/usr/share/doc/libsundials-serial-dev/examples/cvode/serial/cvAdvDiff_bnd.c is in libsundials-serial-dev 2.5.0-3ubuntu3.
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* -----------------------------------------------------------------
* $Revision: 1.3 $
* $Date: 2010/12/01 22:51:32 $
* -----------------------------------------------------------------
* Programmer(s): Scott D. Cohen, Alan C. Hindmarsh and
* Radu Serban @ LLNL
* -----------------------------------------------------------------
* Example problem:
*
* The following is a simple example problem with a banded Jacobian,
* with the program for its solution by CVODE.
* The problem is the semi-discrete form of the advection-diffusion
* equation in 2-D:
* du/dt = d^2 u / dx^2 + .5 du/dx + d^2 u / dy^2
* on the rectangle 0 <= x <= 2, 0 <= y <= 1, and the time
* interval 0 <= t <= 1. Homogeneous Dirichlet boundary conditions
* are posed, and the initial condition is
* u(x,y,t=0) = x(2-x)y(1-y)exp(5xy).
* The PDE is discretized on a uniform MX+2 by MY+2 grid with
* central differencing, and with boundary values eliminated,
* leaving an ODE system of size NEQ = MX*MY.
* This program solves the problem with the BDF method, Newton
* iteration with the CVBAND band linear solver, and a user-supplied
* Jacobian routine.
* It uses scalar relative and absolute tolerances.
* Output is printed at t = .1, .2, ..., 1.
* Run statistics (optional outputs) are printed at the end.
* -----------------------------------------------------------------
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/* Header files with a description of contents used in cvbanx.c */
#include <cvode/cvode.h> /* prototypes for CVODE fcts., consts. */
#include <cvode/cvode_band.h> /* prototype for CVBand */
#include <nvector/nvector_serial.h> /* serial N_Vector types, fcts., macros */
#include <sundials/sundials_band.h> /* definitions of type DlsMat and macros */
#include <sundials/sundials_types.h> /* definition of type realtype */
#include <sundials/sundials_math.h> /* definition of ABS and EXP */
/* Problem Constants */
#define XMAX RCONST(2.0) /* domain boundaries */
#define YMAX RCONST(1.0)
#define MX 10 /* mesh dimensions */
#define MY 5
#define NEQ MX*MY /* number of equations */
#define ATOL RCONST(1.0e-5) /* scalar absolute tolerance */
#define T0 RCONST(0.0) /* initial time */
#define T1 RCONST(0.1) /* first output time */
#define DTOUT RCONST(0.1) /* output time increment */
#define NOUT 10 /* number of output times */
#define ZERO RCONST(0.0)
#define HALF RCONST(0.5)
#define ONE RCONST(1.0)
#define TWO RCONST(2.0)
#define FIVE RCONST(5.0)
/* User-defined vector access macro IJth */
/* IJth is defined in order to isolate the translation from the
mathematical 2-dimensional structure of the dependent variable vector
to the underlying 1-dimensional storage.
IJth(vdata,i,j) references the element in the vdata array for
u at mesh point (i,j), where 1 <= i <= MX, 1 <= j <= MY.
The vdata array is obtained via the macro call vdata = NV_DATA_S(v),
where v is an N_Vector.
The variables are ordered by the y index j, then by the x index i. */
#define IJth(vdata,i,j) (vdata[(j-1) + (i-1)*MY])
/* Type : UserData (contains grid constants) */
typedef struct {
realtype dx, dy, hdcoef, hacoef, vdcoef;
} *UserData;
/* Private Helper Functions */
static void SetIC(N_Vector u, UserData data);
static void PrintHeader(realtype reltol, realtype abstol, realtype umax);
static void PrintOutput(realtype t, realtype umax, long int nst);
static void PrintFinalStats(void *cvode_mem);
/* Private function to check function return values */
static int check_flag(void *flagvalue, char *funcname, int opt);
/* Functions Called by the Solver */
static int f(realtype t, N_Vector u, N_Vector udot, void *user_data);
static int Jac(long int N, long int mu, long int ml,
realtype t, N_Vector u, N_Vector fu,
