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/*@@
@file RK45.c
@date Sun May 26 03:47:15 2002
@author Ian Hawke
@desc
RK45 following Forsythe, Malcolm and Moler
(Computer Methods for Mathematical Computations).
@enddesc
@version $Header$
@@*/
#include <assert.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "ExternalVariables.h"
static const char *rcsid = "$Header$";
CCTK_FILEVERSION(CactusBase_MoL_RK45_c);
/********************************************************************
********************* Local Data Types ***********************
********************************************************************/
/********************************************************************
********************* Local Routine Prototypes *********************
********************************************************************/
/********************************************************************
***************** Scheduled Routine Prototypes *********************
********************************************************************/
void MoL_RK45Add(CCTK_ARGUMENTS);
/********************************************************************
********************* Other Routine Prototypes *********************
********************************************************************/
/********************************************************************
********************* Local Data *****************************
********************************************************************/
/********************************************************************
********************* External Routines **********************
********************************************************************/
/*@@
@routine MoL_RK45Add
@date Sun May 26 03:50:44 2002
@author Ian Hawke
@desc
Performs a single step of a Runge-Kutta 45 type time
integration, storing the error estimate.
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
void MoL_RK45Add(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_REAL * restrict UpdateVar;
CCTK_REAL const * restrict RHSVar;
CCTK_REAL * restrict ScratchVar;
CCTK_REAL * restrict ErrorVar;
CCTK_REAL const * restrict OldVar;
CCTK_REAL beta, gamma, gamma_error;
/* Fehlberg coefficients */
static const CCTK_REAL beta_array_F[5][5] = {
{ 0.25, 0.0, 0.0, 0.0, 0.0 },
{ 0.09375, 0.28125, 0.0, 0.0, 0.0 },
{ 0.879380974055530268548020027310, -3.27719617660446062812926718252, 3.32089212562585343650432407829, 0.0, 0.0 },
{ 2.03240740740740740740740740741, -8.0, 7.17348927875243664717348927875, -0.205896686159844054580896686160, 0.0 },
{ -0.296296296296296296296296296296, 2.0, -1.38167641325536062378167641326, 0.452972709551656920077972709552, -0.275 }
};
static const CCTK_REAL gamma_array_F[6] =
{ 0.118518518518518518518518518519,
0.0,
0.518986354775828460038986354776,
0.506131490342016657806131490342,
-0.18,
0.0363636363636363636363636363636
};
static const CCTK_REAL gammastar_array_F[6] =
{ 0.115740740740740740740740740741,
0.0,
0.548927875243664717348927875244,
0.535331384015594541910331384016,
-0.2,
0.0
};
/* Cash-Karp coefficients */
static const CCTK_REAL beta_array_CK[5][5] = {
{ 1.0/5.0, 0.0, 0.0, 0.0, 0.0, },
{ 3.0/40.0, 9.0/40.0, 0.0, 0.0, 0.0, },
{ 3.0/10.0, -9.0/10.0, 6.0/5.0, 0.0, 0.0, },
{ -11.0/54.0, 5.0/2.0, -70.0/27.0, 35.0/27.0, 0.0, },
{ 1631.0/55296.0, 175.0/512.0, 575.0/13824.0, 44275.0/110592.0, 253.0/4096.0, },
};
static const CCTK_REAL gamma_array_CK[6] = {
37.0/378.0,
0.0,
250.0/621.0,
125.0/594.0,
0.0,
512.0/1771.0,
};
static const CCTK_REAL gammastar_array_CK[6] = {
2825.0/27648.0,
