[2696] | 1 | #define MAX(a,b) ( ((a) >= (b)) ?(a):(b) ) |
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| 2 | #define MIN(b,c) ( ((b) < (c)) ?(b):(c) ) |
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| 3 | #define ABS(x) ( ((x) >= 0 ) ?(x):(-x) ) |
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| 4 | #define SQRT(d) ( pow((d),0.5) ) |
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| 5 | #define SIGN(x,y)( ( (x*y) >= 0 ) ?(x):(-x) )/* Sign transfer function */ |
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| 6 | #define MOD(A,B) (int)((A)%(B)) |
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| 7 | |
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| 8 | /* ~~~> Numerical constants */ |
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| 9 | #define ZERO (KPP_REAL)0.0 |
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| 10 | #define ONE (KPP_REAL)1.0 |
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| 11 | |
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| 12 | /* ~~~> Statistics on the work performed by the SDIRK method */ |
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| 13 | #define Nfun 1 |
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| 14 | #define Njac 2 |
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| 15 | #define Nstp 3 |
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| 16 | #define Nacc 4 |
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| 17 | #define Nrej 5 |
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| 18 | #define Ndec 6 |
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| 19 | #define Nsol 7 |
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| 20 | #define Nsng 8 |
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| 21 | #define Ntexit 1 |
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| 22 | #define Nhexit 2 |
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| 23 | #define Nhnew 3 |
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| 24 | |
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| 25 | /*~~~> SDIRK method coefficients, up to 5 stages */ |
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| 26 | #define Smax 5 |
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| 27 | |
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| 28 | int S2A=1, |
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| 29 | S2B=2, |
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| 30 | S3A=3, |
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| 31 | S4A=4, |
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| 32 | S4B=5; |
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| 33 | |
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| 34 | int sdMethod, |
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| 35 | rkS; |
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| 36 | |
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| 37 | KPP_REAL rkGamma, |
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| 38 | rkA[Smax][Smax], |
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| 39 | rkB[Smax], |
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| 40 | rkELO, |
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| 41 | rkBhat[Smax], |
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| 42 | rkC[Smax], |
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| 43 | rkD[Smax], |
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| 44 | rkE[Smax], |
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| 45 | rkTheta[Smax][Smax], |
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| 46 | rkAlpha[Smax][Smax]; |
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| 47 | |
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| 48 | /*~~~> Function headers */ |
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| 49 | //void INTEGRATE(KPP_REAL TIN, KPP_REAL TOUT, int ICNTRL_U[], KPP_REAL RCNTRL_U[], |
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| 50 | // int ISTATUS_U[], KPP_REAL RSTATUS_U[], int Ierr); |
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| 51 | void INTEGRATE(KPP_REAL TIN, KPP_REAL TOUT); |
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| 52 | int SDIRK(int N, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
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| 53 | KPP_REAL RelTol[], KPP_REAL AbsTol[], KPP_REAL RCNTRL[], int ICNTRL[], |
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| 54 | KPP_REAL RSTATUS[], int ISTATUS[]); |
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| 55 | int SDIRK_Integrator(int N, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
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| 56 | int Ierr, KPP_REAL Hstart, KPP_REAL Hmin, KPP_REAL Hmax, KPP_REAL Roundoff, |
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| 57 | KPP_REAL AbsTol[], KPP_REAL RelTol[], int ISTATUS[], KPP_REAL RSTATUS[], |
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| 58 | int ITOL, int Max_no_steps, int StartNewton, KPP_REAL NewtonTol, |
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| 59 | KPP_REAL ThetaMin, KPP_REAL FacSafe, KPP_REAL FacMin, KPP_REAL FacMax, |
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| 60 | KPP_REAL FacRej, KPP_REAL Qmin, KPP_REAL Qmax, int NewtonMaxit); |
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| 61 | void SDIRK_ErrorScale(int N, int ITOL, KPP_REAL AbsTol[], KPP_REAL RelTol[], |
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| 62 | KPP_REAL Y[], KPP_REAL SCAL[]); |
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| 63 | KPP_REAL SDIRK_ErrorNorm(int N, KPP_REAL Y[], KPP_REAL SCAL[]); |
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| 64 | int SDIRK_ErrorMsg(int code, KPP_REAL T, KPP_REAL H, int Ierr); |
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| 65 | void SDIRK_PrepareMatrix(KPP_REAL H, KPP_REAL T, KPP_REAL Y[], KPP_REAL FJAC[], |
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| 66 | int SkipJac, int SkipLU, KPP_REAL E[], int IP[], int Reject, |
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| 67 | int ISING, int ISTATUS[]); |
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| 68 | void SDIRK_Solve(KPP_REAL H, int N, KPP_REAL E[], int IP[], int ISING, |
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| 69 | KPP_REAL RHS[], int ISTATUS[]); |
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| 70 | void Sdirk4a(void); |
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| 71 | void Sdirk4b(void); |
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| 72 | void Sdirk2a(void); |
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| 73 | void Sdirk2b(void); |
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| 74 | void Sdirk3a(void); |
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| 75 | void FUN_CHEM(KPP_REAL T, KPP_REAL Y[], KPP_REAL P[]); |
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| 76 | void JAC_CHEM(KPP_REAL T, KPP_REAL Y[], KPP_REAL JV[]); |
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| 77 | void Fun(KPP_REAL Y[], KPP_REAL FIX[], KPP_REAL RCONST[], KPP_REAL Ydot[]); |
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| 78 | void Jac_SP(KPP_REAL Y[], KPP_REAL FIX[], KPP_REAL RCONST[], KPP_REAL Ydot[]); |
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| 79 | void WAXPY(int N, KPP_REAL Alpha, KPP_REAL X[], int incX, KPP_REAL Y[], int incY); |
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| 80 | void WSCAL(int N, KPP_REAL Alpha, KPP_REAL X[], int incX); |
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| 81 | KPP_REAL WLAMCH(char C); |
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| 82 | void WADD(int N, KPP_REAL Y[], KPP_REAL Z[], KPP_REAL TMP[]); |
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| 83 | void Set2Zero(int N, KPP_REAL Y[]); |
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| 84 | void KppSolve(KPP_REAL A[], KPP_REAL b[]); |
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| 85 | int KppDecomp(KPP_REAL A[]); |
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| 86 | void Update_SUN(); |
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| 87 | void Update_RCONST(); |
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| 88 | |
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| 89 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 90 | //void INTEGRATE(KPP_REAL TIN, KPP_REAL TOUT, int ICNTRL_U[], KPP_REAL RCNTRL_U[], |
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| 91 | // int ISTATUS_U[], KPP_REAL RSTATUS_U[], int Ierr_U) |
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| 92 | void INTEGRATE(KPP_REAL TIN, KPP_REAL TOUT) |
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| 93 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 94 | { |
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| 95 | |
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| 96 | /* int Ntotal = 0; *//* Used for debug option below to print the number of steps */ |
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| 97 | KPP_REAL RCNTRL[20], |
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| 98 | RSTATUS[20], |
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| 99 | T1, |
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| 100 | T2; |
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| 101 | |
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| 102 | int ICNTRL[20], |
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| 103 | ISTATUS[20], |
