/usr/share/doc/libsundials-serial-dev/examples/cvodes/parallel/cvsAdvDiff_FSA_non_p.c is in libsundials-serial-dev 2.5.0-3+b3.
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* -----------------------------------------------------------------
* $Revision: 1.1 $
* $Date: 2007/10/25 20:03:30 $
* -----------------------------------------------------------------
* Programmer(s): Scott D. Cohen, Alan C. Hindmarsh, George D. Byrne,
* and Radu Serban @ LLNL
* -----------------------------------------------------------------
* Example problem:
*
* The following is a simple example problem, with the program for
* its solution by CVODES. The problem is the semi-discrete form of
* the advection-diffusion equation in 1-D:
* du/dt = q1 * d^2 u / dx^2 + q2 * du/dx
* on the interval 0 <= x <= 2, and the time interval 0 <= t <= 5.
* Homogeneous Dirichlet boundary conditions are posed, and the
* initial condition is:
* u(x,y,t=0) = x(2-x)exp(2x).
* The PDE is discretized on a uniform grid of size MX+2 with
* central differencing, and with boundary values eliminated,
* leaving an ODE system of size NEQ = MX.
* This program solves the problem with the option for nonstiff
* systems: ADAMS method and functional iteration.
* It uses scalar relative and absolute tolerances.
* Output is printed at t = .5, 1.0, ..., 5.
* Run statistics (optional outputs) are printed at the end.
*
* Optionally, CVODES can compute sensitivities with respect to the
* problem parameters q1 and q2.
* Any of three sensitivity methods (SIMULTANEOUS, STAGGERED, and
* STAGGERED1) can be used and sensitivities may be included in the
* error test or not (error control set on FULL or PARTIAL,
* respectively).
*
* Execution:
*
* Note: This version uses MPI for user routines, and the CVODES
* solver. In what follows, N is the number of processors,
* N = NPEX*NPEY (see constants below) and it is assumed that
* the MPI script mpirun is used to run a parallel
* application.
* If no sensitivities are desired:
* % mpirun -np N cvsAdvDiff_FSA_non_p -nosensi
* If sensitivities are to be computed:
* % mpirun -np N cvsAdvDiff_FSA_non_p -sensi sensi_meth err_con
* where sensi_meth is one of {sim, stg, stg1} and err_con is one of
* {t, f}.
* -----------------------------------------------------------------
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <cvodes/cvodes.h>
#include <nvector/nvector_parallel.h>
#include <sundials/sundials_types.h>
#include <sundials/sundials_math.h>
#include <mpi.h>
/* Problem Constants */
#define XMAX RCONST(2.0) /* domain boundary */
#define MX 10 /* mesh dimension */
#define NEQ MX /* number of equations */
#define ATOL RCONST(1.e-5) /* scalar absolute tolerance */
#define T0 RCONST(0.0) /* initial time */
#define T1 RCONST(0.5) /* first output time */
#define DTOUT RCONST(0.5) /* output time increment */
#define NOUT 10 /* number of output times */
#define NP 2
#define NS 2
#define ZERO RCONST(0.0)
/* Type : UserData
contains problem parameters, grid constants, work array. */
typedef struct {
realtype *p;
realtype dx;
int npes, my_pe;
MPI_Comm comm;
realtype z[100];
} *UserData;
/* Prototypes of user-supplied functins */
static int f(realtype t, N_Vector u, N_Vector udot, void *user_data);
/* Prototypes of private functions */
static void ProcessArgs(int argc, char *argv[], int my_pe,
booleantype *sensi, int *sensi_meth, booleantype *err_con);
static void WrongArgs(int my_pe, char *name);
static void SetIC(N_Vector u, realtype dx, long int my_length, long int my_base);
static void PrintOutput(void *cvode_mem, int my_pe, realtype t, N_Vector u);
static void PrintOutputS(int my_pe, N_Vector *uS);
static void PrintFinalStats(void *cvode_mem, booleantype sensi);