0.0,
18575.0/48384.0,
13525.0/55296.0,
277.0/14336.0,
1.0/4.0,
};
const CCTK_REAL (* restrict beta_array)[5];
const CCTK_REAL * restrict gamma_array;
const CCTK_REAL * restrict gammastar_array;
if (CCTK_EQUALS(ODE_Method, "RK45"))
{
beta_array = beta_array_F;
gamma_array = gamma_array_F;
gammastar_array = gammastar_array_F;
}
else if (CCTK_EQUALS(ODE_Method, "RK45CK"))
{
beta_array = beta_array_CK;
gamma_array = gamma_array_CK;
gammastar_array = gammastar_array_CK;
}
else
{
CCTK_WARN (0, "internal error");
}
int totalsize = 1;
for (int arraydim = 0; arraydim < cctk_dim; arraydim++)
{
totalsize *= cctk_lsh[arraydim];
}
/* Real GFs */
/* First store (dt times) the rhs in the scratch array. */
for (int var = 0; var < MoLNumEvolvedVariables; var++)
{
const CCTK_REAL tmp = (*Original_Delta_Time) / cctkGH->cctk_timefac;
UpdateVar = (CCTK_REAL *)CCTK_VarDataPtrI(cctkGH, 0,
EvolvedVariableIndex[var]);
RHSVar = (CCTK_REAL const *)CCTK_VarDataPtrI(cctkGH, 0,
RHSVariableIndex[var]);
ScratchVar = (CCTK_REAL*)CCTK_VarDataPtrI(cctkGH, 0,
CCTK_FirstVarIndex("MOL::SCRATCHSPACE")
+ var
+ MoL_Num_Evolved_Vars *
(MoL_Intermediate_Steps -
(*MoL_Intermediate_Step)));
#pragma omp parallel for
for (int index = 0; index < totalsize; index++)
{
ScratchVar[index] = tmp * RHSVar[index];
}
}
for (int var = 0; var < MoLNumEvolvedVariables; var++)
{
OldVar = (CCTK_REAL const *)CCTK_VarDataPtrI(cctkGH, 1,
EvolvedVariableIndex[var]);
UpdateVar = (CCTK_REAL *)CCTK_VarDataPtrI(cctkGH, 0,
EvolvedVariableIndex[var]);
RHSVar = (CCTK_REAL const *)CCTK_VarDataPtrI(cctkGH, 0,
CCTK_FirstVarIndex("MOL::SCRATCHSPACE")
+ var
+ MoL_Num_Evolved_Vars *
(MoL_Intermediate_Steps -
(*MoL_Intermediate_Step)));
ErrorVar = (CCTK_REAL*)CCTK_VarDataPtrI(cctkGH, 0,
CCTK_FirstVarIndex("MOL::ERRORESTIMATE")
+ var);
if (*MoL_Intermediate_Step - 1)
{
#pragma omp parallel for
for (int index = 0; index < totalsize; index++)
{
UpdateVar[index] = OldVar[index];
}
for (int scratchstep = 0;
scratchstep < MoL_Intermediate_Steps - (*MoL_Intermediate_Step) + 1;
scratchstep++)
{
ScratchVar = (CCTK_REAL*)CCTK_VarDataPtrI(cctkGH, 0,
CCTK_FirstVarIndex("MOL::SCRATCHSPACE")
+ var
+ MoL_Num_Evolved_Vars * scratchstep);
beta = beta_array[MoL_Intermediate_Steps - (*MoL_Intermediate_Step)][scratchstep];
if ( (beta > MoL_Tiny)||(beta < -MoL_Tiny) )
{
#pragma omp parallel for
for (int index = 0; index < totalsize; index++)
{
UpdateVar[index] += beta * ScratchVar[index];
}
}
}
}
else
{
#pragma omp parallel for
for (int index = 0; index < totalsize; index++)
{
UpdateVar[index] = OldVar[index];
ErrorVar[index] = 0;
}
for (int scratchstep = 0; scratchstep < 6; scratchstep++)
{
ScratchVar = (CCTK_REAL*)CCTK_VarDataPtrI(cctkGH, 0,
CCTK_FirstVarIndex("MOL::SCRATCHSPACE")
+ var
+ MoL_Num_Evolved_Vars * scratchstep);
gamma = gamma_array[scratchstep];
gamma_error = gamma - gammastar_array[scratchstep];
if ( (gamma > MoL_Tiny)||(gamma < -MoL_Tiny) )
{
#pragma omp parallel for
for (int index = 0; index < totalsize; index++)
{
UpdateVar[index] += gamma * ScratchVar[index];
ErrorVar[index] += gamma_error * ScratchVar[index];
}
}
}
}
}
/* Real arrays */
int arrayscratchlocation = 0;
for (int var = 0; var < MoLNumEvolvedArrayVariables; var++)
{
CCTK_WARN(0, "Ian has been too lazy to write the RK45 routine "
"out for array variables. Better send him an email...");
}
return;
}
/********************************************************************
********************* Local Routines *************************
********************************************************************/
|