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| 104 | Ierr; |
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| 105 | |
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| 106 | Ierr = 0; |
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| 107 | |
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| 108 | int i; |
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| 109 | for(i=0; i<20; i++) { |
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| 110 | ICNTRL[i] = 0; |
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| 111 | RCNTRL[i] = (KPP_REAL)0.0; |
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| 112 | ISTATUS[i] = 0; |
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| 113 | RSTATUS[i] = (KPP_REAL)0.0; |
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| 114 | } /* end for */ |
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| 115 | |
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| 116 | /*~> fine-tune the integrator: */ |
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| 117 | ICNTRL[1] = 0; /* 0 - vector tolerances, 1 - scalar tolerances */ |
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| 118 | ICNTRL[5] = 0; /* starting values of N. iter.: interpolated 0), zero (1) */ |
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| 119 | |
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| 120 | ///* If optional parameters are given, and if they are >0, |
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| 121 | // then they overwrite default settings. */ |
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| 122 | //if(ICNTRL_U != NULL) { /* Check to see if ICNTRL_U is not NULL */ |
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| 123 | // for(i=0; i<20; i++) { |
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| 124 | // if(ICNTRL_U[i] > 0) { |
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| 125 | // ICNTRL[i] = ICNTRL_U[i]; |
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| 126 | // } /* end if */ |
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| 127 | // } /* end for */ |
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| 128 | //} /* end if */ |
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| 129 | // |
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| 130 | //if(RCNTRL_U != NULL) { /* Check to see if RCNTRL_U is not NULL */ |
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| 131 | // for(i=0; i<20; i++) { |
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| 132 | // if(RCNTRL_U[i] > 0) { |
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| 133 | // RCNTRL[i] = RCNTRL_U[i]; |
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| 134 | // } /* end if */ |
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| 135 | // } /* end for */ |
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| 136 | //} /* end if */ |
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| 137 | |
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| 138 | |
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| 139 | T1 = TIN; |
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| 140 | T2 = TOUT; |
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| 141 | Ierr = SDIRK( NVAR, T1, T2, VAR, RTOL, ATOL, RCNTRL, ICNTRL, RSTATUS, |
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| 142 | ISTATUS); |
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| 143 | |
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| 144 | |
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| 145 | /*~~~> Debug option: print number of steps |
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| 146 | Ntotal += ISTATUS[Nstp]; */ |
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| 147 | |
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| 148 | if(Ierr < 0) { |
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| 149 | printf("SDIRK: Unsuccessful exit at T=%f(Ierr=%d)", TIN, Ierr); |
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| 150 | } |
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| 151 | |
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| 152 | ///*if optional parameters are given for output they to return information */ |
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| 153 | //if(ISTATUS_U != NULL) { /* Check to see if ISTATUS_U is not NULL */ |
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| 154 | // for(i=0; i<20; i++) { |
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| 155 | // ISTATUS_U[i] = ISTATUS[i]; |
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| 156 | // } /* end for */ |
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| 157 | //} /* end if */ |
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| 158 | // |
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| 159 | //if(RSTATUS_U != NULL) { /* Check to see if RSTATUS_U is not NULL */ |
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| 160 | // for(i=0; i<20; i++) { |
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| 161 | // RSTATUS_U[i] = RSTATUS[i]; |
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| 162 | // } /* end for */ |
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| 163 | //} /* end if */ |
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| 164 | // |
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| 165 | //Ierr_U = Ierr; |
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| 166 | |
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| 167 | } |
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| 168 | |
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| 169 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 170 | int SDIRK(int N, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
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| 171 | KPP_REAL RelTol[], KPP_REAL AbsTol[], KPP_REAL RCNTRL[], |
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| 172 | int ICNTRL[], KPP_REAL RSTATUS[], int ISTATUS[]) |
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| 173 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 174 | |
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| 175 | Solves the system y'=F(t,y) using a Singly-Diagonally-Implicit |
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| 176 | Runge-Kutta (SDIRK) method. |
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| 177 | |
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| 178 | This implementation is based on the book and the code Sdirk4: |
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| 179 | |
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| 180 | E. Hairer and G. Wanner |
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| 181 | "Solving ODEs II. Stiff and differential-algebraic problems". |
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| 182 | Springer series in computational mathematics, Springer-Verlag, 1996. |
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| 183 | This code is based on the SDIRK4 routine in the above book. |
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| 184 | |
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| 185 | Methods: |
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| 186 | * Sdirk 2a, 2b: L-stable, 2 stages, order 2 |
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| 187 | * Sdirk 3a: L-stable, 3 stages, order 2, adjoint-invariant |
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| 188 | * Sdirk 4a, 4b: L-stable, 5 stages, order 4 |
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| 189 | |
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| 190 | (C) Adrian Sandu, July 2005 |
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| 191 | Virginia Polytechnic Institute and State University |
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| 192 | Contact: sandu@cs.vt.edu |
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| 193 | Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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| 194 | Translation F90 to C by Paul Eller and Nicholas Hobbs, July 2006 |
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| 195 | This implementation is part of KPP - the Kinetic PreProcessor |
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| 196 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 197 | |
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| 198 | ~~~> INPUT ARGUMENTS: |
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| 199 | |
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| 200 | - Y[NVAR] = vector of initial conditions (at T=Tinitial) |
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| 201 | - [Tinitial,Tfinal] = time range of integration |
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| 202 | (if Tinitial>Tfinal the integration is performed backwards in time) |
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| 203 | - RelTol, AbsTol = user precribed accuracy |
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| 204 | - SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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| 205 | returns Ydot = Y' = F(T,Y) |
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| 206 | - SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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| 207 | returns Jcb = dF/dY |
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| 208 | - ICNTRL[1:20] = integer inputs parameters |
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| 209 | - RCNTRL[1:20] = real inputs parameters |