static int check_flag(void *flagvalue, char *funcname, int opt, int id);
/*
*--------------------------------------------------------------------
* MAIN PROGRAM
*--------------------------------------------------------------------
*/
int main(int argc, char *argv[])
{
realtype dx, reltol, abstol, t, tout;
N_Vector u;
UserData data;
void *cvode_mem;
int iout, flag, my_pe, npes;
long int local_N, nperpe, nrem, my_base;
realtype *pbar;
int is, *plist;
N_Vector *uS;
booleantype sensi, err_con;
int sensi_meth;
MPI_Comm comm;
u = NULL;
data = NULL;
cvode_mem = NULL;
pbar = NULL;
plist = NULL;
uS = NULL;
/* Get processor number, total number of pe's, and my_pe. */
MPI_Init(&argc, &argv);
comm = MPI_COMM_WORLD;
MPI_Comm_size(comm, &npes);
MPI_Comm_rank(comm, &my_pe);
/* Process arguments */
ProcessArgs(argc, argv, my_pe, &sensi, &sensi_meth, &err_con);
/* Set local vector length. */
nperpe = NEQ/npes;
nrem = NEQ - npes*nperpe;
local_N = (my_pe < nrem) ? nperpe+1 : nperpe;
my_base = (my_pe < nrem) ? my_pe*local_N : my_pe*nperpe + nrem;
/* USER DATA STRUCTURE */
data = (UserData) malloc(sizeof *data); /* Allocate data memory */
data->p = NULL;
if(check_flag((void *)data, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
data->comm = comm;
data->npes = npes;
data->my_pe = my_pe;
data->p = (realtype *) malloc(NP * sizeof(realtype));
if(check_flag((void *)data->p, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
dx = data->dx = XMAX/((realtype)(MX+1));
data->p[0] = RCONST(1.0);
data->p[1] = RCONST(0.5);
/* INITIAL STATES */
u = N_VNew_Parallel(comm, local_N, NEQ); /* Allocate u vector */
if(check_flag((void *)u, "N_VNew_Parallel", 0, my_pe)) MPI_Abort(comm, 1);
SetIC(u, dx, local_N, my_base); /* Initialize u vector */
/* TOLERANCES */
reltol = ZERO; /* Set the tolerances */
abstol = ATOL;
/* CVODE_CREATE & CVODE_MALLOC */
cvode_mem = CVodeCreate(CV_ADAMS, CV_FUNCTIONAL);
if(check_flag((void *)cvode_mem, "CVodeCreate", 0, my_pe)) MPI_Abort(comm, 1);
flag = CVodeSetUserData(cvode_mem, data);
if(check_flag(&flag, "CVodeSetUserData", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVodeInit(cvode_mem, f, T0, u);
if(check_flag(&flag, "CVodeInit", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVodeSStolerances(cvode_mem, reltol, abstol);
if(check_flag(&flag, "CVodeSStolerances", 1, my_pe)) MPI_Abort(comm, 1);
if (my_pe == 0) {
printf("\n1-D advection-diffusion equation, mesh size =%3d \n", MX);
printf("\nNumber of PEs = %3d \n",npes);
}
if(sensi) {
plist = (int *) malloc(NS * sizeof(int));
if(check_flag((void *)plist, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
for(is=0; is<NS; is++)
plist[is] = is; /* sensitivity w.r.t. i-th parameter */
pbar = (realtype *) malloc(NS * sizeof(realtype));
if(check_flag((void *)pbar, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
for(is=0; is<NS; is++) pbar[is] = data->p[plist[is]];
uS = N_VCloneVectorArray_Parallel(NS, u);
if(check_flag((void *)uS, "N_VCloneVectorArray_Parallel", 0, my_pe))
MPI_Abort(comm, 1);
for(is=0;is<NS;is++)
N_VConst(ZERO,uS[is]);
flag = CVodeSensInit1(cvode_mem, NS, sensi_meth, NULL, uS);
if(check_flag(&flag, "CVodeSensInit1", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVodeSensEEtolerances(cvode_mem);
if(check_flag(&flag, "CVodeSensEEtolerances", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVodeSetSensErrCon(cvode_mem, err_con);
if(check_flag(&flag, "CVodeSetSensErrCon", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVodeSetSensDQMethod(cvode_mem, CV_CENTERED, ZERO);
if(check_flag(&flag, "CVodeSetSensDQMethod", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVodeSetSensParams(cvode_mem, data->p, pbar, plist);
if(check_flag(&flag, "CVodeSetSensParams", 1, my_pe)) MPI_Abort(comm, 1);
if(my_pe == 0) {
