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* -----------------------------------------------------------------
* $Revision: 1.4 $
* $Date: 2010/12/01 23:00:48 $
* -----------------------------------------------------------------
* Programmer(s): S. D. Cohen, A. C. Hindmarsh, Radu Serban,
* and M. R. Wittman @ LLNL
* -----------------------------------------------------------------
* Example problem:
*
* An ODE system is generated from the following 2-species diurnal
* kinetics advection-diffusion PDE system in 2 space dimensions:
*
* dc(i)/dt = Kh*(d/dx)^2 c(i) + V*dc(i)/dx + (d/dy)(Kv(y)*dc(i)/dy)
* + Ri(c1,c2,t) for i = 1,2, where
* R1(c1,c2,t) = -q1*c1*c3 - q2*c1*c2 + 2*q3(t)*c3 + q4(t)*c2 ,
* R2(c1,c2,t) = q1*c1*c3 - q2*c1*c2 - q4(t)*c2 ,
* Kv(y) = Kv0*exp(y/5) ,
* Kh, V, Kv0, q1, q2, and c3 are constants, and q3(t) and q4(t)
* vary diurnally. The problem is posed on the square
* 0 <= x <= 20, 30 <= y <= 50 (all in km),
* with homogeneous Neumann boundary conditions, and for time t in
* 0 <= t <= 86400 sec (1 day).
* The PDE system is treated by central differences on a uniform
* mesh, with simple polynomial initial profiles.
*
* The problem is solved by CVODES on NPE processors, treated
* as a rectangular process grid of size NPEX by NPEY, with
* NPE = NPEX*NPEY. Each processor contains a subgrid of size
* MXSUB by MYSUB of the (x,y) mesh. Thus the actual mesh sizes
* are MX = MXSUB*NPEX and MY = MYSUB*NPEY, and the ODE system size
* is neq = 2*MX*MY.
*
* The solution with CVODES is done with the BDF/GMRES method (i.e.
* using the CVSPGMR linear solver) and the block-diagonal part of
* the Newton matrix as a left preconditioner. A copy of the
* block-diagonal part of the Jacobian is saved and conditionally
* reused within the Precond routine.
*
* Performance data and sampled solution values are printed at
* selected output times, and all performance counters are printed
* on completion.
*
* 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 paralles
* application.
* If no sensitivities are desired:
* % mpirun -np N cvsDiurnal_FSA_kry_p -nosensi
* If sensitivities are to be computed:
* % mpirun -np N cvsDiurnal_FSA_kry_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> /* main CVODES header file */
#include <cvodes/cvodes_spgmr.h> /* defs. for CVSPGMR fcts. and constants */
#include <nvector/nvector_parallel.h> /* defs of par. NVECTOR fcts. and macros */
#include <sundials/sundials_dense.h> /* generic DENSE solver used in prec. */
#include <sundials/sundials_math.h> /* contains macros SQR and EXP */
#include <sundials/sundials_types.h> /* def. of realtype */
#include <mpi.h>
/* Problem Constants */
#define NVARS 2 /* number of species */
#define C1_SCALE RCONST(1.0e6) /* coefficients in initial profiles */
#define C2_SCALE RCONST(1.0e12)
#define T0 RCONST(0.0) /* initial time */
#define NOUT 12 /* number of output times */
#define TWOHR RCONST(7200.0) /* number of seconds in two hours */
#define HALFDAY RCONST(4.32e4) /* number of seconds in a half day */
#define PI RCONST(3.1415926535898) /* pi */
#define XMIN RCONST(0.0) /* grid boundaries in x */
#define XMAX RCONST(20.0)
#define YMIN RCONST(30.0) /* grid boundaries in y */
#define YMAX RCONST(50.0)
#define NPEX 2 /* no. PEs in x direction of PE array */
#define NPEY 2 /* no. PEs in y direction of PE array */
/* Total no. PEs = NPEX*NPEY */
#define MXSUB 5 /* no. x points per subgrid */
#define MYSUB 5 /* no. y points per subgrid */
#define MX (NPEX*MXSUB) /* MX = number of x mesh points */
#define MY (NPEY*MYSUB) /* MY = number of y mesh points */
/* Spatial mesh is MX by MY */
/* CVodeInit Constants */
#define RTOL RCONST(1.0e-5) /* scalar relative tolerance */
#define FLOOR RCONST(100.0) /* value of C1 or C2 at which tols. */
/* change from relative to absolute */
#define ATOL (RTOL*FLOOR) /* scalar absolute tolerance */
/* Sensitivity constants */
#define NP 8 /* number of problem parameters */
#define NS 2 /* number of sensitivities */
#define ZERO RCONST(0.0)
/* User-defined matrix accessor macro: IJth */
/* IJth is defined in order to write code which indexes into small dense
matrices with a (row,column) pair, where 1 <= row,column <= NVARS.
