND ALL ITS INTERNAL PROCEDURES |
---|
1663 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1664 | |
---|
1665 | |
---|
1666 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1667 | SUBROUTINE FUN_CHEM( T, Y, P ) |
---|
1668 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1669 | |
---|
1670 | USE KPP_ROOT_Parameters, ONLY: NVAR |
---|
1671 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
1672 | USE KPP_ROOT_Function, ONLY: Fun |
---|
1673 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
1674 | |
---|
1675 | KPP_REAL :: T, Told |
---|
1676 | KPP_REAL :: Y(NVAR), P(NVAR) |
---|
1677 | |
---|
1678 | ! Told = TIME |
---|
1679 | TIME = T |
---|
1680 | CALL Update_SUN() |
---|
1681 | CALL Update_RCONST() |
---|
1682 | |
---|
1683 | CALL Fun( Y, FIX, RCONST, P ) |
---|
1684 | |
---|
1685 | ! TIME = Told |
---|
1686 | |
---|
1687 | END SUBROUTINE FUN_CHEM |
---|
1688 | |
---|
1689 | |
---|
1690 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1691 | SUBROUTINE JAC_CHEM( T, Y, JV ) |
---|
1692 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1693 | |
---|
1694 | USE KPP_ROOT_Parameters, ONLY: NVAR, LU_NONZERO |
---|
1695 | USE KPP_ROOT_Global, ONLY: TIME, FIX, RCONST |
---|
1696 | USE KPP_ROOT_Jacobian, ONLY: Jac_SP,LU_IROW,LU_ICOL |
---|
1697 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
1698 | |
---|
1699 | KPP_REAL :: T, Told |
---|
1700 | KPP_REAL :: Y(NVAR) |
---|
1701 | #ifdef FULL_ALGEBRA |
---|
1702 | KPP_REAL :: JS(LU_NONZERO), JV(NVAR,NVAR) |
---|
1703 | INTEGER :: i, j |
---|
1704 | #else |
---|
1705 | KPP_REAL :: JV(LU_NONZERO) |
---|
1706 | #endif |
---|
1707 | |
---|
1708 | ! Told = TIME |
---|
1709 | TIME = T |
---|
1710 | CALL Update_SUN() |
---|
1711 | CALL Update_RCONST() |
---|
1712 | |
---|
1713 | #ifdef FULL_ALGEBRA |
---|
1714 | CALL Jac_SP(Y, FIX, RCONST, JS) |
---|
1715 | DO j=1,NVAR |
---|
1716 | DO j=1,NVAR |
---|
1717 | JV(i,j) = 0.0d0 |
---|
1718 | END DO |
---|
1719 | END DO |
---|
1720 | DO i=1,LU_NONZERO |
---|
1721 | JV(LU_IROW(i),LU_ICOL(i)) = JS(i) |
---|
1722 | END DO |
---|
1723 | #else |
---|
1724 | CALL Jac_SP(Y, FIX, RCONST, JV) |
---|
1725 | #endif |
---|
1726 | |
---|
1727 | ! TIME = Told |
---|
1728 | |
---|
1729 | END SUBROUTINE JAC_CHEM |
---|
1730 | |
---|
1731 | |
---|
1732 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1733 | SUBROUTINE HESS_CHEM( T, Y, Hes ) |
---|
1734 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1735 | |
---|
1736 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
1737 | |
---|
1738 | !~~~> Input variables |
---|
1739 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
---|
1740 | !~~~> Output variables |
---|
1741 | KPP_REAL, INTENT(OUT) :: Hes(NHESS) |
---|
1742 | !~~~> Local variables |
---|
1743 | KPP_REAL :: Told |
---|
1744 | |
---|
1745 | ! Told = TIME |
---|
1746 | TIME = T |
---|
1747 | CALL Update_SUN() |
---|
1748 | CALL Update_RCONST() |
---|
1749 | |
---|
1750 | CALL Hessian( Y, FIX, RCONST, Hes ) |
---|
1751 | |
---|
1752 | ! TIME = Told |
---|
1753 | |
---|
1754 | END SUBROUTINE HESS_CHEM |
---|
1755 | |
---|
1756 | END MODULE KPP_ROOT_Integrator |
---|
1757 | |
---|
1758 | |
---|