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| 210 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 211 | |
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| 212 | ~~~> OUTPUT ARGUMENTS: |
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| 213 | |
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| 214 | - Y[NVAR] -> vector of final states (at T->Tfinal) |
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| 215 | - ISTATUS[1:20] -> integer output parameters |
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| 216 | - RSTATUS[1:20] -> real output parameters |
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| 217 | - Ierr -> job status upon return |
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| 218 | success (positive value) or |
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| 219 | failure (negative value) |
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| 220 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 221 | ~~~> INPUT PARAMETERS: |
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| 222 | Note: For input parameters equal to zero the default values of the |
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| 223 | corresponding variables are used. |
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| 224 | |
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| 225 | Note: For input parameters equal to zero the default values of the |
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| 226 | corresponding variables are used. |
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| 227 | ~~~> |
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| 228 | ICNTRL[0] = not used |
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| 229 | ICNTRL[1] = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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| 230 | = 1: AbsTol, RelTol are scalars |
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| 231 | ICNTRL[2] = Method |
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| 232 | ICNTRL[3] -> maximum number of integration steps |
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| 233 | For ICNTRL[3]=0 the default value of 100000 is used |
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| 234 | ICNTRL[4] -> maximum number of Newton iterations |
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| 235 | For ICNTRL(4)=0 the default value of 8 is used |
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| 236 | ICNTRL[5] -> starting values of Newton iterations: |
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| 237 | ICNTRL[5]=0 : starting values are interpolated (the default) |
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| 238 | ICNTRL[5]=1 : starting values are zero |
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| 239 | |
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| 240 | ~~~> Real parameters |
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| 241 | |
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| 242 | RCNTRL[0] -> Hmin, lower bound for the integration step size |
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| 243 | It is strongly recommended to keep Hmin = ZERO |
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| 244 | RCNTRL[1] -> Hmax, upper bound for the integration step size |
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| 245 | RCNTRL[2] -> Hstart, starting value for the integration step size |
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| 246 | RCNTRL[3] -> FacMin, lower bound on step decrease factor (default=0.2) |
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| 247 | RCNTRL[4] -> FacMax, upper bound on step increase factor (default=6) |
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| 248 | RCNTRL[5] -> FacRej, step decrease factor after multiple rejections |
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| 249 | (default=0.1) |
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| 250 | RCNTRL[6] -> FacSafe, by which the new step is slightly smaller |
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| 251 | than the predicted value (default=0.9) |
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| 252 | RCNTRL[7] -> ThetaMin. If Newton convergence rate smaller |
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| 253 | than ThetaMin the Jacobian is not recomputed; |
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| 254 | (default=0.001) |
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| 255 | RCNTRL[8] -> NewtonTol, stopping criterion for Newton's method |
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| 256 | (default=0.03) |
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| 257 | RCNTRL[9] -> Qmin |
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| 258 | RCNTRL[10] -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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| 259 | step size is kept constant and the LU factorization |
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| 260 | reused (default Qmin=1, Qmax=1.2) |
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| 261 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 262 | ~~~> OUTPUT PARAMETERS: |
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| 263 | Note: each call to Rosenbrock adds the current no. of fcn calls |
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| 264 | to previous value of ISTATUS(1), and similar for the other params. |
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| 265 | Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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| 266 | ISTATUS[0] = No. of function calls |
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| 267 | ISTATUS[1] = No. of jacobian calls |
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| 268 | ISTATUS[2] = No. of steps |
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| 269 | ISTATUS[3] = No. of accepted steps |
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| 270 | ISTATUS[4] = No. of rejected steps (except at the beginning) |
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| 271 | ISTATUS[5] = No. of LU decompositions |
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| 272 | ISTATUS[6] = No. of forward/backward substitutions |
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| 273 | ISTATUS[7] = No. of singular matrix decompositions |
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| 274 | RSTATUS[0] -> Texit, the time corresponding to the computed Y upon return |
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| 275 | RSTATUS[1] -> Hexit,last accepted step before return |
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| 276 | RSTATUS[2] -> Hnew, last predicted step before return |
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| 277 | For multiple restarts, use Hnew as Hstart in the following run |
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| 278 | |
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| 279 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 280 | { |
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| 281 | |
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| 282 | int Max_no_steps=0; |
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| 283 | |
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| 284 | /*~~~> Local variables */ |
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| 285 | int StartNewton; |
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| 286 | |
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| 287 | KPP_REAL Hmin=0, |
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| 288 | Hmax=0, |
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| 289 | Hstart=0, |
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| 290 | Roundoff, |
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| 291 | FacMin=0, |
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| 292 | FacMax=0, |
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| 293 | FacSafe=0, |
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| 294 | FacRej=0, |
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| 295 | ThetaMin, |
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| 296 | NewtonTol, |
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| 297 | Qmin, |
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| 298 | Qmax; |
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| 299 | |
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| 300 | int ITOL, |
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| 301 | NewtonMaxit, |
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| 302 | i, |
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| 303 | Ierr = 0; |
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| 304 | |
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| 305 | /*~~~> For Scalar tolerances (ICNTRL[1] !=0 ) the code uses AbsTol[1] and RelTol[1) |
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| 306 | For Vector tolerances (ICNTRL[1] == 0) the code uses AbsTol[1:NVAR] and RelTol[1:NVAR] */ |
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| 307 | if (ICNTRL[1]==0){ |
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| 308 | ITOL = 1; |
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| 309 | } |
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| 310 | else { |
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| 311 | ITOL = 0; |