printf("Sensitivity: YES ");
if(sensi_meth == CV_SIMULTANEOUS)
printf("( SIMULTANEOUS +");
else
if(sensi_meth == CV_STAGGERED) printf("( STAGGERED +");
else printf("( STAGGERED1 +");
if(err_con) printf(" FULL ERROR CONTROL )");
else printf(" PARTIAL ERROR CONTROL )");
}
} else {
if(my_pe == 0) printf("Sensitivity: NO ");
}
/* In loop over output points, call CVode, print results, test for error */
if(my_pe == 0) {
printf("\n\n");
printf("============================================================\n");
printf(" T Q H NST Max norm \n");
printf("============================================================\n");
}
for (iout=1, tout=T1; iout <= NOUT; iout++, tout += DTOUT) {
flag = CVode(cvode_mem, tout, u, &t, CV_NORMAL);
if(check_flag(&flag, "CVode", 1, my_pe)) break;
PrintOutput(cvode_mem, my_pe, t, u);
if (sensi) {
flag = CVodeGetSens(cvode_mem, &t, uS);
if(check_flag(&flag, "CVodeGetSens", 1, my_pe)) break;
PrintOutputS(my_pe, uS);
}
if (my_pe == 0)
printf("------------------------------------------------------------\n");
}
/* Print final statistics */
if (my_pe == 0)
PrintFinalStats(cvode_mem, sensi);
/* Free memory */
N_VDestroy(u); /* Free the u vector */
if (sensi)
N_VDestroyVectorArray(uS, NS); /* Free the uS vectors */
free(data->p); /* Free the p vector */
free(data); /* Free block of UserData */
CVodeFree(&cvode_mem); /* Free the CVODES problem memory */
free(pbar);
if(sensi) free(plist);
MPI_Finalize();
return(0);
}
/*
*--------------------------------------------------------------------
* FUNCTIONS CALLED BY CVODES
*--------------------------------------------------------------------
*/
/*
* f routine. Compute f(t,u).
*/
static int f(realtype t, N_Vector u, N_Vector udot, void *user_data)
{
realtype ui, ult, urt, hordc, horac, hdiff, hadv;
realtype *udata, *dudata, *z;
realtype dx;
int i;
int npes, my_pe, my_length, my_pe_m1, my_pe_p1, last_pe, my_last;
UserData data;
MPI_Status status;
MPI_Comm comm;
udata = NV_DATA_P(u);
dudata = NV_DATA_P(udot);
/* Extract needed problem constants from data */
data = (UserData) user_data;
dx = data->dx;
hordc = data->p[0]/(dx*dx);
horac = data->p[1]/(RCONST(2.0)*dx);
/* Extract parameters for parallel computation. */
comm = data->comm;
npes = data->npes; /* Number of processes. */
my_pe = data->my_pe; /* Current process number. */
my_length = NV_LOCLENGTH_P(u); /* Number of local elements of u. */
z = data->z;
/* Compute related parameters. */
my_pe_m1 = my_pe - 1;
my_pe_p1 = my_pe + 1;
last_pe = npes - 1;
my_last = my_length - 1;
/* Store local segment of u in the working array z. */
for (i = 1; i <= my_length; i++)
z[i] = udata[i - 1];
/* Pass needed data to processes before and after current process. */
if (my_pe != 0)
MPI_Send(&z[1], 1, PVEC_REAL_MPI_TYPE, my_pe_m1, 0, comm);
if (my_pe != last_pe)
MPI_Send(&z[my_length], 1, PVEC_REAL_MPI_TYPE, my_pe_p1, 0, comm);
/* Receive needed data from processes before and after current process. */
if (my_pe != 0)
MPI_Recv(&z[0], 1, PVEC_REAL_MPI_TYPE, my_pe_m1, 0, comm, &status);
else z[0] = ZERO;
if (my_pe != last_pe)
MPI_Recv(&z[my_length+1], 1, PVEC_REAL_MPI_TYPE, my_pe_p1, 0, comm,
&status);
else z[my_length + 1] = ZERO;
/* Loop over all grid points in current process. */
for (i=1; i<=my_length; i++) {
/* Extract u at x_i and two neighboring points */
ui = z[i];
ult = z[i-1];
urt = z[i+1];
/* Set diffusion and advection terms and load into udot */
hdiff = hordc*(ult - RCONST(2.0)*ui + urt);
hadv = horac*(urt - ult);
dudata[i-1] = hdiff + hadv;
}
return(0);
}
/*
*--------------------------------------------------------------------
* PRIVATE FUNCTIONS
*--------------------------------------------------------------------
*/
/*
* Process and verify arguments to cvsfwdnonx_p.