IJth(a,i,j) references the (i,j)th entry of the small matrix realtype **a,
where 1 <= i,j <= NVARS. The small matrix routines in sundials_dense.h
work with matrices stored by column in a 2-dimensional array. In C,
arrays are indexed starting at 0, not 1. */
#define IJth(a,i,j) (a[j-1][i-1])
/* Types : UserData and PreconData
contain problem parameters, problem constants, preconditioner blocks,
pivot arrays, grid constants, and processor indices, as
well as data needed for preconditioning */
typedef struct {
realtype *p;
realtype q4, om, dx, dy, hdco, haco, vdco;
realtype uext[NVARS*(MXSUB+2)*(MYSUB+2)];
long int my_pe, isubx, isuby, nvmxsub, nvmxsub2;
MPI_Comm comm;
/* For preconditioner */
realtype **P[MXSUB][MYSUB], **Jbd[MXSUB][MYSUB];
long int *pivot[MXSUB][MYSUB];
} *UserData;
/* Functions Called by the CVODES Solver */
static int f(realtype t, N_Vector u, N_Vector udot, void *user_data);
static int Precond(realtype tn, N_Vector u, N_Vector fu,
booleantype jok, booleantype *jcurPtr,
realtype gamma, void *user_data,
N_Vector vtemp1, N_Vector vtemp2, N_Vector vtemp3);
static int PSolve(realtype tn, N_Vector u, N_Vector fu,
N_Vector r, N_Vector z,
realtype gamma, realtype delta,
int lr, void *user_data, N_Vector vtemp);
/* Private Helper 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 InitUserData(int my_pe, MPI_Comm comm, UserData data);
static void FreeUserData(UserData data);
static void SetInitialProfiles(N_Vector u, UserData data);
static void BSend(MPI_Comm comm, int my_pe, long int isubx,
long int isuby, long int dsizex,
long int dsizey, realtype udata[]);
static void BRecvPost(MPI_Comm comm, MPI_Request request[], int my_pe,
long int isubx, long int isuby,
long int dsizex, long int dsizey,
realtype uext[], realtype buffer[]);
static void BRecvWait(MPI_Request request[], long int isubx, long int isuby,
long int dsizex, realtype uext[], realtype buffer[]);
static void ucomm(realtype t, N_Vector u, UserData data);
static void fcalc(realtype t, realtype udata[], realtype dudata[], UserData data);
static void PrintOutput(void *cvode_mem, int my_pe, MPI_Comm comm,
realtype t, N_Vector u);
static void PrintOutputS(int my_pe, MPI_Comm comm, 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 abstol, reltol, t, tout;
N_Vector u;
UserData data;
void *cvode_mem;
int iout, flag, my_pe, npes;
long int neq, local_N;
MPI_Comm comm;
realtype *pbar;
int is, *plist;
N_Vector *uS;
booleantype sensi, err_con;
int sensi_meth;
u = NULL;
data = NULL;
cvode_mem = NULL;
pbar = NULL;
plist = NULL;
uS = NULL;
/* Set problem size neq */
neq = NVARS*MX*MY;
/* Get processor number and total number of pe's */
MPI_Init(&argc, &argv);
comm = MPI_COMM_WORLD;
MPI_Comm_size(comm, &npes);
MPI_Comm_rank(comm, &my_pe);
if (npes != NPEX*NPEY) {
if (my_pe == 0)
fprintf(stderr,
"\nMPI_ERROR(0): npes = %d is not equal to NPEX*NPEY = %d\n\n",
npes, NPEX*NPEY);
MPI_Finalize();
return(1);
}
/* Process arguments */
ProcessArgs(argc, argv, my_pe, &sensi, &sensi_meth, &err_con);
/* Set local length */
local_N = NVARS*MXSUB*MYSUB;
/* Allocate and load user data block; allocate preconditioner block */
data = (UserData) malloc(sizeof *data);
if (check_flag((void *)data, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
data->p = NULL;
data->p = (realtype *) malloc(NP*sizeof(realtype));
if (check_flag((void *)data->p, "malloc", 2, my_pe)) MPI_Abort(comm, 1);
InitUserData(my_pe, comm, data);
/* Allocate u, and set initial values and tolerances */
u = N_VNew_Parallel(comm, local_N, neq);
if (check_flag((void *)u, "N_VNew_Parallel", 0, my_pe)) MPI_Abort(comm, 1);
SetInitialProfiles(u, data);
abstol = ATOL; reltol = RTOL;
/* Create CVODES object, set optional input, allocate memory */
cvode_mem = CVodeCreate(CV_BDF, CV_NEWTON);