DlsMat J, void *user_data,
N_Vector tmp1, N_Vector tmp2, N_Vector tmp3);
/*
*-------------------------------
* Main Program
*-------------------------------
*/
int main(void)
{
realtype dx, dy, reltol, abstol, t, tout, umax;
N_Vector u;
UserData data;
void *cvode_mem;
int iout, flag;
long int nst;
u = NULL;
data = NULL;
cvode_mem = NULL;
/* Create a serial vector */
u = N_VNew_Serial(NEQ); /* Allocate u vector */
if(check_flag((void*)u, "N_VNew_Serial", 0)) return(1);
reltol = ZERO; /* Set the tolerances */
abstol = ATOL;
data = (UserData) malloc(sizeof *data); /* Allocate data memory */
if(check_flag((void *)data, "malloc", 2)) return(1);
dx = data->dx = XMAX/(MX+1); /* Set grid coefficients in data */
dy = data->dy = YMAX/(MY+1);
data->hdcoef = ONE/(dx*dx);
data->hacoef = HALF/(TWO*dx);
data->vdcoef = ONE/(dy*dy);
SetIC(u, data); /* Initialize u vector */
/* Call CVodeCreate to create the solver memory and specify the
* Backward Differentiation Formula and the use of a Newton iteration */
cvode_mem = CVodeCreate(CV_BDF, CV_NEWTON);
if(check_flag((void *)cvode_mem, "CVodeCreate", 0)) return(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)) return(1);
/* Call CVodeSStolerances to specify the scalar relative tolerance
* and scalar absolute tolerance */
flag = CVodeSStolerances(cvode_mem, reltol, abstol);
if (check_flag(&flag, "CVodeSStolerances", 1)) return(1);
/* Set the pointer to user-defined data */
flag = CVodeSetUserData(cvode_mem, data);
if(check_flag(&flag, "CVodeSetUserData", 1)) return(1);
/* Call CVBand to specify the CVBAND band linear solver */
flag = CVBand(cvode_mem, NEQ, MY, MY);
if(check_flag(&flag, "CVBand", 1)) return(1);
/* Set the user-supplied Jacobian routine Jac */
flag = CVDlsSetBandJacFn(cvode_mem, Jac);
if(check_flag(&flag, "CVDlsSetBandJacFn", 1)) return(1);
/* In loop over output points: call CVode, print results, test for errors */
umax = N_VMaxNorm(u);
PrintHeader(reltol, abstol, umax);
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)) break;
umax = N_VMaxNorm(u);
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1);
PrintOutput(t, umax, nst);
}
PrintFinalStats(cvode_mem); /* Print some final statistics */
N_VDestroy_Serial(u); /* Free the u vector */
CVodeFree(&cvode_mem); /* Free the integrator memory */
free(data); /* Free the user data */
return(0);
}
/*
*-------------------------------
* Functions 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 uij, udn, uup, ult, urt, hordc, horac, verdc, hdiff, hadv, vdiff;
realtype *udata, *dudata;
int i, j;
UserData data;
udata = NV_DATA_S(u);
dudata = NV_DATA_S(udot);
/* Extract needed constants from data */
data = (UserData) user_data;
hordc = data->hdcoef;
horac = data->hacoef;
verdc = data->vdcoef;
/* Loop over all grid points. */
for (j=1; j <= MY; j++) {
for (i=1; i <= MX; i++) {
/* Extract u at x_i, y_j and four neighboring points */
uij = IJth(udata, i, j);
udn = (j == 1) ? ZERO : IJth(udata, i, j-1);
uup = (j == MY) ? ZERO : IJth(udata, i, j+1);
ult = (i == 1) ? ZERO : IJth(udata, i-1, j);
urt = (i == MX) ? ZERO : IJth(udata, i+1, j);
/* Set diffusion and advection terms and load into udot */
hdiff = hordc*(ult - TWO*uij + urt);
hadv = horac*(urt - ult);
vdiff = verdc*(uup - TWO*uij + udn);
IJth(dudata, i, j) = hdiff + hadv + vdiff;
}
}
return(0);
}
/* Jacobian routine. Compute J(t,u). */
static int Jac(long int N, long int mu, long int ml,
realtype t, N_Vector u, N_Vector fu,
DlsMat J, void *user_data,
N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
{
long int i, j, k;
realtype *kthCol, hordc, horac, verdc;
UserData data;
/*
The components of f = udot that depend on u(i,j) are
f(i,j), f(i-1,j), f(i+1,j), f(i,j-1), f(i,j+1), with
df(i,j)/du(i,j) = -2 (1/dx^2 + 1/dy^2)
df(i-1,j)/du(i,j) = 1/dx^2 + .25/dx (if i > 1)
df(i+1,j)/du(i,j) = 1/dx^2 - .25/dx (if i < MX)
df(i,j-1)/du(i,j) = 1/dy^2 (if j > 1)