*/
static void ProcessArgs(int argc, char *argv[], int my_pe,
booleantype *sensi, int *sensi_meth, booleantype *err_con)
{
*sensi = FALSE;
*sensi_meth = -1;
*err_con = FALSE;
if (argc < 2) WrongArgs(my_pe, argv[0]);
if (strcmp(argv[1],"-nosensi") == 0)
*sensi = FALSE;
else if (strcmp(argv[1],"-sensi") == 0)
*sensi = TRUE;
else
WrongArgs(my_pe, argv[0]);
if (*sensi) {
if (argc != 4)
WrongArgs(my_pe, argv[0]);
if (strcmp(argv[2],"sim") == 0)
*sensi_meth = CV_SIMULTANEOUS;
else if (strcmp(argv[2],"stg") == 0)
*sensi_meth = CV_STAGGERED;
else if (strcmp(argv[2],"stg1") == 0)
*sensi_meth = CV_STAGGERED1;
else
WrongArgs(my_pe, argv[0]);
if (strcmp(argv[3],"t") == 0)
*err_con = TRUE;
else if (strcmp(argv[3],"f") == 0)
*err_con = FALSE;
else
WrongArgs(my_pe, argv[0]);
}
}
static void WrongArgs(int my_pe, char *name)
{
if (my_pe == 0) {
printf("\nUsage: %s [-nosensi] [-sensi sensi_meth err_con]\n",name);
printf(" sensi_meth = sim, stg, or stg1\n");
printf(" err_con = t or f\n");
}
MPI_Finalize();
exit(0);
}
/*
* Set initial conditions in u vector
*/
static void SetIC(N_Vector u, realtype dx, long int my_length,
long int my_base)
{
int i;
long int iglobal;
realtype x;
realtype *udata;
/* Set pointer to data array and get local length of u. */
udata = NV_DATA_P(u);
my_length = NV_LOCLENGTH_P(u);
/* Load initial profile into u vector */
for (i=1; i<=my_length; i++) {
iglobal = my_base + i;
x = iglobal*dx;
udata[i-1] = x*(XMAX - x)*EXP(2.0*x);
}
}
/*
* Print current t, step count, order, stepsize, and max norm of solution
*/
static void PrintOutput(void *cvode_mem, int my_pe, realtype t, N_Vector u)
{
long int nst;
int qu, flag;
realtype hu, umax;
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1, my_pe);
flag = CVodeGetLastOrder(cvode_mem, &qu);
check_flag(&flag, "CVodeGetLastOrder", 1, my_pe);
flag = CVodeGetLastStep(cvode_mem, &hu);
check_flag(&flag, "CVodeGetLastStep", 1, my_pe);
umax = N_VMaxNorm(u);
if (my_pe == 0) {
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%8.3Le %2d %8.3Le %5ld\n", t,qu,hu,nst);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%8.3le %2d %8.3le %5ld\n", t,qu,hu,nst);
#else
printf("%8.3e %2d %8.3e %5ld\n", t,qu,hu,nst);
#endif
printf(" Solution ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le \n", umax);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le \n", umax);
#else
printf("%12.4e \n", umax);
#endif
}
}
/*
* Print max norm of sensitivities
*/
static void PrintOutputS(int my_pe, N_Vector *uS)
{
realtype smax;
smax = N_VMaxNorm(uS[0]);
if (my_pe == 0) {
printf(" Sensitivity 1 ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le \n", smax);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le \n", smax);
#else
printf("%12.4e \n", smax);
#endif
}
smax = N_VMaxNorm(uS[1]);
if (my_pe == 0) {
printf(" Sensitivity 2 ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le \n", smax);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le \n", smax);
#else
printf("%12.4e \n", smax);
#endif
