/usr/share/doc/libsundials-serial-dev/examples/cvodes/parallel/cvsAdvDiff_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 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 = d^2 u / dx^2 + .5 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 the following:
* u(x,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.
*
* This version uses MPI for user routines.
* Execute with Number of Processors = N, with 1 <= N <= MX.
* -----------------------------------------------------------------
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <cvodes/cvodes.h> /* prototypes for CVODE fcts. */
#include <nvector/nvector_parallel.h> /* definition of N_Vector and macros */
#include <sundials/sundials_types.h> /* definition of realtype */
#include <sundials/sundials_math.h> /* definition of EXP */
#include <mpi.h> /* MPI constants and types */
/* Problem Constants */
#define ZERO RCONST(0.0)
#define XMAX RCONST(2.0) /* domain boundary */
#define MX 10 /* mesh dimension */
#define NEQ MX /* number of equations */
#define ATOL RCONST(1.0e-5) /* scalar absolute tolerance */
#define T0 ZERO /* 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 */
/* Type : UserData
contains grid constants, parallel machine parameters, work array. */
typedef struct {
realtype dx, hdcoef, hacoef;
int npes, my_pe;
MPI_Comm comm;
realtype z[100];
} *UserData;
/* Private Helper Functions */
static void SetIC(N_Vector u, realtype dx, long int my_length,
long int my_base);
static void PrintIntro(int npes);
static void PrintData(realtype t, realtype umax, long int nst);
static void PrintFinalStats(void *cvode_mem);
/* Functions Called by the Solver */
static int f(realtype t, N_Vector u, N_Vector udot, void *user_data);
/* Private function to check function return values */
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, umax;
N_Vector u;
UserData data;
void *cvode_mem;
int iout, flag, my_pe, npes;
long int local_N, nperpe, nrem, my_base, nst;
MPI_Comm comm;
u = NULL;
data = NULL;
cvode_mem = 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);
/* 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;
data = (UserData) malloc(sizeof *data); /* Allocate data memory */
if(check_flag((void *)data, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
data->comm = comm;
data->npes = npes;
data->my_pe = my_pe;
u = N_VNew_Parallel(comm, local_N, NEQ); /* Allocate u vector */
if(check_flag((void *)u, "N_VNew", 0, my_pe)) MPI_Abort(comm, 1);
reltol = ZERO; /* Set the tolerances */
abstol = ATOL;
dx = data->dx = XMAX/((realtype)(MX+1)); /* Set grid coefficients in data */
data->hdcoef = RCONST(1.0)/(dx*dx);
data->hacoef = RCONST(0.5)/(RCONST(2.0)*dx);
SetIC(u, dx, local_N, my_base); /* Initialize u vector */
/* Call CVodeCreate to create the solver memory and specify the
* Adams-Moulton LMM and the use of a functional iteration */
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);
/* Call CVodeInit to initialize the integrator memory and specify the
* user's right hand side function in u'=f(t,u), the inital time T0, and
* the initial dependent variable vector u. */
flag = CVodeInit(cvode_mem, f, T0, u);
if(check_flag(&flag, "CVodeInit", 1, my_pe)) return(1);
/* Call CVodeSStolerances to specify the scalar relative tolerance
* and scalar absolute tolerances */
flag = CVodeSStolerances(cvode_mem, reltol, abstol);
if (check_flag(&flag, "CVodeSStolerances", 1, my_pe)) return(1);
if (my_pe == 0) PrintIntro(npes);
umax = N_VMaxNorm(u);
if (my_pe == 0) {
t = T0;
PrintData(t, umax, 0);
}
/* In loop over output points, call CVode, print results, test for error */
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;
umax = N_VMaxNorm(u);
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1, my_pe);
if (my_pe == 0) PrintData(t, umax, nst);
}
if (my_pe == 0)
PrintFinalStats(cvode_mem); /* Print some final statistics */
N_VDestroy_Parallel(u); /* Free the u vector */
CVodeFree(&cvode_mem); /* Free the integrator memory */
free(data); /* Free user data */
MPI_Finalize();
return(0);
}
/************************ Private Helper Functions ***********************/
/* 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(RCONST(2.0)*x);
}
}
/* Print problem introduction */
static void PrintIntro(int npes)
{
printf("\n 1-D advection-diffusion equation, mesh size =%3d \n", MX);
printf("\n Number of PEs = %3d \n\n", npes);
return;
}
/* Print data */
static void PrintData(realtype t, realtype umax, long int nst)
{
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("At t = %4.2Lf max.norm(u) =%14.6Le nst =%4ld \n", t, umax, nst);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("At t = %4.2f max.norm(u) =%14.6le nst =%4ld \n", t, umax, nst);
#else
printf("At t = %4.2f max.norm(u) =%14.6e nst =%4ld \n", t, umax, nst);
#endif
return;
}
/* Print some final statistics located in the iopt array */
static void PrintFinalStats(void *cvode_mem)
{
long int nst, nfe, nni, ncfn, netf;
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 = 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);
printf("\nFinal Statistics: \n\n");
printf("nst = %-6ld nfe = %-6ld ", nst, nfe);
printf("nni = %-6ld ncfn = %-6ld netf = %ld\n \n", nni, ncfn, netf);
}
/***************** Function Called by the Solver ***********************/
/* 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;
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;
hordc = data->hdcoef;
horac = data->hacoef;
/* 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);
}
/* 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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