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 = CVodeSetMaxNumSteps(cvode_mem, 2000);
if (check_flag(&flag, "CVodeSetMaxNumSteps", 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);
/* Attach linear solver CVSPGMR */
flag = CVSpgmr(cvode_mem, PREC_LEFT, 0);
if (check_flag(&flag, "CVSpgmr", 1, my_pe)) MPI_Abort(comm, 1);
flag = CVSpilsSetPreconditioner(cvode_mem, Precond, PSolve);
if (check_flag(&flag, "CVSpilsSetPreconditioner", 1, my_pe)) MPI_Abort(comm, 1);
if(my_pe == 0)
printf("\n2-species diurnal advection-diffusion problem\n");
/* Sensitivity-related settings */
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;
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 ");
}
if (my_pe == 0) {
printf("\n\n");
printf("========================================================================\n");
printf(" T Q H NST Bottom left Top right \n");
printf("========================================================================\n");
}
/* In loop over output points, call CVode, print results, test for error */
for (iout=1, tout = TWOHR; iout <= NOUT; iout++, tout += TWOHR) {
flag = CVode(cvode_mem, tout, u, &t, CV_NORMAL);
if (check_flag(&flag, "CVode", 1, my_pe)) break;
PrintOutput(cvode_mem, my_pe, comm, t, u);
if (sensi) {
flag = CVodeGetSens(cvode_mem, &t, uS);
if (check_flag(&flag, "CVodeGetSens", 1, my_pe)) break;
PrintOutputS(my_pe, comm, uS);
}
if (my_pe == 0)
printf("------------------------------------------------------------------------\n");
}
/* Print final statistics */
if (my_pe == 0) PrintFinalStats(cvode_mem, sensi);
/* Free memory */
N_VDestroy_Parallel(u);
if (sensi) {
N_VDestroyVectorArray_Parallel(uS, NS);
free(plist);
free(pbar);
}
FreeUserData(data);
CVodeFree(&cvode_mem);
MPI_Finalize();
return(0);
}
/*
*--------------------------------------------------------------------
* FUNCTIONS CALLED BY CVODES
*--------------------------------------------------------------------
*/
/*
* f routine. Evaluate f(t,y). First call ucomm to do communication of
* subgrid boundary data into uext. Then calculate f by a call to fcalc.
*/
static int f(realtype t, N_Vector u, N_Vector udot, void *user_data)
{
realtype *udata, *dudata;
UserData data;
udata = NV_DATA_P(u);
dudata = NV_DATA_P(udot);
data = (UserData) user_data;
/* Call ucomm to do inter-processor communicaiton */
ucomm (t, u, data);
/* Call fcalc to calculate all right-hand sides */
fcalc (t, udata, dudata, data);
return(0);
}
/*
* Preconditioner setup routine. Generate and preprocess P.
*/
static int Precond(realtype tn, N_Vector u, N_Vector fu,
booleantype jok, booleantype *jcurPtr,
realtype gamma, void *user_data,
N_Vector vtemp1, N_Vector vtemp2, N_Vector vtemp3)
{
realtype c1, c2, cydn, cyup, diag, ydn, yup, q4coef, dely, verdco, hordco;
realtype **(*P)[MYSUB], **(*Jbd)[MYSUB];
long int *(*pivot)[MYSUB], ier, nvmxsub, offset;
int lx, ly, jx, jy, isubx, isuby;
realtype *udata, **a, **j;
UserData data;
realtype Q1, Q2, C3, A3, A4, KH, VEL, KV0;
/* Make local copies of pointers in user_data, pointer to u's data,
and PE index pair */
data = (UserData) user_data;
P = data->P;
Jbd = data->Jbd;
pivot = data->pivot;
udata = NV_DATA_P(u);
isubx = data->isubx; isuby = data->isuby;
nvmxsub = data->nvmxsub;
/* Load problem coefficients and parameters */
Q1 = data->p[0];
Q2 = data->p[1];
C3 = data->p[2];
A3 = data->p[3];
A4 = data->p[4];
KH = data->p[5];
VEL = data->p[6];
KV0 = data->p[7];
if (jok) { /* jok = TRUE: Copy Jbd to P */
for (ly = 0; ly < MYSUB; ly++)
for (lx = 0; lx < MXSUB; lx++)
denseCopy(Jbd[lx][ly], P[lx][ly], NVARS, NVARS);
*jcurPtr = FALSE;
} else { /* jok = FALSE: Generate Jbd from scratch and copy to P */
/* Make local copies of problem variables, for efficiency */
q4coef = data->q4;