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| 312 | } /* end if */ |
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| 313 | |
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| 314 | /*~~~> ICNTRL[3] - method selection */ |
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| 315 | |
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| 316 | switch (ICNTRL[2]) { |
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| 317 | |
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| 318 | case 0: Sdirk2a(); |
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| 319 | break; |
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| 320 | |
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| 321 | case 1: Sdirk2a(); |
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| 322 | break; |
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| 323 | |
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| 324 | case 2: Sdirk2b(); |
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| 325 | break; |
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| 326 | |
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| 327 | case 3: Sdirk3a(); |
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| 328 | break; |
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| 329 | |
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| 330 | case 4: Sdirk4a(); |
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| 331 | break; |
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| 332 | |
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| 333 | case 5: Sdirk4b(); |
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| 334 | break; |
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| 335 | |
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| 336 | default: Sdirk2a(); |
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| 337 | |
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| 338 | } /* end switch */ |
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| 339 | |
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| 340 | /*~~~> The maximum number of time steps admitted */ |
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| 341 | if (ICNTRL[3] == 0) { |
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| 342 | Max_no_steps = 200000; |
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| 343 | } |
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| 344 | else if (ICNTRL[3] > 0) { |
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| 345 | Max_no_steps = ICNTRL[3]; |
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| 346 | } |
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| 347 | else { |
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| 348 | printf("User-selected ICNTRL(4)=%d", ICNTRL[3]); |
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| 349 | SDIRK_ErrorMsg(-1,Tinitial,ZERO,Ierr); |
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| 350 | } /*end if */ |
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| 351 | |
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| 352 | /*~~~>The maximum number of Newton iterations admitted */ |
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| 353 | if(ICNTRL[4]==0) { |
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| 354 | NewtonMaxit = 8; |
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| 355 | } |
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| 356 | else { |
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| 357 | NewtonMaxit=ICNTRL[4]; |
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| 358 | if(NewtonMaxit <=0) { |
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| 359 | printf("User-selected ICNTRL(5)=%d", ICNTRL[4] ); |
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| 360 | SDIRK_ErrorMsg(-2,Tinitial,ZERO,Ierr); |
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| 361 | } |
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| 362 | } |
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| 363 | |
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| 364 | /*~~~> StartNewton: Extrapolate for starting values of Newton iterations */ |
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| 365 | if (ICNTRL[5] == 0) { |
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| 366 | StartNewton = 1; |
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| 367 | } |
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| 368 | else { |
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| 369 | StartNewton = 0; |
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| 370 | } /* end if */ |
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| 371 | |
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| 372 | /*~~~> Unit roundoff (1+Roundoff>1) */ |
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| 373 | Roundoff = WLAMCH('E'); |
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| 374 | |
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| 375 | /*~~~> Lower bound on the step size: (positive value) */ |
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| 376 | if (RCNTRL[0] == ZERO) { |
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| 377 | Hmin = ZERO; |
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| 378 | } |
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| 379 | else if (RCNTRL[0] > ZERO) { |
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| 380 | Hmin = RCNTRL[0]; |
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| 381 | } |
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| 382 | else { |
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| 383 | printf("User-selected RCNTRL[0]=%f", RCNTRL[0]); |
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| 384 | SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr); |
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| 385 | } /* end if */ |
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| 386 | |
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| 387 | /*~~~> Upper bound on the step size: (positive value) */ |
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| 388 | if (RCNTRL[1] == ZERO) { |
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| 389 | Hmax = ABS(Tfinal-Tinitial); |
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| 390 | } |
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| 391 | else if (RCNTRL[1] > ZERO) { |
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| 392 | Hmax = MIN( ABS(RCNTRL[1]), ABS(Tfinal-Tinitial) ); |
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| 393 | } |
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| 394 | else { |
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| 395 | printf("User-selected RCNTRL[1]=%f", RCNTRL[1]); |
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| 396 | SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr); |
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| 397 | } /* end if */ |
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| 398 | |
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| 399 | /*~~~> Starting step size: (positive value) */ |
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| 400 | if (RCNTRL[2] == ZERO) { |
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| 401 | Hstart = MAX( Hmin, Roundoff); |
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| 402 | } |
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| 403 | else if (RCNTRL[2] > ZERO) { |
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| 404 | Hstart = MIN( ABS(RCNTRL[2]), ABS(Tfinal-Tinitial) ); |
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| 405 | } |
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| 406 | else { |
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| 407 | printf("User-selected Hstart: RCNTRL[2]=%f", RCNTRL[2]); |
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| 408 | SDIRK_ErrorMsg(-3,Tinitial,ZERO,Ierr); |
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| 409 | } /* end if */ |
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| 410 | |
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| 411 | /*~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax */ |
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| 412 | if (RCNTRL[3] == ZERO) { |
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| 413 | FacMin = (KPP_REAL)0.2; |
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| 414 | } |
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| 415 | else if (RCNTRL[3] > ZERO) { |
---|
| 416 | FacMin = RCNTRL[3]; |
---|
| 417 | } |
---|
| 418 | else { |
---|
| 419 | printf("User-selected FacMin: RCNTRL[3]=%f", RCNTRL[3]); |
---|
| 420 | SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr); |
---|
| 421 | } /* end if */ |
---|
| 422 | |
---|
| 423 | if (RCNTRL[4] == ZERO) { |
---|
| 424 | FacMax = (KPP_REAL)10.0; |
---|
| 425 | } |
---|
| 426 | else if (RCNTRL[4] > ZERO) { |
---|
| 427 | FacMax = RCNTRL[4]; |
---|
| 428 | } |
---|
| 429 | else { |
---|
| 430 | printf("User-selected FacMax: RCNTRL[4]=%f", RCNTRL[4]); |
---|
| 431 | SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr); |
---|
| 432 | } /* end if */ |
---|
| 433 | |
---|
| 434 | /*~~~> FacRej: Factor to decrease step after 2 succesive rejections */ |
---|
| 435 | if (RCNTRL[5] == ZERO) { |
---|
| 436 | FacRej = (KPP_REAL)0.1; |
---|
| 437 | } |
---|
| 438 | else if (RCNTRL[5] > ZERO) { |
---|
| 439 | FacRej = RCNTRL[5]; |
---|
| 440 | } |
---|
| 441 | else { |
---|
| 442 | printf("User-selected FacRej: RCNTRL[5]=%f", RCNTRL[5]); |