df(i,j+1)/du(i,j) = 1/dy^2 (if j < MY)
*/
data = (UserData) user_data;
hordc = data->hdcoef;
horac = data->hacoef;
verdc = data->vdcoef;
for (j=1; j <= MY; j++) {
for (i=1; i <= MX; i++) {
k = j-1 + (i-1)*MY;
kthCol = BAND_COL(J,k);
/* set the kth column of J */
BAND_COL_ELEM(kthCol,k,k) = -TWO*(verdc+hordc);
if (i != 1) BAND_COL_ELEM(kthCol,k-MY,k) = hordc + horac;
if (i != MX) BAND_COL_ELEM(kthCol,k+MY,k) = hordc - horac;
if (j != 1) BAND_COL_ELEM(kthCol,k-1,k) = verdc;
if (j != MY) BAND_COL_ELEM(kthCol,k+1,k) = verdc;
}
}
return(0);
}
/*
*-------------------------------
* Private helper functions
*-------------------------------
*/
/* Set initial conditions in u vector */
static void SetIC(N_Vector u, UserData data)
{
int i, j;
realtype x, y, dx, dy;
realtype *udata;
/* Extract needed constants from data */
dx = data->dx;
dy = data->dy;
/* Set pointer to data array in vector u. */
udata = NV_DATA_S(u);
/* Load initial profile into u vector */
for (j=1; j <= MY; j++) {
y = j*dy;
for (i=1; i <= MX; i++) {
x = i*dx;
IJth(udata,i,j) = x*(XMAX - x)*y*(YMAX - y)*EXP(FIVE*x*y);
}
}
}
/* Print first lines of output (problem description) */
static void PrintHeader(realtype reltol, realtype abstol, realtype umax)
{
printf("\n2-D Advection-Diffusion Equation\n");
printf("Mesh dimensions = %d X %d\n", MX, MY);
printf("Total system size = %d\n", NEQ);
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("Tolerance parameters: reltol = %Lg abstol = %Lg\n\n",
reltol, abstol);
printf("At t = %Lg max.norm(u) =%14.6Le \n", T0, umax);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("Tolerance parameters: reltol = %lg abstol = %lg\n\n",
reltol, abstol);
printf("At t = %lg max.norm(u) =%14.6le \n", T0, umax);
#else
printf("Tolerance parameters: reltol = %g abstol = %g\n\n", reltol, abstol);
printf("At t = %g max.norm(u) =%14.6e \n", T0, umax);
#endif
return;
}
/* Print current value */
static void PrintOutput(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;
}
/* Get and print some final statistics */
static void PrintFinalStats(void *cvode_mem)
{
int flag;
long int nst, nfe, nsetups, netf, nni, ncfn, nje, nfeLS;
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1);
flag = CVodeGetNumRhsEvals(cvode_mem, &nfe);
check_flag(&flag, "CVodeGetNumRhsEvals", 1);
flag = CVodeGetNumLinSolvSetups(cvode_mem, &nsetups);
check_flag(&flag, "CVodeGetNumLinSolvSetups", 1);
flag = CVodeGetNumErrTestFails(cvode_mem, &netf);
check_flag(&flag, "CVodeGetNumErrTestFails", 1);
flag = CVodeGetNumNonlinSolvIters(cvode_mem, &nni);
check_flag(&flag, "CVodeGetNumNonlinSolvIters", 1);
flag = CVodeGetNumNonlinSolvConvFails(cvode_mem, &ncfn);
check_flag(&flag, "CVodeGetNumNonlinSolvConvFails", 1);
flag = CVDlsGetNumJacEvals(cvode_mem, &nje);
check_flag(&flag, "CVDlsGetNumJacEvals", 1);
flag = CVDlsGetNumRhsEvals(cvode_mem, &nfeLS);
check_flag(&flag, "CVDlsGetNumRhsEvals", 1);
printf("\nFinal Statistics:\n");
printf("nst = %-6ld nfe = %-6ld nsetups = %-6ld nfeLS = %-6ld nje = %ld\n",
nst, nfe, nsetups, nfeLS, nje);
printf("nni = %-6ld ncfn = %-6ld netf = %ld\n \n",
nni, ncfn, netf);
return;
}
/* 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 *errflag;
/* Check if SUNDIALS function returned NULL pointer - no memory allocated */
if (opt == 0 && flagvalue == NULL) {
fprintf(stderr, "\nSUNDIALS_ERROR: %s() failed - returned NULL pointer\n\n",
funcname);
return(1); }
/* Check if flag < 0 */
else if (opt == 1) {
errflag = (int *) flagvalue;
if (*errflag < 0) {
fprintf(stderr, "\nSUNDIALS_ERROR: %s() failed with flag = %d\n\n",
funcname, *errflag);
return(1); }}
/* Check if function returned NULL pointer - no memory allocated */
else if (opt == 2 && flagvalue == NULL) {
fprintf(stderr, "\nMEMORY_ERROR: %s() failed - returned NULL pointer\n\n",
funcname);
return(1); }
return(0);
}
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