dely = data->dy;
verdco = data->vdco;
hordco = data->hdco;
/* Compute 2x2 diagonal Jacobian blocks (using q4 values
computed on the last f call). Load into P. */
for (ly = 0; ly < MYSUB; ly++) {
jy = ly + isuby*MYSUB;
ydn = YMIN + (jy - RCONST(0.5))*dely;
yup = ydn + dely;
cydn = verdco*EXP(RCONST(0.2)*ydn);
cyup = verdco*EXP(RCONST(0.2)*yup);
diag = -(cydn + cyup + RCONST(2.0)*hordco);
for (lx = 0; lx < MXSUB; lx++) {
jx = lx + isubx*MXSUB;
offset = lx*NVARS + ly*nvmxsub;
c1 = udata[offset];
c2 = udata[offset+1];
j = Jbd[lx][ly];
a = P[lx][ly];
IJth(j,1,1) = (-Q1*C3 - Q2*c2) + diag;
IJth(j,1,2) = -Q2*c1 + q4coef;
IJth(j,2,1) = Q1*C3 - Q2*c2;
IJth(j,2,2) = (-Q2*c1 - q4coef) + diag;
denseCopy(j, a, NVARS, NVARS);
}
}
*jcurPtr = TRUE;
}
/* Scale by -gamma */
for (ly = 0; ly < MYSUB; ly++)
for (lx = 0; lx < MXSUB; lx++)
denseScale(-gamma, P[lx][ly], NVARS, NVARS);
/* Add identity matrix and do LU decompositions on blocks in place */
for (lx = 0; lx < MXSUB; lx++) {
for (ly = 0; ly < MYSUB; ly++) {
denseAddIdentity(P[lx][ly], NVARS);
ier = denseGETRF(P[lx][ly], NVARS, NVARS, pivot[lx][ly]);
if (ier != 0) return(1);
}
}
return(0);
}
/*
* Preconditioner solve routine
*/
static int PSolve(realtype tn, N_Vector u, N_Vector fu,
N_Vector r, N_Vector z,
realtype gamma, realtype delta,
int lr, void *user_data, N_Vector vtemp)
{
realtype **(*P)[MYSUB];
long int *(*pivot)[MYSUB], nvmxsub;
int lx, ly;
realtype *zdata, *v;
UserData data;
/* Extract the P and pivot arrays from user_data */
data = (UserData) user_data;
P = data->P;
pivot = data->pivot;
/* Solve the block-diagonal system Px = r using LU factors stored
in P and pivot data in pivot, and return the solution in z.
First copy vector r to z. */
N_VScale(RCONST(1.0), r, z);
nvmxsub = data->nvmxsub;
zdata = NV_DATA_P(z);
for (lx = 0; lx < MXSUB; lx++) {
for (ly = 0; ly < MYSUB; ly++) {
v = &(zdata[lx*NVARS + ly*nvmxsub]);
denseGETRS(P[lx][ly], NVARS, pivot[lx][ly], v);
}
}
return(0);
}
/*
*--------------------------------------------------------------------
* PRIVATE FUNCTIONS
*--------------------------------------------------------------------
*/
/*
* Process and verify arguments to cvsfwdkryx_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 user data.
*/
static void InitUserData(int my_pe, MPI_Comm comm, UserData data)
{
long int isubx, isuby;
int lx, ly;
realtype KH, VEL, KV0;
/* Set problem parameters */
data->p[0] = RCONST(1.63e-16); /* Q1 coeffs. q1, q2, c3 */
data->p[1] = RCONST(4.66e-16); /* Q2 */
data->p[2] = RCONST(3.7e16); /* C3 */
data->p[3] = RCONST(22.62); /* A3 coeff. in expression for q3(t) */
data->p[4] = RCONST(7.601); /* A4 coeff. in expression for q4(t) */
KH = data->p[5] = RCONST(4.0e-6); /* KH horizontal diffusivity Kh */
VEL = data->p[6] = RCONST(0.001); /* VEL advection velocity V */
KV0 = data->p[7] = RCONST(1.0e-8); /* KV0 coeff. in Kv(z) */
/* Set problem constants */
data->om = PI/HALFDAY;
data->dx = (XMAX-XMIN)/((realtype)(MX-1));
data->dy = (YMAX-YMIN)/((realtype)(MY-1));
data->hdco = KH/SQR(data->dx);
data->haco = VEL/(RCONST(2.0)*data->dx);
data->vdco = (RCONST(1.0)/SQR(data->dy))*KV0;
/* Set machine-related constants */
data->comm = comm;
data->my_pe = my_pe;
/* isubx and isuby are the PE grid indices corresponding to my_pe */
isuby = my_pe/NPEX;
isubx = my_pe - isuby*NPEX;
data->isubx = isubx;
data->isuby = isuby;
/* Set the sizes of a boundary x-line in u and uext */
data->nvmxsub = NVARS*MXSUB;
data->nvmxsub2 = NVARS*(MXSUB+2);
/* Preconditioner-related fields */
for (lx = 0; lx < MXSUB; lx++) {
for (ly = 0; ly < MYSUB; ly++) {
(data->P)[lx][ly] = newDenseMat(NVARS, NVARS);
(data->Jbd)[lx][ly] = newDenseMat(NVARS, NVARS);
(data->pivot)[lx][ly] = newLintArray(NVARS);
}
}
}
/*
* Free user data memory.