---|
| 443 | SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr); |
---|
| 444 | } /*end if */ |
---|
| 445 | |
---|
| 446 | /* ~~~> FacSafe: Safety Factor in the computation of new step size */ |
---|
| 447 | if (RCNTRL[6] == ZERO) { |
---|
| 448 | FacSafe = (KPP_REAL)0.9; |
---|
| 449 | } |
---|
| 450 | else if (RCNTRL[6] > ZERO) { |
---|
| 451 | FacSafe = RCNTRL[6]; |
---|
| 452 | } |
---|
| 453 | else { |
---|
| 454 | printf("User-selected FacSafe: RCNTRL[6]=%f", RCNTRL[6]); |
---|
| 455 | SDIRK_ErrorMsg(-4,Tinitial,ZERO,Ierr); |
---|
| 456 | } /* end if */ |
---|
| 457 | |
---|
| 458 | /*~~~> ThetaMin: decides whether the Jacobian should be recomputed */ |
---|
| 459 | if (RCNTRL[7] == ZERO) { |
---|
| 460 | ThetaMin = (KPP_REAL)1.0e-03; |
---|
| 461 | } |
---|
| 462 | else { |
---|
| 463 | ThetaMin = RCNTRL[7]; |
---|
| 464 | } /* end if */ |
---|
| 465 | |
---|
| 466 | /*~~~> Stopping criterion for Newton's method */ |
---|
| 467 | if (RCNTRL[8] == ZERO) { |
---|
| 468 | NewtonTol = (KPP_REAL)3.0e-02; |
---|
| 469 | } |
---|
| 470 | else { |
---|
| 471 | NewtonTol = RCNTRL[8]; |
---|
| 472 | } /* end if */ |
---|
| 473 | |
---|
| 474 | /* ~~~> Qmin, Qmax: IF Qmin < Hnew/Hold < Qmax, STEP SIZE = CONST. */ |
---|
| 475 | if (RCNTRL[9] == ZERO) { |
---|
| 476 | Qmin = ONE; |
---|
| 477 | } |
---|
| 478 | else { |
---|
| 479 | Qmin = RCNTRL[9]; |
---|
| 480 | } /* end if */ |
---|
| 481 | |
---|
| 482 | if (RCNTRL[10] == ZERO) { |
---|
| 483 | Qmax = (KPP_REAL)1.2; |
---|
| 484 | } |
---|
| 485 | else { |
---|
| 486 | Qmax = RCNTRL [10]; |
---|
| 487 | } /* end if */ |
---|
| 488 | |
---|
| 489 | /* ~~~> Check if tolerances are reasonable */ |
---|
| 490 | if (ITOL == 0) { |
---|
| 491 | if ((AbsTol[0]<=ZERO || RelTol[0])<=(((KPP_REAL)10.0)*Roundoff)) { |
---|
| 492 | SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr); |
---|
| 493 | } /* end internal if */ |
---|
| 494 | } |
---|
| 495 | else { |
---|
| 496 | for (i = 0; i < N; i++) { |
---|
| 497 | if((AbsTol[i]<=ZERO)||(RelTol[i]<=((KPP_REAL)10.0)*Roundoff)){ |
---|
| 498 | SDIRK_ErrorMsg(-5,Tinitial,ZERO,Ierr); |
---|
| 499 | } /* end internal if */ |
---|
| 500 | } /* end for */ |
---|
| 501 | } /* end if */ |
---|
| 502 | |
---|
| 503 | if (Ierr < 0) { |
---|
| 504 | return Ierr; |
---|
| 505 | } /*end if */ |
---|
| 506 | |
---|
| 507 | Ierr = SDIRK_Integrator(N, Tinitial, Tfinal, Y, Ierr, Hstart, Hmin, Hmax, |
---|
| 508 | Roundoff, AbsTol, RelTol, ISTATUS, RSTATUS, ITOL, Max_no_steps, |
---|
| 509 | StartNewton, NewtonTol, ThetaMin, FacSafe, FacMin, FacMax, FacRej, |
---|
| 510 | Qmin, Qmax, NewtonMaxit); |
---|
| 511 | |
---|
| 512 | return Ierr; |
---|
| 513 | |
---|
| 514 | } /* end of main SDIRK function */ |
---|
| 515 | |
---|
| 516 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 517 | int SDIRK_Integrator(int N, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
---|
| 518 | int Ierr, KPP_REAL Hstart, KPP_REAL Hmin, KPP_REAL Hmax, KPP_REAL Roundoff, |
---|
| 519 | KPP_REAL AbsTol[], KPP_REAL RelTol[], int ISTATUS[], KPP_REAL RSTATUS[], |
---|
| 520 | int ITOL, int Max_no_steps, int StartNewton, KPP_REAL NewtonTol, |
---|
| 521 | KPP_REAL ThetaMin, KPP_REAL FacSafe, KPP_REAL FacMin, KPP_REAL FacMax, |
---|
| 522 | KPP_REAL FacRej, KPP_REAL Qmin, KPP_REAL Qmax, int NewtonMaxit) |
---|
| 523 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 524 | { |
---|
| 525 | |
---|
| 526 | /*~~~> Local variables: */ |
---|
| 527 | KPP_REAL Z[Smax][NVAR], |
---|
| 528 | G[NVAR], |
---|
| 529 | TMP[NVAR], |
---|
| 530 | NewtonRate, |
---|
| 531 | SCAL[NVAR], |
---|
| 532 | RHS[NVAR], |
---|
| 533 | T, |
---|
| 534 | H, |
---|
| 535 | Theta=0, |
---|
| 536 | Hratio, |
---|
| 537 | NewtonPredictedErr, |
---|
| 538 | Qnewton, |
---|
| 539 | Err=0, |
---|
| 540 | Fac, |
---|
| 541 | Hnew, |
---|
| 542 | Tdirection, |
---|
| 543 | NewtonIncrement=0, |
---|
| 544 | NewtonIncrementOld=0; |
---|
| 545 | |
---|
| 546 | int IER=0, |
---|
| 547 | istage, |
---|
| 548 | NewtonIter, |
---|
| 549 | IP[NVAR], |
---|
| 550 | Reject, |
---|
| 551 | FirstStep, |
---|
| 552 | SkipJac, |
---|
| 553 | SkipLU, |
---|
| 554 | NewtonDone, |
---|
| 555 | CycleTloop, |
---|
| 556 | i, |
---|
| 557 | j; |
---|
| 558 | |
---|
| 559 | #ifdef FULL_ALGEBRA |
---|
| 560 | KPP_REAL FJAC[NVAR][NVAR]; |
---|
| 561 | KPP_REAL E[NVAR][NVAR]; |
---|
| 562 | #else |
---|
| 563 | KPP_REAL FJAC[LU_NONZERO]; |
---|
| 564 | KPP_REAL E[LU_NONZERO]; |
---|
| 565 | #endif |
---|
| 566 | |
---|
| 567 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 568 | /*~~~~> Initializations */ |
---|
| 569 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 570 | T = Tinitial; |
---|
| 571 | Tdirection = SIGN(ONE, Tfinal-Tinitial); |
---|
| 572 | H = MAX(ABS(Hmin), ABS(Hstart)); |
---|
| 573 | |
---|
| 574 | if(ABS(H) <= ((KPP_REAL)10.0 * Roundoff)) { |
---|
| 575 | H = (KPP_REAL)(1.0e-06); |
---|
| 576 | } /* end if */ |
---|
| 577 | |
---|
| 578 | H = MIN(ABS(H), Hmax); |
---|
| 579 | H = SIGN(H, Tdirection); |
---|
| 580 | SkipLU = 0; |
---|
| 581 | SkipJac = 0; |
---|
| 582 | Reject = 0; |
---|
| 583 | FirstStep = 1; |
---|
| 584 | CycleTloop = 0; |
---|
| 585 | |
---|
| 586 | SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL); |
---|
| 587 | |
---|
| 588 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 589 | /*~~~> Time loop begins */ |
---|
| 590 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 591 | while((Tfinal-T)*Tdirection - Roundoff > ZERO) { /* Tloop */ |
---|
| 592 | |
---|
| 593 | /*~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition */ |
---|
| 594 | if(SkipLU == 0) { /* This time around skip the Jac update and LU */ |
---|
| 595 | SDIRK_PrepareMatrix(H, T, Y, FJAC, SkipJac, SkipLU, E, IP, |
---|
| 596 | Reject, IER, ISTATUS); |
---|
| 597 | if(IER != 0) { |
---|
| 598 | SDIRK_ErrorMsg(-8, T, H, Ierr); |
---|
| 599 | return Ierr; |
---|
| 600 | } /* end if */ |
---|
| 601 | } /* end if */ |
---|
| 602 | |
---|
| 603 | if(ISTATUS[Nstp] > Max_no_steps) { |
---|
| 604 | SDIRK_ErrorMsg(-6, T, H, Ierr); |
---|
| 605 | return Ierr; |
---|
| 606 | } /* end if */ |
---|
| 607 | |
---|
| 608 | if((T + ((KPP_REAL)0.1) * H == T) || (ABS(H) <= Roundoff)) { |
---|
| 609 | SDIRK_ErrorMsg(-7, T, H, Ierr); |
---|
| 610 | return Ierr; |
---|
| 611 | } /* end if */ |
---|
| 612 | |
---|
| 613 | /*stages*/ for(istage=0; istage < rkS; istage++) { |
---|
| 614 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 615 | /*~~~> Simplified Newton iterations */ |
---|
| 616 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 617 | |
---|
| 618 | /*~~~> Starting values for Newton iterations */ |
---|
| 619 | Set2Zero(N, &Z[istage][0]); |
---|
| 620 | |
---|
| 621 | /*~~~> Prepare the loop-independent part of the right-hand side */ |
---|
| 622 | Set2Zero(N, G); |
---|
| 623 | if(istage > 0) { |
---|
| 624 | for(j=0; j < istage; j++) { |
---|
| 625 | WAXPY(N, rkTheta[j][istage], |
---|
| 626 | &Z[j][0], 1, G, 1); |
---|
| 627 | if(StartNewton == 1) { |
---|
| 628 | WAXPY(N, rkAlpha[j][istage], |
---|
| 629 | &Z[j][0], 1, |
---|
| 630 | &Z[istage][0], 1); |
---|
| 631 | } /* end if */ |
---|
| 632 | } /* end for */ |
---|
| 633 | } /* end if */ |
---|
| 634 | |
---|
| 635 | /*~~~> Initializations for Newton iteration */ |
---|
| 636 | NewtonDone = 0; /* false */ |
---|
| 637 | Fac = (KPP_REAL)0.5; /* Step reduction factor */ |
---|
| 638 | |
---|
| 639 | /*NewtonLoop*/ for(NewtonIter=0; NewtonIter<NewtonMaxit; NewtonIter++ ) { |
---|
| 640 | |
---|
| 641 | /*~~~> Prepare the loop-dependent part of the right-hand side */ |
---|
| 642 | WADD(N, Y, &Z[istage][0], TMP); |
---|
| 643 | FUN_CHEM(T+rkC[istage]*H, TMP, RHS); |
---|
| 644 | ISTATUS[Nfun]++; |
---|
| 645 | WSCAL(N, H*rkGamma, RHS, 1); |
---|
| 646 | WAXPY(N, -ONE, &Z[istage][0], 1, RHS, 1); |
---|
| 647 | WAXPY(N, ONE, G, 1, RHS, 1 ); |
---|
| 648 | |
---|
| 649 | /*~~~> Solve the linear system */ |
---|
| 650 | SDIRK_Solve(H, N, E, IP, IER, RHS, ISTATUS); |
---|
| 651 | |
---|
| 652 | /*~~~> Check convergence of Newton iterations */ |
---|
| 653 | NewtonIncrement = SDIRK_ErrorNorm(N, RHS, SCAL); |
---|
| 654 | |
---|
| 655 | if(NewtonIter == 0) { |
---|
| 656 | Theta = ABS(ThetaMin); |
---|
| 657 | NewtonRate = (KPP_REAL)2.0; |
---|
| 658 | } |
---|
| 659 | else { |
---|
| 660 | Theta = NewtonIncrement/NewtonIncrementOld; |
---|
| 661 | |
---|
| 662 | if(Theta < (KPP_REAL)0.99) { |
---|
| 663 | NewtonRate = Theta/(ONE-Theta); |
---|
| 664 | /* Predict error at the end of Newton process */ |
---|
| 665 | NewtonPredictedErr = |
---|
| 666 | (NewtonIncrement*pow(Theta, |
---|
| 667 | (NewtonMaxit - (NewtonIter + |
---|
| 668 | 1)) / (ONE - Theta))); |
---|
| 669 | if(NewtonPredictedErr >= NewtonTol) { |
---|
| 670 | /* Non-convergence of Newton: |
---|
| 671 | predicted error too large*/ |
---|
| 672 | Qnewton = MIN((KPP_REAL)10.0, |
---|
| 673 | NewtonPredictedErr/ |
---|
| 674 | NewtonTol); |
---|
| 675 | Fac = (KPP_REAL)0.8 * pow |
---|
| 676 | (Qnewton, (-ONE / (1 |
---|
| 677 | + NewtonMaxit - |
---|
| 678 | NewtonIter + 1))); |
---|
| 679 | break; |
---|
| 680 | } /* end internal if */ |
---|
| 681 | } |
---|
| 682 | else /* Non-convergence of Newton: |
---|
| 683 | Theta too large */ { |
---|
| 684 | break; |
---|
| 685 | } /* end internal if else */ |
---|
| 686 | } /* end if else */ |
---|
| 687 | |
---|
| 688 | NewtonIncrementOld = NewtonIncrement; |
---|
| 689 | |
---|
| 690 | /* Update solution: Z(:) <-- Z(:)+RHS(:) */ |
---|
| 691 | WAXPY(N, ONE, RHS, 1, &Z[istage][0], 1); |
---|
