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/*-----------------------------------------------------------------
* Programmer(s): Daniel R. Reynolds @ SMU
*---------------------------------------------------------------
* SUNDIALS Copyright Start
* Copyright (c) 2002-2022, Lawrence Livermore National Security
* and Southern Methodist University.
* All rights reserved.
*
* See the top-level LICENSE and NOTICE files for details.
*
* SPDX-License-Identifier: BSD-3-Clause
* SUNDIALS Copyright End
*---------------------------------------------------------------
* Example problem:
*
* The following is a simple example problem with analytical
* solution,
* dy/dt = (t+1)*exp(-y)
* for t in the interval [0.0, 10.0], with initial condition: y=0.
* This has analytical solution
* y(t) = log(0.5*t^2 + t + 1)
*
* This program solves the problem with the ERK method.
* Output is printed every 1.0 units of time (10 total).
* Run statistics (optional outputs) are printed at the end.
*-----------------------------------------------------------------*/
/* Header files */
#include <stdio.h>
#include <math.h>
#include <arkode/arkode_erkstep.h> /* prototypes for ERKStep fcts., consts */
#include <nvector/nvector_serial.h> /* serial N_Vector types, fcts., macros */
#include <sundials/sundials_types.h> /* def. of type 'realtype' */
#include <sundials/sundials_math.h> /* def. of SUNRsqrt, etc. */
#if defined(SUNDIALS_EXTENDED_PRECISION)
#define GSYM "Lg"
#define ESYM "Le"
#define FSYM "Lf"
#else
#define GSYM "g"
#define ESYM "e"
#define FSYM "f"
#endif
/* User-supplied Functions Called by the Solver */
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data);
/* Private function to check function return values */
static int check_flag(void *flagvalue, const char *funcname, int opt);
/* Main Program */
int main()
{
/* general problem parameters */
realtype T0 = RCONST(0.0); /* initial time */
realtype Tf = RCONST(10.0); /* final time */
realtype dTout = RCONST(1.0); /* time between outputs */
sunindextype NEQ = 1; /* number of dependent vars. */
realtype reltol = 1.0e-6; /* tolerances */
realtype abstol = 1.0e-10;
/* general problem variables */
int flag; /* reusable error-checking flag */
N_Vector y = NULL; /* empty vector for storing solution */
void *arkode_mem = NULL; /* empty ARKode memory structure */
FILE *UFID, *FID;
realtype t, tout;
/* Create the SUNDIALS context object for this simulation */
SUNContext ctx;
flag = SUNContext_Create(NULL, &ctx);
if (check_flag(&flag, "SUNContext_Create", 1)) return 1;
/* Initial problem output */
printf("\nAnalytical ODE test problem:\n");
printf(" reltol = %.1"ESYM"\n", reltol);
printf(" abstol = %.1"ESYM"\n\n",abstol);
/* Initialize data structures */
y = N_VNew_Serial(NEQ, ctx); /* Create serial vector for solution */
if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
NV_Ith_S(y,0) = 0.0; /* Specify initial condition */
/* Call ERKStepCreate to initialize the ERK timestepper module and
specify the right-hand side function in y'=f(t,y), the inital time
T0, and the initial dependent variable vector y. */
arkode_mem = ERKStepCreate(f, T0, y, ctx);
if (check_flag((void *)arkode_mem, "ERKStepCreate", 0)) return 1;
/* Specify tolerances */
flag = ERKStepSStolerances(arkode_mem, reltol, abstol);
if (check_flag(&flag, "ERKStepSStolerances", 1)) return 1;
/* Open output stream for results, output comment line */
UFID = fopen("solution.txt","w");
fprintf(UFID,"# t u\n");
/* output initial condition to disk */
fprintf(UFID," %.16"ESYM" %.16"ESYM"\n", T0, NV_Ith_S(y,0));
/* Main time-stepping loop: calls ERKStepEvolve to perform the integration, then
prints results. Stops when the final time has been reached */
t = T0;
tout = T0+dTout;
printf(" t u\n");
printf(" ---------------------\n");
while (Tf - t > 1.0e-15) {
flag = ERKStepEvolve(arkode_mem, tout, y, &t, ARK_NORMAL); /* call integrator */
if (check_flag(&flag, "ERKStepEvolve", 1)) break;
printf(" %10.6"FSYM" %10.6"FSYM"\n", t, NV_Ith_S(y,0)); /* access/print solution */
fprintf(UFID," %.16"ESYM" %.16"ESYM"\n", t, NV_Ith_S(y,0));
if (flag >= 0) { /* successful solve: update time */
tout += dTout;
tout = (tout > Tf) ? Tf : tout;
} else { /* unsuccessful solve: break */
fprintf(stderr,"Solver failure, stopping integration\n");
break;
}
}
printf(" ---------------------\n");
fclose(UFID);
/* Print final statistics */
printf("\nFinal Statistics:\n");
flag = ERKStepPrintAllStats(arkode_mem, stdout, SUN_OUTPUTFORMAT_TABLE);
/* Print final statistics to a file in CSV format */
FID = fopen("ark_analytic_nonlin_stats.csv", "w");
flag = ERKStepPrintAllStats(arkode_mem, FID, SUN_OUTPUTFORMAT_CSV);
fclose(FID);
/* Clean up and return with successful completion */
N_VDestroy(y); /* Free y vector */
ERKStepFree(&arkode_mem); /* Free integrator memory */
SUNContext_Free(&ctx); /* Free context */
return 0;
}
/*-------------------------------
* Functions called by the solver
*-------------------------------*/
/* f routine to compute the ODE RHS function f(t,y). */
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data)
{
NV_Ith_S(ydot,0) = (t+1.0)*SUNRexp(-NV_Ith_S(y,0));
return 0;
}
/*-------------------------------
* Private helper functions
*-------------------------------*/
/* 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, const 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;
}
/*---- end of file ----*/
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