*/
static void FreeUserData(UserData data)
{
int lx, ly;
for (lx = 0; lx < MXSUB; lx++) {
for (ly = 0; ly < MYSUB; ly++) {
destroyMat((data->P)[lx][ly]);
destroyMat((data->Jbd)[lx][ly]);
destroyArray((data->pivot)[lx][ly]);
}
}
free(data->p);
free(data);
}
/*
* Set initial conditions in u.
*/
static void SetInitialProfiles(N_Vector u, UserData data)
{
long int isubx, isuby, lx, ly, jx, jy, offset;
realtype dx, dy, x, y, cx, cy, xmid, ymid;
realtype *udata;
/* Set pointer to data array in vector u */
udata = NV_DATA_P(u);
/* Get mesh spacings, and subgrid indices for this PE */
dx = data->dx; dy = data->dy;
isubx = data->isubx; isuby = data->isuby;
/* Load initial profiles of c1 and c2 into local u vector.
Here lx and ly are local mesh point indices on the local subgrid,
and jx and jy are the global mesh point indices. */
offset = 0;
xmid = RCONST(0.5)*(XMIN + XMAX);
ymid = RCONST(0.5)*(YMIN + YMAX);
for (ly = 0; ly < MYSUB; ly++) {
jy = ly + isuby*MYSUB;
y = YMIN + jy*dy;
cy = SQR(RCONST(0.1)*(y - ymid));
cy = RCONST(1.0) - cy + RCONST(0.5)*SQR(cy);
for (lx = 0; lx < MXSUB; lx++) {
jx = lx + isubx*MXSUB;
x = XMIN + jx*dx;
cx = SQR(RCONST(0.1)*(x - xmid));
cx = RCONST(1.0) - cx + RCONST(0.5)*SQR(cx);
udata[offset ] = C1_SCALE*cx*cy;
udata[offset+1] = C2_SCALE*cx*cy;
offset = offset + 2;
}
}
}
/*
* Routine to send boundary data to neighboring PEs.
*/
static void BSend(MPI_Comm comm, int my_pe, long int isubx,
long int isuby, long int dsizex, long int dsizey,
realtype udata[])
{
int i, ly;
long int offsetu, offsetbuf;
realtype bufleft[NVARS*MYSUB], bufright[NVARS*MYSUB];
/* If isuby > 0, send data from bottom x-line of u */
if (isuby != 0)
MPI_Send(&udata[0], dsizex, PVEC_REAL_MPI_TYPE, my_pe-NPEX, 0, comm);
/* If isuby < NPEY-1, send data from top x-line of u */
if (isuby != NPEY-1) {
offsetu = (MYSUB-1)*dsizex;
MPI_Send(&udata[offsetu], dsizex, PVEC_REAL_MPI_TYPE, my_pe+NPEX, 0, comm);
}
/* If isubx > 0, send data from left y-line of u (via bufleft) */
if (isubx != 0) {
for (ly = 0; ly < MYSUB; ly++) {
offsetbuf = ly*NVARS;
offsetu = ly*dsizex;
for (i = 0; i < NVARS; i++)
bufleft[offsetbuf+i] = udata[offsetu+i];
}
MPI_Send(&bufleft[0], dsizey, PVEC_REAL_MPI_TYPE, my_pe-1, 0, comm);
}
/* If isubx < NPEX-1, send data from right y-line of u (via bufright) */
if (isubx != NPEX-1) {
for (ly = 0; ly < MYSUB; ly++) {
offsetbuf = ly*NVARS;
offsetu = offsetbuf*MXSUB + (MXSUB-1)*NVARS;
for (i = 0; i < NVARS; i++)
bufright[offsetbuf+i] = udata[offsetu+i];
}
MPI_Send(&bufright[0], dsizey, PVEC_REAL_MPI_TYPE, my_pe+1, 0, comm);
}
}
/*
* Routine to start receiving boundary data from neighboring PEs.
* Notes:
* 1) buffer should be able to hold 2*NVARS*MYSUB realtype entries, should be
* passed to both the BRecvPost and BRecvWait functions, and should not
* be manipulated between the two calls.
* 2) request should have 4 entries, and should be passed in both calls also.