| 692 | |
---|
| 693 | /* Check error in Newton iterations */ |
---|
| 694 | NewtonDone=(NewtonRate*NewtonIncrement<=NewtonTol); |
---|
| 695 | |
---|
| 696 | if(NewtonDone == 1) { |
---|
| 697 | break; |
---|
| 698 | } |
---|
| 699 | } /* end NewtonLoop for */ |
---|
| 700 | |
---|
| 701 | if(NewtonDone == 0) { |
---|
| 702 | /* CALL RK_ErrorMsg(-12,T,H,Ierr); */ |
---|
| 703 | H = Fac*H; |
---|
| 704 | Reject = 1; /* true */ |
---|
| 705 | SkipJac = 1;/* true */ |
---|
| 706 | SkipLU = 0;/* false */ |
---|
| 707 | CycleTloop = 1; /* cycle Tloop */ |
---|
| 708 | } /* end if */ |
---|
| 709 | |
---|
| 710 | if(CycleTloop == 1) { |
---|
| 711 | CycleTloop=0; |
---|
| 712 | break; |
---|
| 713 | } |
---|
| 714 | } /* end stages for */ |
---|
| 715 | |
---|
| 716 | if(CycleTloop==0) { |
---|
| 717 | |
---|
| 718 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 719 | /*~~~> Error estimation */ |
---|
| 720 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 721 | ISTATUS[Nstp]++; |
---|
| 722 | Set2Zero(N, TMP); |
---|
| 723 | |
---|
| 724 | for(i=0; i<rkS; i++) { |
---|
| 725 | if(rkE[i] != ZERO) { |
---|
| 726 | WAXPY(N, rkE[i], &Z[i][0], 1, TMP, 1); |
---|
| 727 | } /* end if */ |
---|
| 728 | } /* end for */ |
---|
| 729 | |
---|
| 730 | SDIRK_Solve(H, N, E, IP, IER, TMP, ISTATUS); |
---|
| 731 | Err = SDIRK_ErrorNorm(N, TMP, SCAL); |
---|
| 732 | |
---|
| 733 | /*~~~~> Computation of new step size Hnew */ |
---|
| 734 | Fac = FacSafe * pow((Err), (-ONE/rkELO)); |
---|
| 735 | Fac = MAX(FacMin, MIN(FacMax, Fac)); |
---|
| 736 | Hnew = H*Fac; |
---|
| 737 | |
---|
| 738 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 739 | /*~~~> Accept/Reject step */ |
---|
| 740 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 741 | |
---|
| 742 | if(Err < ONE) { /*~~~> Step is accepted */ |
---|
| 743 | FirstStep = 0; /* false */ |
---|
| 744 | ISTATUS[Nacc]++; |
---|
| 745 | |
---|
| 746 | /*~~~> Update time and solution */ |
---|
| 747 | T = T + H; |
---|
| 748 | |
---|
| 749 | /* Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) */ |
---|
| 750 | for(i=0; i<rkS; i++) { |
---|
| 751 | if(rkD[i] != ZERO) { |
---|
| 752 | WAXPY(N, rkD[i], &Z[i][0], 1, Y, 1); |
---|
| 753 | } /* end if */ |
---|
| 754 | } /* end for */ |
---|
| 755 | |
---|
| 756 | /*~~~> Update scaling coefficients */ |
---|
| 757 | SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL); |
---|
| 758 | |
---|
| 759 | /*~~~> Next time step */ |
---|
| 760 | Hnew = Tdirection*MIN(ABS(Hnew), Hmax); |
---|
| 761 | |
---|
| 762 | /* Last T and H */ |
---|
| 763 | RSTATUS[Ntexit] = T; |
---|
| 764 | RSTATUS[Nhexit] = H; |
---|
| 765 | RSTATUS[Nhnew] = Hnew; |
---|
| 766 | |
---|
| 767 | /* No step increase after a rejection */ |
---|
| 768 | if(Reject==1) { |
---|
| 769 | Hnew = Tdirection*MIN(ABS(Hnew), ABS(H)); |
---|
| 770 | } /* end if */ |
---|
| 771 | |
---|
| 772 | Reject = 0; /* false */ |
---|
| 773 | |
---|
| 774 | if((T+Hnew/Qmin-Tfinal)*Tdirection > ZERO) { |
---|
| 775 | H = Tfinal-T; |
---|
| 776 | } |
---|
| 777 | else { |
---|
| 778 | Hratio = Hnew/H; |
---|
| 779 | /* If step not changed too much keep Jacobian and reuse LU */ |
---|
| 780 | SkipLU = ((Theta <= ThetaMin) && (Hratio >= Qmin) && |
---|
| 781 | (Hratio <= Qmax)); |
---|
| 782 | |
---|
| 783 | if(SkipLU==0) { |
---|
| 784 | H = Hnew; |
---|
| 785 | } /* end internal if */ |
---|
| 786 | } /* end if else */ |
---|
| 787 | |
---|
| 788 | SkipJac = (Theta <= ThetaMin); |
---|
| 789 | SkipJac = 0; /* false */ |
---|
| 790 | } |
---|
| 791 | else { /*~~~> Step is rejected */ |
---|
| 792 | if((FirstStep==1) || (Reject==1)) { |
---|
| 793 | H = FacRej * H; |
---|
| 794 | } |
---|
| 795 | else { |
---|
| 796 | H = Hnew; |
---|
| 797 | } /* end internal if */ |
---|
| 798 | |
---|
| 799 | Reject = 1; |
---|
| 800 | SkipJac = 1; |
---|
| 801 | SkipLU = 0; |
---|
| 802 | |
---|
| 803 | if(ISTATUS[Nacc] >=1) { |
---|
| 804 | ISTATUS[Nrej]++; |
---|
| 805 | } /* end if */ |
---|
| 806 | } /* end if else */ |
---|
| 807 | } /* end CycleTloop if */ |
---|
| 808 | } /* end Tloop */ |
---|
| 809 | |
---|
| 810 | /* Successful return */ |
---|
| 811 | Ierr = 1; |
---|
| 812 | return Ierr; |
---|
| 813 | |
---|
| 814 | } /* end SDIRK_Integrator */ |
---|
| 815 | |
---|
| 816 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 817 | void SDIRK_ErrorScale(int N, int ITOL, KPP_REAL AbsTol[], KPP_REAL RelTol[], |
---|
| 818 | KPP_REAL Y[],KPP_REAL SCAL[]) |
---|
| 819 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 820 | { |
---|
| 821 | |
---|
| 822 | int i; |
---|
| 823 | if (ITOL == 0){ |
---|
| 824 | for (i = 0; i < NVAR; i++){ |
---|
| 825 | SCAL[i] = ONE / (AbsTol[0]+RelTol[0]*ABS(Y[i]) ); |
---|
| 826 | } /* end for */ |
---|
| 827 | } |
---|
| 828 | else { |
---|
| 829 | for (i = 0; i < NVAR; i++){ |
---|
| 830 | SCAL[i] = ONE / (AbsTol[i]+RelTol[i]*ABS(Y[i]) ); |
---|
| 831 | } /* end for */ |
---|
| 832 | } /* end if */ |
---|
| 833 | |
---|
| 834 | } /* end SDIRK_ErrorScale */ |
---|
| 835 | |
---|
| 836 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 837 | KPP_REAL SDIRK_ErrorNorm(int N, KPP_REAL Y[], KPP_REAL SCAL[]) |
---|
| 838 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 839 | { |
---|
| 840 | |
---|
| 841 | int i; |
---|
| 842 | KPP_REAL Err = ZERO; |
---|
| 843 | |
---|
| 844 | for (i = 0; i < N; i++) { |
---|
| 845 | Err = Err + pow( (Y[i]*SCAL[i]), 2); |
---|
| 846 | } /* end for */ |
---|
| 847 | |
---|
| 848 | Err = MAX( SQRT(Err/(KPP_REAL)N), (KPP_REAL)1.0e-10); |
---|
| 849 | |
---|
| 850 | return Err; |
---|
| 851 | |
---|
| 852 | } /* end SDIRK_ErrorNorm */ |
---|
| 853 | |
---|
| 854 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 855 | int SDIRK_ErrorMsg(int code, KPP_REAL T, KPP_REAL H, int Ierr) |
---|
| 856 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 857 | * Handles all error messages |
---|
| 858 | *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */ |
---|
| 859 | { |
---|
| 860 | |
---|
| 861 | Ierr = code; |
---|
| 862 | |
---|
| 863 | printf("\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); |
---|
| 864 | printf("\nForced exit from Sdirk due to the following error:\n"); |
---|
| 865 | |
---|
| 866 | switch (code) { |
---|
| 867 | |
---|
| 868 | case -1: |
---|
| 869 | printf("--> Improper value for maximal no of steps"); |
---|
| 870 | break; |
---|
| 871 | case -2: |
---|
| 872 | printf("--> Selected Rosenbrock method not implemented"); |
---|
| 873 | break; |
---|
| 874 | case -3: |
---|
| 875 | printf("--> Hmin/Hmax/Hstart must be positive"); |
---|
| 876 | break; |
---|
| 877 | case -4: |
---|
| 878 | printf("--> FacMin/FacMax/FacRej must be positive"); |
---|
| 879 | break; |
---|
| 880 | case -5: |
---|
| 881 | printf("--> Improper tolerance values"); |
---|
| 882 | break; |
---|
| 883 | case -6: |
---|
| 884 | printf("--> No of steps exceeds maximum bound"); |
---|
| 885 | break; |
---|
| 886 | case -7: |
---|
| 887 | printf("--> Step size too small (T + H/10 = T) or H < Roundoff"); |
---|
| 888 | break; |
---|
| 889 | case -8: |
---|
| 890 | printf("--> Matrix is repeatedly singular"); |
---|
| 891 | break; |
---|
| 892 | default: /* causing an error */ |
---|
| 893 | printf("Unknown Error code: %d", code); |
---|
| 894 | |
---|
| 895 | } /* end switch */ |
---|
| 896 | |
---|
| 897 | printf("\n Time = %f and H = %f", T, H ); |
---|
| 898 | printf("\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"); |
---|
| 899 | |
---|
| 900 | return code; |
---|
| 901 | |
---|
| 902 | } /* end SDIRK_ErrorMsg */ |
---|
| 903 | |
---|
| 904 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 905 | void SDIRK_PrepareMatrix(KPP_REAL H, KPP_REAL T, KPP_REAL Y[], KPP_REAL FJAC[], |
---|
| 906 | int SkipJac, int SkipLU, KPP_REAL E[], int IP[], |
---|
| 907 | int Reject, int ISING, int ISTATUS[] ) |
---|
| 908 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 909 | * Compute the matrix E = 1/(H*GAMMA)*Jac, and its decomposition |
---|
| 910 | *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 911 | { |
---|
| 912 | |
---|
| 913 | KPP_REAL HGammaInv; |
---|
| 914 | int i, j; |
---|
| 915 | int ConsecutiveSng = 0; |
---|
| 916 | ISING = 1; |
---|
| 917 | |
---|
| 918 | |
---|
| 919 | while( ISING != 0) { |
---|
| 920 | HGammaInv = ONE/(H*rkGamma); |
---|
| 921 | |
---|
| 922 | /*~~~> Compute the Jacobian */ |
---|
| 923 | if(SkipJac==0) { |
---|
| 924 | JAC_CHEM(T,Y,FJAC); |
---|
| 925 | ISTATUS[Njac]++; |
---|
| 926 | } /* end if */ |
---|
| 927 | |
---|
| 928 | #ifdef FULL_ALGEBRA |
---|
| 929 | for(j=0; j<NVAR; j++) { |
---|
| 930 | for(i=0; i<NVAR; i++) { |
---|
| 931 | E[j][i] = -FJAC[j][i]; |
---|
| 932 | } /* end for */ |
---|
| 933 | |
---|
| 934 | E[j][j] = E[j][j] + HGammaInv; |
---|
| 935 | } /* end for */ |
---|
| 936 | |
---|
| 937 | DGETRF(NVAR, NVAR, E, NVAR, IP, ISING); |
---|
| 938 | #else |
---|
| 939 | for(i=0; i<LU_NONZERO; i++) { |
---|
| 940 | E[i] = -FJAC[i]; |
---|
| 941 | } /* end for */ |
---|
| 942 | |
---|
| 943 | for(i=0; i<NVAR; i++) { |
---|
| 944 | j = LU_DIAG[i]; |
---|
| 945 | E[j]=E[j] + HGammaInv; |
---|
| 946 | } /* end for */ |
---|
| 947 | |
---|
| 948 | ISING = KppDecomp(E); |
---|
| 949 | IP[0] = 1; |
---|
| 950 | #endif |
---|
| 951 | |
---|
| 952 | ISTATUS[Ndec]++; |
---|
| 953 | |
---|
| 954 | if(ISING != 0) { |
---|
| 955 | ISTATUS[Nsng]++; |
---|
| 956 | ConsecutiveSng++; |
---|
| 957 | |
---|
| 958 | if(ConsecutiveSng >= 6) { |
---|
| 959 | return; /* Failure */ |
---|
| 960 | } /* end internal if */ |
---|
| 961 | |
---|
| 962 | H = (KPP_REAL)(0.5) * H; |