}
}
/*
* Print some final statistics located in the iopt array
*/
static void PrintFinalStats(void *cvode_mem, booleantype sensi)
{
long int nst;
long int nfe, nsetups, nni, ncfn, netf;
long int nfSe, nfeS, nsetupsS, nniS, ncfnS, netfS;
int flag;
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1, 0);
flag = CVodeGetNumRhsEvals(cvode_mem, &nfe);
check_flag(&flag, "CVodeGetNumRhsEvals", 1, 0);
flag = CVodeGetNumLinSolvSetups(cvode_mem, &nsetups);
check_flag(&flag, "CVodeGetNumLinSolvSetups", 1, 0);
flag = CVodeGetNumErrTestFails(cvode_mem, &netf);
check_flag(&flag, "CVodeGetNumErrTestFails", 1, 0);
flag = CVodeGetNumNonlinSolvIters(cvode_mem, &nni);
check_flag(&flag, "CVodeGetNumNonlinSolvIters", 1, 0);
flag = CVodeGetNumNonlinSolvConvFails(cvode_mem, &ncfn);
check_flag(&flag, "CVodeGetNumNonlinSolvConvFails", 1, 0);
if (sensi) {
flag = CVodeGetSensNumRhsEvals(cvode_mem, &nfSe);
check_flag(&flag, "CVodeGetSensNumRhsEvals", 1, 0);
flag = CVodeGetNumRhsEvalsSens(cvode_mem, &nfeS);
check_flag(&flag, "CVodeGetNumRhsEvalsSens", 1, 0);
flag = CVodeGetSensNumLinSolvSetups(cvode_mem, &nsetupsS);
check_flag(&flag, "CVodeGetSensNumLinSolvSetups", 1, 0);
flag = CVodeGetSensNumErrTestFails(cvode_mem, &netfS);
check_flag(&flag, "CVodeGetSensNumErrTestFails", 1, 0);
flag = CVodeGetSensNumNonlinSolvIters(cvode_mem, &nniS);
check_flag(&flag, "CVodeGetSensNumNonlinSolvIters", 1, 0);
flag = CVodeGetSensNumNonlinSolvConvFails(cvode_mem, &ncfnS);
check_flag(&flag, "CVodeGetSensNumNonlinSolvConvFails", 1, 0);
}
printf("\nFinal Statistics\n\n");
printf("nst = %5ld\n\n", nst);
printf("nfe = %5ld\n", nfe);
printf("netf = %5ld nsetups = %5ld\n", netf, nsetups);
printf("nni = %5ld ncfn = %5ld\n", nni, ncfn);
if(sensi) {
printf("\n");
printf("nfSe = %5ld nfeS = %5ld\n", nfSe, nfeS);
printf("netfs = %5ld nsetupsS = %5ld\n", netfS, nsetupsS);
printf("nniS = %5ld ncfnS = %5ld\n", nniS, ncfnS);
}
}
/*
* Check function return value...
* opt == 0 means SUNDIALS function allocates memory so check if
* returned NULL pointer
* opt == 1 means SUNDIALS function returns a flag so check if
* flag >= 0
* opt == 2 means function allocates memory so check if returned
* NULL pointer
*/
static int check_flag(void *flagvalue, char *funcname, int opt, int id)
{
int *errflag;
/* Check if SUNDIALS function returned NULL pointer - no memory allocated */
if (opt == 0 && flagvalue == NULL) {
fprintf(stderr, "\nSUNDIALS_ERROR(%d): %s() failed - returned NULL pointer\n\n",
id, funcname);
return(1); }
/* Check if flag < 0 */
else if (opt == 1) {
errflag = (int *) flagvalue;
if (*errflag < 0) {
fprintf(stderr, "\nSUNDIALS_ERROR(%d): %s() failed with flag = %d\n\n",
id, funcname, *errflag);
return(1); }}
/* Check if function returned NULL pointer - no memory allocated */
else if (opt == 2 && flagvalue == NULL) {
fprintf(stderr, "\nMEMORY_ERROR(%d): %s() failed - returned NULL pointer\n\n",
id, funcname);
return(1); }
return(0);
}
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