*/
static void BRecvPost(MPI_Comm comm, MPI_Request request[], int my_pe,
long int isubx, long int isuby,
long int dsizex, long int dsizey,
realtype uext[], realtype buffer[])
{
long int offsetue;
/* Have bufleft and bufright use the same buffer */
realtype *bufleft = buffer, *bufright = buffer+NVARS*MYSUB;
/* If isuby > 0, receive data for bottom x-line of uext */
if (isuby != 0)
MPI_Irecv(&uext[NVARS], dsizex, PVEC_REAL_MPI_TYPE,
my_pe-NPEX, 0, comm, &request[0]);
/* If isuby < NPEY-1, receive data for top x-line of uext */
if (isuby != NPEY-1) {
offsetue = NVARS*(1 + (MYSUB+1)*(MXSUB+2));
MPI_Irecv(&uext[offsetue], dsizex, PVEC_REAL_MPI_TYPE,
my_pe+NPEX, 0, comm, &request[1]);
}
/* If isubx > 0, receive data for left y-line of uext (via bufleft) */
if (isubx != 0) {
MPI_Irecv(&bufleft[0], dsizey, PVEC_REAL_MPI_TYPE,
my_pe-1, 0, comm, &request[2]);
}
/* If isubx < NPEX-1, receive data for right y-line of uext (via bufright) */
if (isubx != NPEX-1) {
MPI_Irecv(&bufright[0], dsizey, PVEC_REAL_MPI_TYPE,
my_pe+1, 0, comm, &request[3]);
}
}
/*
* Routine to finish receiving boundary data from neighboring PEs.
* Notes:
* 1) buffer should be able to hold 2*NVARS*MYSUB realtype entries, should be
* passed to both the BRecvPost and BRecvWait functions, and should not
* be manipulated between the two calls.
* 2) request should have 4 entries, and should be passed in both calls also.
*/
static void BRecvWait(MPI_Request request[], long int isubx, long int isuby,
long int dsizex, realtype uext[], realtype buffer[])
{
int i, ly;
long int dsizex2, offsetue, offsetbuf;
realtype *bufleft = buffer, *bufright = buffer+NVARS*MYSUB;
MPI_Status status;
dsizex2 = dsizex + 2*NVARS;
/* If isuby > 0, receive data for bottom x-line of uext */
if (isuby != 0)
MPI_Wait(&request[0],&status);
/* If isuby < NPEY-1, receive data for top x-line of uext */
if (isuby != NPEY-1)
MPI_Wait(&request[1],&status);
/* If isubx > 0, receive data for left y-line of uext (via bufleft) */
if (isubx != 0) {
MPI_Wait(&request[2],&status);
/* Copy the buffer to uext */
for (ly = 0; ly < MYSUB; ly++) {
offsetbuf = ly*NVARS;
offsetue = (ly+1)*dsizex2;
for (i = 0; i < NVARS; i++)
uext[offsetue+i] = bufleft[offsetbuf+i];
}
}
/* If isubx < NPEX-1, receive data for right y-line of uext (via bufright) */
if (isubx != NPEX-1) {
MPI_Wait(&request[3],&status);
/* Copy the buffer to uext */
for (ly = 0; ly < MYSUB; ly++) {
offsetbuf = ly*NVARS;
offsetue = (ly+2)*dsizex2 - NVARS;
for (i = 0; i < NVARS; i++)
uext[offsetue+i] = bufright[offsetbuf+i];
}
}
}
/*
* ucomm routine. This routine performs all communication
* between processors of data needed to calculate f.
*/
static void ucomm(realtype t, N_Vector u, UserData data)
{
realtype *udata, *uext, buffer[2*NVARS*MYSUB];
MPI_Comm comm;
int my_pe;
long int isubx, isuby, nvmxsub, nvmysub;
MPI_Request request[4];
udata = NV_DATA_P(u);
/* Get comm, my_pe, subgrid indices, data sizes, extended array uext */
comm = data->comm; my_pe = data->my_pe;
isubx = data->isubx; isuby = data->isuby;
nvmxsub = data->nvmxsub;
nvmysub = NVARS*MYSUB;
uext = data->uext;
/* Start receiving boundary data from neighboring PEs */
BRecvPost(comm, request, my_pe, isubx, isuby, nvmxsub, nvmysub, uext, buffer);
/* Send data from boundary of local grid to neighboring PEs */
BSend(comm, my_pe, isubx, isuby, nvmxsub, nvmysub, udata);
/* Finish receiving boundary data from neighboring PEs */
BRecvWait(request, isubx, isuby, nvmxsub, uext, buffer);
}
/*
* fcalc routine. Compute f(t,y). This routine assumes that communication
* between processors of data needed to calculate f has already been done,
* and this data is in the work array uext.
