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/*@@
@file RK87.c
@date Sun May 26 03:47:15 2002
@author Peter Diener (based on RK45.c by Ian Hawke)
@desc
RK87 following P. J. Prince and J. R. Dormand
Journal of Computational and Applied Mathematics, volume 7, no 1, 1981
@enddesc
@version $Header$
@@*/
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "ExternalVariables.h"
#include "Operators.h"
static const char *rcsid = "$Header$";
CCTK_FILEVERSION(CactusBase_MoL_RK87_c);
/********************************************************************
********************* Local Data Types ***********************
********************************************************************/
/********************************************************************
********************* Local Routine Prototypes *********************
********************************************************************/
/********************************************************************
***************** Scheduled Routine Prototypes *********************
********************************************************************/
void MoL_RK87Add(CCTK_ARGUMENTS);
/********************************************************************
********************* Other Routine Prototypes *********************
********************************************************************/
/********************************************************************
********************* Local Data *****************************
********************************************************************/
/********************************************************************
********************* External Routines **********************
********************************************************************/
/*@@
@routine MoL_RK87Add
@date Sun May 26 03:50:44 2002
@author Peter Diener (based on MoL_RK45Add by Ian Hawke)
@desc
Performs a single step of a Runge-Kutta 87 type time
integration, storing the error estimate.
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
void MoL_RK87Add(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_INT arraydim;
static CCTK_INT scratchspace_firstindex = -99;
CCTK_INT var, scratchstep;
CCTK_INT totalsize;
static const CCTK_REAL beta_array[12][12] = {
{ 1.0/18.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 1.0/48.0, 1.0/16.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 1.0/32.0, 0.0, 3.0/32.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 5.0/16.0, 0.0, -75.0/64.0, 75.0/64.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 3.0/80.0, 0.0, 0.0, 3.0/16.0, 3.0/20.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 29443841.0/614563906.0, 0.0, 0.0, 77736538.0/692538347.0, -28693883.0/1125000000.0, 23124283.0/1800000000.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 16016141.0/946692911.0, 0.0, 0.0, 61564180.0/158732637.0, 22789713.0/633445777.0, 545815736.0/2771057229.0, -180193667.0/1043307555.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 39632708.0/573591083.0, 0.0, 0.0, -433636366.0/683701615.0, -421739975.0/2616292301.0, 100302831.0/723423059.0, 790204164.0/839813087.0, 800635310.0/3783071287.0, 0.0, 0.0, 0.0, 0.0 },
{ 246121993.0/1340847787.0, 0.0, 0.0, -37695042795.0/15268766246.0, -309121744.0/1061227803.0, -12992083.0/490766935.0, 6005943493.0/2108947869.0, 393006217.0/1396673457.0, 123872331.0/1001029789.0, 0.0, 0.0, 0.0 },
{ -1028468189.0/846180014.0, 0.0, 0.0, 8478235783.0/508512852.0, 1311729495.0/1432422823.0, -10304129995.0/1701304382.0, -48777925059.0/3047939560.0, 15336726248.0/1032824649.0, -45442868181.0/3398467696.0, 3065993473.0/597172653.0, 0.0, 0.0 },
{ 185892177.0/718116043.0, 0.0, 0.0, -3185094517.0/667107341.0, -477755414.0/1098053517.0, -703635378.0/230739211.0, 5731566787.0/1027545527.0, 5232866602.0/850066563.0, -4093664535.0/808688257.0, 3962137247.0/1805957418.0, 65686358.0/487910083.0, 0.0 },