---|
| 963 | SkipJac = 1; /* true */ |
---|
| 964 | SkipLU = 0; /* false */ |
---|
| 965 | Reject = 1; /* true */ |
---|
| 966 | } /* end if */ |
---|
| 967 | } /* end while */ |
---|
| 968 | |
---|
| 969 | } /* end SDIRK_PrepareMatrix */ |
---|
| 970 | |
---|
| 971 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 972 | void SDIRK_Solve( KPP_REAL H, int N, KPP_REAL E[], int IP[], int ISING, |
---|
| 973 | KPP_REAL RHS[], int ISTATUS[] ) |
---|
| 974 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 975 | * Solves the system (H*Gamma-Jac)*x = RHS |
---|
| 976 | * using the LU decomposition of E = I - 1/(H*Gamma)*Jac |
---|
| 977 | *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 978 | { |
---|
| 979 | |
---|
| 980 | KPP_REAL HGammaInv = ONE/(H * rkGamma); |
---|
| 981 | |
---|
| 982 | WSCAL(N, HGammaInv, RHS, 1); |
---|
| 983 | |
---|
| 984 | #ifdef FULL_ALGEBRA |
---|
| 985 | DGETRS('N', N, 1, E, N, IP, RHS, N, ISING); |
---|
| 986 | #else |
---|
| 987 | KppSolve(E, RHS); |
---|
| 988 | #endif |
---|
| 989 | ISTATUS[Nsol]++; |
---|
| 990 | |
---|
| 991 | } /* end SDIRK_Solve */ |
---|
| 992 | |
---|
| 993 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 994 | void Sdirk4a() |
---|
| 995 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 996 | { |
---|
| 997 | |
---|
| 998 | sdMethod = S4A; |
---|
| 999 | |
---|
| 1000 | /* Number of stages */ |
---|
| 1001 | rkS = 5; |
---|
| 1002 | |
---|
| 1003 | /* Method Coefficients */ |
---|
| 1004 | rkGamma = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1005 | |
---|
| 1006 | rkA[0][0] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1007 | rkA[0][1] = (KPP_REAL)0.5000000000000000000000000000000000; |
---|
| 1008 | rkA[1][1] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1009 | rkA[0][2] = (KPP_REAL)0.3541539528432732316227461858529820; |
---|
| 1010 | rkA[1][2] = (KPP_REAL)(-0.5415395284327323162274618585298197e-01); |
---|
| 1011 | rkA[2][2] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1012 | rkA[0][3] = (KPP_REAL)0.8515494131138652076337791881433756e-01; |
---|
| 1013 | rkA[1][3] = (KPP_REAL)(-0.6484332287891555171683963466229754e-01); |
---|
| 1014 | rkA[2][3] = (KPP_REAL)0.7915325296404206392428857585141242e-01; |
---|
| 1015 | rkA[3][3] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1016 | rkA[0][4] = (KPP_REAL)2.100115700566932777970612055999074; |
---|
| 1017 | rkA[1][4] = (KPP_REAL)(-0.7677800284445976813343102185062276); |
---|
| 1018 | rkA[2][4] = (KPP_REAL)2.399816361080026398094746205273880; |
---|
| 1019 | rkA[3][4] = (KPP_REAL)(-2.998818699869028161397714709433394); |
---|
| 1020 | rkA[4][4] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1021 | rkB[0] = (KPP_REAL)2.100115700566932777970612055999074; |
---|
| 1022 | rkB[1] = (KPP_REAL)(-0.7677800284445976813343102185062276); |
---|
| 1023 | rkB[2] = (KPP_REAL)2.399816361080026398094746205273880; |
---|
| 1024 | rkB[3] = (KPP_REAL)(-2.998818699869028161397714709433394); |
---|
| 1025 | rkB[4] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1026 | |
---|
| 1027 | rkBhat[0] = (KPP_REAL)2.885264204387193942183851612883390; |
---|
| 1028 | rkBhat[1] = (KPP_REAL)(-0.1458793482962771337341223443218041); |
---|
| 1029 | rkBhat[2] = (KPP_REAL)2.390008682465139866479830743628554; |
---|
| 1030 | rkBhat[3] = (KPP_REAL)(-4.129393538556056674929560012190140); |
---|
| 1031 | rkBhat[4] = ZERO; |
---|
| 1032 | |
---|
| 1033 | rkC[0] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1034 | rkC[1] = (KPP_REAL)0.7666666666666666666666666666666667; |
---|
| 1035 | rkC[2] = (KPP_REAL)0.5666666666666666666666666666666667; |
---|
| 1036 | rkC[3] = (KPP_REAL)0.3661315380631796996374935266701191; |
---|
| 1037 | rkC[4] = ONE; |
---|
| 1038 | |
---|
| 1039 | /* Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1040 | rkD[0] = ZERO; |
---|
| 1041 | rkD[1] = ZERO; |
---|
| 1042 | rkD[2] = ZERO; |
---|
| 1043 | rkD[3] = ZERO; |
---|
| 1044 | rkD[4] = ONE; |
---|
| 1045 | |
---|
| 1046 | /* Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1047 | rkE[0] = (KPP_REAL)(-0.6804000050475287124787034884002302); |
---|
| 1048 | rkE[1] = (KPP_REAL)(1.558961944525217193393931795738823); |
---|
| 1049 | rkE[2] = (KPP_REAL)(-13.55893003128907927748632408763868); |
---|
| 1050 | rkE[3] = (KPP_REAL)(15.48522576958521253098585004571302); |
---|
| 1051 | rkE[4] = ONE; |
---|
| 1052 | |
---|
| 1053 | /* Local order of Err estimate */ |
---|
| 1054 | rkELO = 4; |
---|
| 1055 | |
---|
| 1056 | /* h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1057 | rkTheta[0][1] = (KPP_REAL)1.875000000000000000000000000000000; |
---|
| 1058 | rkTheta[0][2] = (KPP_REAL)1.708847304091539528432732316227462; |
---|
| 1059 | rkTheta[1][2] = (KPP_REAL)(-0.2030773231622746185852981969486824); |
---|
| 1060 | rkTheta[0][3] = (KPP_REAL)0.2680325578937783958847157206823118; |
---|
| 1061 | rkTheta[1][3] = (KPP_REAL)(-0.1828840955527181631794050728644549); |
---|
| 1062 | rkTheta[2][3] = (KPP_REAL)0.2968246986151577397160821594427966; |
---|
| 1063 | rkTheta[0][4] = (KPP_REAL)0.9096171815241460655379433581446771; |
---|
| 1064 | rkTheta[1][4] = (KPP_REAL)(-3.108254967778352416114774430509465); |
---|
| 1065 | rkTheta[2][4] = (KPP_REAL)12.33727431701306195581826123274001; |
---|
| 1066 | rkTheta[3][4] = (KPP_REAL)(-11.24557012450885560524143016037523); |
---|
| 1067 | |
---|
| 1068 | /* Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} */ |
---|
| 1069 | rkAlpha[0][1] = (KPP_REAL)2.875000000000000000000000000000000; |
---|
| 1070 | rkAlpha[0][2] = (KPP_REAL)0.8500000000000000000000000000000000; |
---|
| 1071 | rkAlpha[1][2] = (KPP_REAL)0.4434782608695652173913043478260870; |
---|
| 1072 | rkAlpha[0][3] = (KPP_REAL)0.7352046091658870564637910527807370; |
---|
| 1073 | rkAlpha[1][3] = (KPP_REAL)(-0.9525565003057343527941920657462074e-01); |
---|
| 1074 | rkAlpha[2][3] = (KPP_REAL)0.4290111305453813852259481840631738; |
---|
| 1075 | rkAlpha[0][4] = (KPP_REAL)(-16.10898993405067684831655675112808); |
---|
| 1076 | rkAlpha[1][4] = (KPP_REAL)6.559571569643355712998131800797873; |
---|
| 1077 | rkAlpha[2][4] = (KPP_REAL)(-15.90772144271326504260996815012482); |
---|
| 1078 | rkAlpha[3][4] = (KPP_REAL)25.34908987169226073668861694892683; |
---|
| 1079 | |
---|
| 1080 | rkELO = (KPP_REAL)4.0; |
---|
| 1081 | |
---|
| 1082 | } /* end Sdirk4a */ |
---|
| 1083 | |
---|
| 1084 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1085 | void Sdirk4b() |
---|
| 1086 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1087 | { |
---|
| 1088 | |
---|
| 1089 | sdMethod = S4B; |
---|
| 1090 | |
---|
| 1091 | /* Number of stages */ |
---|
| 1092 | rkS = 5; |
---|
| 1093 | |
---|
| 1094 | /* Method coefficients */ |
---|
| 1095 | rkGamma = (KPP_REAL)0.25; |
---|
| 1096 | |
---|
| 1097 | rkA[0][0] = (KPP_REAL)0.25; |
---|
| 1098 | rkA[0][1] = (KPP_REAL)0.5; |
---|
| 1099 | rkA[1][1] = (KPP_REAL)0.25; |
---|
| 1100 | rkA[0][2] = (KPP_REAL)0.34; |
---|
| 1101 | rkA[1][2] = (KPP_REAL)(-0.40e-01); |
---|
| 1102 | rkA[2][2] = (KPP_REAL)0.25; |
---|
| 1103 | rkA[0][3] = (KPP_REAL)0.2727941176470588235294117647058824; |
---|
| 1104 | rkA[1][3] = (KPP_REAL)(-0.5036764705882352941176470588235294e-01); |
---|
| 1105 | rkA[2][3] = (KPP_REAL)0.2757352941176470588235294117647059e-01; |
---|
| 1106 | rkA[3][3] = (KPP_REAL)0.25; |
---|
| 1107 | rkA[0][4] = (KPP_REAL)1.041666666666666666666666666666667; |
---|
| 1108 | rkA[1][4] = (KPP_REAL)(-1.020833333333333333333333333333333); |
---|
| 1109 | rkA[2][4] = (KPP_REAL)7.812500000000000000000000000000000; |
---|
| 1110 | rkA[3][4] = (KPP_REAL)(-7.083333333333333333333333333333333); |
---|
| 1111 | rkA[4][4] = (KPP_REAL)0.25; |
---|
| 1112 | |
---|
| 1113 | rkB[0] = (KPP_REAL)1.041666666666666666666666666666667; |
---|
| 1114 | rkB[1] = (KPP_REAL)(-1.020833333333333333333333333333333); |
---|
| 1115 | rkB[2] = (KPP_REAL)7.812500000000000000000000000000000; |
---|
| 1116 | rkB[3] = (KPP_REAL)(-7.083333333333333333333333333333333); |
---|
| 1117 | rkB[4] = (KPP_REAL)0.250000000000000000000000000000000; |
---|
| 1118 | |
---|
| 1119 | rkBhat[0] = (KPP_REAL)1.069791666666666666666666666666667; |
---|
| 1120 | rkBhat[1] = (KPP_REAL)(-0.894270833333333333333333333333333); |
---|
| 1121 | rkBhat[2] = (KPP_REAL)7.695312500000000000000000000000000; |
---|
| 1122 | rkBhat[3] = (KPP_REAL)(-7.083333333333333333333333333333333); |
---|
| 1123 | rkBhat[4] = (KPP_REAL)0.212500000000000000000000000000000; |
---|
| 1124 | |
---|
| 1125 | rkC[0] = (KPP_REAL)0.25; |
---|
| 1126 | rkC[1] = (KPP_REAL)0.75; |
---|
| 1127 | rkC[2] = (KPP_REAL)0.55; |
---|
| 1128 | rkC[3] = (KPP_REAL)0.5; |
---|
| 1129 | rkC[4] = ONE; |
---|
| 1130 | |
---|
| 1131 | /* Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1132 | rkD[0] = ZERO; |
---|
| 1133 | rkD[1] = ZERO; |
---|
| 1134 | rkD[2] = ZERO; |
---|
| 1135 | rkD[3] = ZERO; |
---|
| 1136 | rkD[4] = ONE; |
---|
| 1137 | |
---|
| 1138 | /* Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1139 | rkE[0] = (KPP_REAL)0.5750; |
---|
| 1140 | rkE[1] = (KPP_REAL)0.2125; |
---|
| 1141 | rkE[2] = (KPP_REAL)(-4.6875); |
---|
| 1142 | rkE[3] = (KPP_REAL)4.2500; |
---|
| 1143 | rkE[4] = (KPP_REAL)0.1500; |
---|
| 1144 | |
---|
| 1145 | /* Local order of Err estimate */ |
---|
| 1146 | rkELO = 4; |
---|
| 1147 | |
---|
| 1148 | /* h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1149 | rkTheta[0][1] = (KPP_REAL)2.0; |
---|
| 1150 | rkTheta[0][2] = (KPP_REAL)1.680000000000000000000000000000000; |
---|
| 1151 | rkTheta[1][2] = (KPP_REAL)(-0.1600000000000000000000000000000000); |