*/
static void fcalc(realtype t, realtype udata[], realtype dudata[], UserData data)
{
realtype *uext;
realtype q3, c1, c2, c1dn, c2dn, c1up, c2up, c1lt, c2lt;
realtype c1rt, c2rt, cydn, cyup, hord1, hord2, horad1, horad2;
realtype qq1, qq2, qq3, qq4, rkin1, rkin2, s, vertd1, vertd2, ydn, yup;
realtype q4coef, dely, verdco, hordco, horaco;
int i, lx, ly, jx, jy;
long int isubx, isuby, nvmxsub, nvmxsub2, offsetu, offsetue;
realtype Q1, Q2, C3, A3, A4, KH, VEL, KV0;
/* Get subgrid indices, data sizes, extended work array uext */
isubx = data->isubx; isuby = data->isuby;
nvmxsub = data->nvmxsub; nvmxsub2 = data->nvmxsub2;
uext = data->uext;
/* Load problem coefficients and parameters */
Q1 = data->p[0];
Q2 = data->p[1];
C3 = data->p[2];
A3 = data->p[3];
A4 = data->p[4];
KH = data->p[5];
VEL = data->p[6];
KV0 = data->p[7];
/* Copy local segment of u vector into the working extended array uext */
offsetu = 0;
offsetue = nvmxsub2 + NVARS;
for (ly = 0; ly < MYSUB; ly++) {
for (i = 0; i < nvmxsub; i++) uext[offsetue+i] = udata[offsetu+i];
offsetu = offsetu + nvmxsub;
offsetue = offsetue + nvmxsub2;
}
/* To facilitate homogeneous Neumann boundary conditions, when this is
a boundary PE, copy data from the first interior mesh line of u to uext */
/* If isuby = 0, copy x-line 2 of u to uext */
if (isuby == 0) {
for (i = 0; i < nvmxsub; i++) uext[NVARS+i] = udata[nvmxsub+i];
}
/* If isuby = NPEY-1, copy x-line MYSUB-1 of u to uext */
if (isuby == NPEY-1) {
offsetu = (MYSUB-2)*nvmxsub;
offsetue = (MYSUB+1)*nvmxsub2 + NVARS;
for (i = 0; i < nvmxsub; i++) uext[offsetue+i] = udata[offsetu+i];
}
/* If isubx = 0, copy y-line 2 of u to uext */
if (isubx == 0) {
for (ly = 0; ly < MYSUB; ly++) {
offsetu = ly*nvmxsub + NVARS;
offsetue = (ly+1)*nvmxsub2;
for (i = 0; i < NVARS; i++) uext[offsetue+i] = udata[offsetu+i];
}
}
/* If isubx = NPEX-1, copy y-line MXSUB-1 of u to uext */
if (isubx == NPEX-1) {
for (ly = 0; ly < MYSUB; ly++) {
offsetu = (ly+1)*nvmxsub - 2*NVARS;
offsetue = (ly+2)*nvmxsub2 - NVARS;
for (i = 0; i < NVARS; i++) uext[offsetue+i] = udata[offsetu+i];
}
}
/* Make local copies of problem variables, for efficiency */
dely = data->dy;
verdco = data->vdco;
hordco = data->hdco;
horaco = data->haco;
/* Set diurnal rate coefficients as functions of t, and save q4 in
data block for use by preconditioner evaluation routine */
s = sin((data->om)*t);
if (s > ZERO) {
q3 = EXP(-A3/s);
q4coef = EXP(-A4/s);
} else {
q3 = ZERO;
q4coef = ZERO;
}
data->q4 = q4coef;
/* Loop over all grid points in local subgrid */
for (ly = 0; ly < MYSUB; ly++) {
jy = ly + isuby*MYSUB;
/* Set vertical diffusion coefficients at jy +- 1/2 */
ydn = YMIN + (jy - .5)*dely;
yup = ydn + dely;
cydn = verdco*EXP(RCONST(0.2)*ydn);
cyup = verdco*EXP(RCONST(0.2)*yup);
for (lx = 0; lx < MXSUB; lx++) {
jx = lx + isubx*MXSUB;
/* Extract c1 and c2, and set kinetic rate terms */
offsetue = (lx+1)*NVARS + (ly+1)*nvmxsub2;
c1 = uext[offsetue];
c2 = uext[offsetue+1];
qq1 = Q1*c1*C3;
qq2 = Q2*c1*c2;
qq3 = q3*C3;
qq4 = q4coef*c2;
rkin1 = -qq1 - qq2 + RCONST(2.0)*qq3 + qq4;
rkin2 = qq1 - qq2 - qq4;
/* Set vertical diffusion terms */
c1dn = uext[offsetue-nvmxsub2];
c2dn = uext[offsetue-nvmxsub2+1];
c1up = uext[offsetue+nvmxsub2];
c2up = uext[offsetue+nvmxsub2+1];
vertd1 = cyup*(c1up - c1) - cydn*(c1 - c1dn);
vertd2 = cyup*(c2up - c2) - cydn*(c2 - c2dn);
/* Set horizontal diffusion and advection terms */
c1lt = uext[offsetue-2];
c2lt = uext[offsetue-1];
c1rt = uext[offsetue+2];
c2rt = uext[offsetue+3];
hord1 = hordco*(c1rt - 2.0*c1 + c1lt);
hord2 = hordco*(c2rt - 2.0*c2 + c2lt);
horad1 = horaco*(c1rt - c1lt);
horad2 = horaco*(c2rt - c2lt);
/* Load all terms into dudata */
offsetu = lx*NVARS + ly*nvmxsub;
dudata[offsetu] = vertd1 + hord1 + horad1 + rkin1;
dudata[offsetu+1] = vertd2 + hord2 + horad2 + rkin2;
}
}
}
/*
* Print current t, step count, order, stepsize, and sampled c1,c2 values.