{ 403863854.0/491063109.0, 0.0, 0.0, -5068492393.0/434740067.0, -411421997.0/543043805.0, 652783627.0/914296604.0, 11173962825.0/925320556.0, -13158990841.0/6184727034.0, 3936647629.0/1978049680.0, -160528059.0/685178525.0, 248638103.0/1413531060.0, 0.0 }
};
static const CCTK_REAL gamma_array[13] =
{ 14005451.0/335480064.0,
0.0,
0.0,
0.0,
0.0,
-59238493.0/1068277825.0,
181606767.0/758867731.0,
561292985.0/797845732.0,
-1041891430.0/1371343529.0,
760417239.0/1151165299.0,
118820643.0/751138087.0,
-528747749.0/2220607170.0,
1.0/4.0
};
static const CCTK_REAL gammastar_array[13] =
{ 13451932.0/455176623.0,
0.0,
0.0,
0.0,
0.0,
-808719846.0/976000145.0,
1757004468.0/5645159321.0,
656045339.0/265891186.0,
-3867574721.0/1518517206.0,
465885868.0/322736535.0,
53011238.0/667516719.0,
2.0/45.0,
0.0
};
totalsize = 1;
for (arraydim = 0; arraydim < cctk_dim; arraydim++)
{
totalsize *= cctk_ash[arraydim];
}
if (scratchspace_firstindex == -99)
{
scratchspace_firstindex = CCTK_FirstVarIndex("MOL::SCRATCHSPACE");
}
/* Real GFs */
/* First store (dt times) the rhs in the scratch array. */
for (var = 0; var < MoLNumEvolvedVariables; var++)
{
int const step = MoL_Intermediate_Steps - (*MoL_Intermediate_Step);
int const scratchvarindex =
scratchspace_firstindex + MoL_Num_Evolved_Vars * step + var;
int const nsrcs = 1;
CCTK_INT const srcs[] = {RHSVariableIndex[var]};
CCTK_INT const tls[] = {0};
CCTK_REAL const facts[] = {(*Original_Delta_Time) / cctkGH->cctk_timefac};
MoL_LinearCombination(cctkGH,
scratchvarindex, 1.0,
srcs, tls, facts, nsrcs);
}
for (var = 0; var < MoLNumEvolvedVariables; var++)
{
int const error_firstindex = CCTK_FirstVarIndex("MOL::ERRORESTIMATE");
int const step = MoL_Intermediate_Steps - (*MoL_Intermediate_Step);
if (*MoL_Intermediate_Step - 1)
{
int const nsrcs = step + 2;
CCTK_INT srcs[nsrcs];
CCTK_INT tls[nsrcs];
CCTK_REAL facts[nsrcs];
srcs[0] = EvolvedVariableIndex[var];
tls[0] = 1;
facts[0] = 1.0;
for (scratchstep = 0; scratchstep < step + 1; scratchstep++)
{
int const scratchvarindex =
scratchspace_firstindex + MoL_Num_Evolved_Vars * scratchstep + var;
srcs [scratchstep+1] = scratchvarindex;
tls [scratchstep+1] = 0;
facts[scratchstep+1] = beta_array[step][scratchstep];
}
MoL_LinearCombination(cctkGH,
EvolvedVariableIndex[var], 0.0,
srcs, tls, facts, nsrcs);
}
else
{
{
int const nsrcs = 14;
CCTK_INT srcs[nsrcs];
CCTK_INT tls[nsrcs];
CCTK_REAL facts[nsrcs];
srcs[0] = EvolvedVariableIndex[var];
tls[0] = 1;
facts[0] = 1.0;
for (scratchstep = 0; scratchstep < 13; scratchstep++)
{
int const scratchvarindex =
scratchspace_firstindex + MoL_Num_Evolved_Vars * scratchstep + var;
srcs [scratchstep+1] = scratchvarindex;
tls [scratchstep+1] = 0;
facts[scratchstep+1] = gamma_array[scratchstep];
}
MoL_LinearCombination(cctkGH,
EvolvedVariableIndex[var], 0.0,
srcs, tls, facts, nsrcs);
}
{
int const nsrcs = 13;
CCTK_INT srcs[nsrcs];
CCTK_INT tls[nsrcs];
CCTK_REAL facts[nsrcs];
for (scratchstep = 0; scratchstep < 13; scratchstep++)
{
int const scratchvarindex =
scratchspace_firstindex + MoL_Num_Evolved_Vars * scratchstep + var;
srcs [scratchstep] = scratchvarindex;
tls [scratchstep] = 0;
facts[scratchstep] =
gamma_array[scratchstep] - gammastar_array[scratchstep];
}
MoL_LinearCombination(cctkGH,
error_firstindex + var, 0.0,
srcs, tls, facts, nsrcs);
}
}
}
/* Real arrays */
CCTK_WARN(0, "Peter has been too lazy to write the RK87 routine "
"out for array variables. Better send him an email...");
return;
}
/********************************************************************
********************* Local Routines *************************
********************************************************************/
|