---|
| 1152 | rkTheta[0][3] = (KPP_REAL)1.308823529411764705882352941176471; |
---|
| 1153 | rkTheta[1][3] = (KPP_REAL)(-0.1838235294117647058823529411764706); |
---|
| 1154 | rkTheta[2][3] = (KPP_REAL)0.1102941176470588235294117647058824; |
---|
| 1155 | rkTheta[0][4] = (KPP_REAL)(-3.083333333333333333333333333333333); |
---|
| 1156 | rkTheta[1][4] = (KPP_REAL)(-4.291666666666666666666666666666667); |
---|
| 1157 | rkTheta[2][4] = (KPP_REAL)34.37500000000000000000000000000000; |
---|
| 1158 | rkTheta[3][4] = (KPP_REAL)(-28.3333333333333333333333333333); |
---|
| 1159 | |
---|
| 1160 | /* Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} */ |
---|
| 1161 | rkAlpha[0][1] = (KPP_REAL)3.0; |
---|
| 1162 | rkAlpha[0][2] = (KPP_REAL)0.8800000000000000000000000000000000; |
---|
| 1163 | rkAlpha[1][2] = (KPP_REAL)0.4400000000000000000000000000000000; |
---|
| 1164 | rkAlpha[0][3] = (KPP_REAL)0.1666666666666666666666666666666667; |
---|
| 1165 | rkAlpha[1][3] = (KPP_REAL)(-0.8333333333333333333333333333333333e-01); |
---|
| 1166 | rkAlpha[2][3] = (KPP_REAL)0.9469696969696969696969696969696970; |
---|
| 1167 | rkAlpha[0][4] = (KPP_REAL)(-6.0); |
---|
| 1168 | rkAlpha[1][4] = (KPP_REAL)9.0; |
---|
| 1169 | rkAlpha[2][4] = (KPP_REAL)(-56.81818181818181818181818181818182); |
---|
| 1170 | rkAlpha[3][4] = (KPP_REAL)54.0; |
---|
| 1171 | |
---|
| 1172 | } /* end Sdirk4b */ |
---|
| 1173 | |
---|
| 1174 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1175 | void Sdirk2a() |
---|
| 1176 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1177 | { |
---|
| 1178 | |
---|
| 1179 | sdMethod = S2A; |
---|
| 1180 | |
---|
| 1181 | /* ~~~> Number of stages */ |
---|
| 1182 | rkS = 2; |
---|
| 1183 | |
---|
| 1184 | /* ~~~> Method coefficients */ |
---|
| 1185 | rkGamma = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1186 | rkA[0][0] = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1187 | rkA[0][1] = (KPP_REAL)0.7071067811865475244008443621048490; |
---|
| 1188 | rkA[1][1] = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1189 | rkB[0] = (KPP_REAL)0.7071067811865475244008443621048490; |
---|
| 1190 | rkB[1] = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1191 | rkBhat[0] = (KPP_REAL)0.6666666666666666666666666666666667; |
---|
| 1192 | rkBhat[1] = (KPP_REAL)0.3333333333333333333333333333333333; |
---|
| 1193 | rkC[0] = (KPP_REAL)0.292893218813452475599155637895151; |
---|
| 1194 | rkC[1] = ONE; |
---|
| 1195 | |
---|
| 1196 | /* ~~~> Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1197 | rkD[0] = ZERO; |
---|
| 1198 | rkD[1] = ONE; |
---|
| 1199 | |
---|
| 1200 | /* ~~~> Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1201 | rkE[0] = (KPP_REAL)0.4714045207910316829338962414032326; |
---|
| 1202 | rkE[1] = (KPP_REAL)(-0.1380711874576983496005629080698993); |
---|
| 1203 | |
---|
| 1204 | /* ~~~> Local order of Err estimate */ |
---|
| 1205 | rkELO = 2; |
---|
| 1206 | |
---|
| 1207 | /* ~~~> h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1208 | rkTheta[0][1] = (KPP_REAL)2.414213562373095048801688724209698; |
---|
| 1209 | |
---|
| 1210 | /* ~~~> Starting value for Newton iterations */ |
---|
| 1211 | rkAlpha[0][1] = (KPP_REAL)3.414213562373095048801688724209698; |
---|
| 1212 | |
---|
| 1213 | } /* end Sdirk2a */ |
---|
| 1214 | |
---|
| 1215 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1216 | void Sdirk2b() |
---|
| 1217 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1218 | { |
---|
| 1219 | |
---|
| 1220 | sdMethod = S2B; |
---|
| 1221 | |
---|
| 1222 | /* ~~~> Number of stages */ |
---|
| 1223 | rkS = 2; |
---|
| 1224 | |
---|
| 1225 | /* ~~~> Method coefficients */ |
---|
| 1226 | rkGamma = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1227 | rkA[0][0] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1228 | rkA[0][1] = (KPP_REAL)(-0.707106781186547524400844362104849); |
---|
| 1229 | rkA[1][1] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1230 | rkB[0] = (KPP_REAL)(-0.707106781186547524400844362104849); |
---|
| 1231 | rkB[1] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1232 | rkBhat[0] = (KPP_REAL)0.6666666666666666666666666666666667; |
---|
| 1233 | rkBhat[1] = (KPP_REAL)0.3333333333333333333333333333333333; |
---|
| 1234 | rkC[0] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1235 | rkC[1] = ONE; |
---|
| 1236 | |
---|
| 1237 | /* ~~~> Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1238 | rkD[0] = ZERO; |
---|
| 1239 | rkD[1] = ONE; |
---|
| 1240 | |
---|
| 1241 | /* ~~~> Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1242 | rkE[0] = (KPP_REAL)(-0.4714045207910316829338962414032326); |
---|
| 1243 | rkE[1] = (KPP_REAL)0.8047378541243650162672295747365659; |
---|
| 1244 | |
---|
| 1245 | /* ~~~> Local order of Err estimate */ |
---|
| 1246 | rkELO = 2; |
---|
| 1247 | |
---|
| 1248 | /* ~~~> h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1249 | rkTheta[0][1] = (KPP_REAL)(-0.414213562373095048801688724209698); |
---|
| 1250 | |
---|
| 1251 | /* ~~~> Starting value for Newton iterations */ |
---|
| 1252 | rkAlpha[0][1] = (KPP_REAL)0.5857864376269049511983112757903019; |
---|
| 1253 | |
---|
| 1254 | } /* end Sdirk2b */ |
---|
| 1255 | |
---|
| 1256 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1257 | void Sdirk3a() |
---|
| 1258 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1259 | { |
---|
| 1260 | |
---|
| 1261 | sdMethod = S3A; |
---|
| 1262 | |
---|
| 1263 | /* ~~~> Number of stages */ |
---|
| 1264 | rkS = 3; |
---|
| 1265 | |
---|
| 1266 | /* ~~~> Method coefficients */ |
---|
| 1267 | rkGamma = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1268 | rkA[0][0] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1269 | rkA[0][1] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1270 | rkA[1][1] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1271 | rkA[0][2] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1272 | rkA[1][2] = (KPP_REAL)0.5773502691896257645091487805019573; |
---|
| 1273 | rkA[2][2] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1274 | rkB[0] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1275 | rkB[1] = (KPP_REAL)0.5773502691896257645091487805019573; |
---|
| 1276 | rkB[2] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1277 | rkBhat[0]= (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1278 | rkBhat[1]= (KPP_REAL)0.6477918909913548037576239837516312; |
---|
| 1279 | rkBhat[2]= (KPP_REAL)0.1408832436034580784969504064993475; |
---|
| 1280 | rkC[0] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1281 | rkC[1] = (KPP_REAL)0.4226497308103742354908512194980427; |
---|
| 1282 | rkC[2] = ONE; |
---|
| 1283 | |
---|
| 1284 | /* ~~~> Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1285 | rkD[0] = ZERO; |
---|
| 1286 | rkD[1] = ZERO; |
---|
| 1287 | rkD[2] = ONE; |
---|
| 1288 | |
---|
| 1289 | /* ~~~> Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1290 | rkE[0] = (KPP_REAL)0.9106836025229590978424821138352906; |
---|
| 1291 | rkE[1] = (KPP_REAL)(-1.244016935856292431175815447168624); |
---|
| 1292 | rkE[2] = (KPP_REAL)0.3333333333333333333333333333333333; |
---|
| 1293 | |
---|
| 1294 | /* ~~~> Local order of Err estimate */ |
---|
| 1295 | rkELO = 2; |
---|
| 1296 | |
---|
| 1297 | /* ~~~> h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1298 | rkTheta[0][1] = ONE; |
---|
| 1299 | rkTheta[0][2] = (KPP_REAL)(-1.732050807568877293527446341505872); |
---|
| 1300 | rkTheta[1][2] = (KPP_REAL)2.732050807568877293527446341505872; |
---|
| 1301 | |
---|
| 1302 | /* ~~~> Starting value for Newton iterations */ |
---|
| 1303 | rkAlpha[0][1] = (KPP_REAL)2.0; |
---|
| 1304 | rkAlpha[0][2] = (KPP_REAL)(-12.92820323027550917410978536602349); |
---|
| 1305 | rkAlpha[1][2] = (KPP_REAL)8.83012701892219323381861585376468; |
---|
| 1306 | |
---|
| 1307 | } /* end Sdirk3a */ |
---|
| 1308 | |
---|
| 1309 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1310 | void FUN_CHEM(KPP_REAL T, KPP_REAL Y[], KPP_REAL P[]) |
---|
| 1311 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1312 | { |
---|
| 1313 | |
---|
| 1314 | KPP_REAL Told; |
---|
| 1315 | |
---|
| 1316 | Told = TIME; |
---|
| 1317 | TIME = T; |
---|
| 1318 | Update_SUN(); |
---|
| 1319 | Update_RCONST(); |
---|
| 1320 | Fun( Y, FIX, RCONST, P ); |
---|
| 1321 | TIME = Told; |
---|
| 1322 | |
---|
| 1323 | |
---|
| 1324 | } /* end FUN_CHEM */ |
---|
| 1325 | |
---|
| 1326 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1327 | void JAC_CHEM(KPP_REAL T, KPP_REAL Y[], KPP_REAL JV[]) |
---|
| 1328 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1329 | { |
---|
| 1330 | |
---|
| 1331 | KPP_REAL Told; |
---|
| 1332 | |
---|
| 1333 | #ifdef FULL_ALGEBRA |
---|
| 1334 | KPP_REAL JS[LU_NONZERO]; |
---|
| 1335 | int i,j; |
---|
| 1336 | #endif |
---|
| 1337 | |
---|
| 1338 | Told = TIME; |
---|
| 1339 | TIME = T; |
---|
| 1340 | Update_SUN(); |
---|
| 1341 | Update_RCONST(); |
---|
| 1342 | |
---|
| 1343 | #ifdef FULL_ALGEBRA |
---|
| 1344 | Jac_SP( Y, FIX, RCONST, JS); |
---|
| 1345 | |
---|
| 1346 | for(j=0; j<NVAR; j++) { |
---|
| 1347 | for(i=0; i<NVAR; i++) { |
---|
| 1348 | JV[j][i] = (KPP_REAL)0.0; |
---|
| 1349 | } /* end for */ |
---|
| 1350 | } /* end for */ |
---|
| 1351 | |
---|
| 1352 | for(i=0; i<LU_NONZERO; i++) { |
---|
| 1353 | JV[LU_ICOL[i]][LU_IROW[i]] = JS[i]; |
---|
| 1354 | } /* end for */ |
---|
| 1355 | #else |
---|
| 1356 | Jac_SP(Y, FIX, RCONST, JV); |
---|
| 1357 | #endif |
---|
| 1358 | |
---|
| 1359 | TIME = Told; |
---|
| 1360 | |
---|
| 1361 | } /* end JAC_CHEM */ |
---|