*/
static void PrintOutput(void *cvode_mem, int my_pe, MPI_Comm comm,
realtype t, N_Vector u)
{
long int nst;
int qu, flag;
realtype hu, *udata, tempu[2];
long int npelast, i0, i1;
MPI_Status status;
npelast = NPEX*NPEY - 1;
udata = NV_DATA_P(u);
/* Send c at top right mesh point to PE 0 */
if (my_pe == npelast) {
i0 = NVARS*MXSUB*MYSUB - 2;
i1 = i0 + 1;
if (npelast != 0)
MPI_Send(&udata[i0], 2, PVEC_REAL_MPI_TYPE, 0, 0, comm);
else {
tempu[0] = udata[i0];
tempu[1] = udata[i1];
}
}
/* On PE 0, receive c at top right, then print performance data
and sampled solution values */
if (my_pe == 0) {
if (npelast != 0)
MPI_Recv(&tempu[0], 2, PVEC_REAL_MPI_TYPE, npelast, 0, comm, &status);
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);
#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 %12.4Le \n", udata[0], tempu[0]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le %12.4le \n", udata[0], tempu[0]);
#else
printf("%12.4e %12.4e \n", udata[0], tempu[0]);
#endif
printf(" ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le %12.4Le \n", udata[1], tempu[1]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le %12.4le \n", udata[1], tempu[1]);
#else
printf("%12.4e %12.4e \n", udata[1], tempu[1]);
#endif
}
}
/*
* Print sampled sensitivity values.
*/
static void PrintOutputS(int my_pe, MPI_Comm comm, N_Vector *uS)
{
realtype *sdata, temps[2];
long int npelast, i0, i1;
MPI_Status status;
npelast = NPEX*NPEY - 1;
sdata = NV_DATA_P(uS[0]);
/* Send s1 at top right mesh point to PE 0 */
if (my_pe == npelast) {
i0 = NVARS*MXSUB*MYSUB - 2;
i1 = i0 + 1;
if (npelast != 0)
MPI_Send(&sdata[i0], 2, PVEC_REAL_MPI_TYPE, 0, 0, comm);
else {
temps[0] = sdata[i0];
temps[1] = sdata[i1];
}
}
/* On PE 0, receive s1 at top right, then print sampled sensitivity values */
if (my_pe == 0) {
if (npelast != 0)
MPI_Recv(&temps[0], 2, PVEC_REAL_MPI_TYPE, npelast, 0, comm, &status);
printf(" ----------------------------------------\n");
printf(" Sensitivity 1 ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le %12.4Le \n", sdata[0], temps[0]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le %12.4le \n", sdata[0], temps[0]);
#else
printf("%12.4e %12.4e \n", sdata[0], temps[0]);
#endif
printf(" ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le %12.4Le \n", sdata[1], temps[1]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le %12.4le \n", sdata[1], temps[1]);
#else
printf("%12.4e %12.4e \n", sdata[1], temps[1]);
#endif
}
sdata = NV_DATA_P(uS[1]);
/* Send s2 at top right mesh point to PE 0 */
if (my_pe == npelast) {
i0 = NVARS*MXSUB*MYSUB - 2;
i1 = i0 + 1;
if (npelast != 0)
MPI_Send(&sdata[i0], 2, PVEC_REAL_MPI_TYPE, 0, 0, comm);
else {
temps[0] = sdata[i0];
temps[1] = sdata[i1];
}
}
/* On PE 0, receive s2 at top right, then print sampled sensitivity values */
if (my_pe == 0) {
if (npelast != 0)
MPI_Recv(&temps[0], 2, PVEC_REAL_MPI_TYPE, npelast, 0, comm, &status);
printf(" ----------------------------------------\n");
printf(" Sensitivity 2 ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le %12.4Le \n", sdata[0], temps[0]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le %12.4le \n", sdata[0], temps[0]);
#else
printf("%12.4e %12.4e \n", sdata[0], temps[0]);
#endif
printf(" ");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%12.4Le %12.4Le \n", sdata[1], temps[1]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%12.4le %12.4le \n", sdata[1], temps[1]);
#else
printf("%12.4e %12.4e \n", sdata[1], temps[1]);
#endif
}
}
/*
* Print final statistics from the CVODES memory.
*/
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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