static void PrintOutput(void *arkode_mem, realtype t)
{
long int nst, nfe, nfi, nni;
int flag;
realtype hu;
flag = ARKodeGetNumSteps(arkode_mem, &nst);
check_flag(&flag, "ARKodeGetNumSteps", 1);
flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
flag = ARKodeGetLastStep(arkode_mem, &hu);
check_flag(&flag, "ARKodeGetLastStep", 1);
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("t = %10.2Le nst = %ld nfe = %ld nfi = %ld nni = %ld", t, nst, nfe, nfi, nni);
printf(" hu = %11.2Le\n\n", hu);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("t = %10.2e nst = %ld nfe = %ld nfi = %ld nni = %ld", t, nst, nfe, nfi, nni);
printf(" hu = %11.2e\n\n", hu);
#else
printf("t = %10.2e nst = %ld nfe = %ld nfi = %ld nni = %ld", t, nst, nfe, nfi, nni);
printf(" hu = %11.2e\n\n", hu);
#endif
}
/* Print final statistics contained in iopt */
static void PrintFinalStats(void *arkode_mem)
{
long int lenrw, leniw ;
long int lenrwLS, leniwLS;
long int lenrwBBDP, leniwBBDP, ngevalsBBDP;
long int nst, nfe, nfi, nsetups, nni, ncfn, netf;
long int nli, npe, nps, ncfl, nfeLS;
int flag;
flag = ARKodeGetWorkSpace(arkode_mem, &lenrw, &leniw);
check_flag(&flag, "ARKodeGetWorkSpace", 1, 0);
flag = ARKodeGetNumSteps(arkode_mem, &nst);
check_flag(&flag, "ARKodeGetNumSteps", 1, 0);
flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
check_flag(&flag, "ARKodeGetNumRhsEvals", 1, 0);
flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1, 0);
flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
check_flag(&flag, "ARKodeGetNumErrTestFails", 1, 0);
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1, 0);
flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1, 0);
flag = ARKSpilsGetWorkSpace(arkode_mem, &lenrwLS, &leniwLS);
check_flag(&flag, "ARKSpilsGetWorkSpace", 1, 0);
flag = ARKSpilsGetNumLinIters(arkode_mem, &nli);
check_flag(&flag, "ARKSpilsGetNumLinIters", 1, 0);
flag = ARKSpilsGetNumPrecEvals(arkode_mem, &npe);
check_flag(&flag, "ARKSpilsGetNumPrecEvals", 1, 0);
flag = ARKSpilsGetNumPrecSolves(arkode_mem, &nps);
check_flag(&flag, "ARKSpilsGetNumPrecSolves", 1, 0);
flag = ARKSpilsGetNumConvFails(arkode_mem, &ncfl);
check_flag(&flag, "ARKSpilsGetNumConvFails", 1, 0);
flag = ARKSpilsGetNumRhsEvals(arkode_mem, &nfeLS);
check_flag(&flag, "ARKSpilsGetNumRhsEvals", 1, 0);
printf("\nFinal Statistics: \n\n");
printf("lenrw = %5ld leniw = %5ld\n", lenrw, leniw);
printf("lenrwls = %5ld leniwls = %5ld\n", lenrwLS, leniwLS);
printf("nst = %5ld nfe = %5ld\n", nst, nfe);
printf("nfe = %5ld nfels = %5ld\n", nfi, nfeLS);
printf("nni = %5ld nli = %5ld\n", nni, nli);
printf("nsetups = %5ld netf = %5ld\n", nsetups, netf);
printf("npe = %5ld nps = %5ld\n", npe, nps);
printf("ncfn = %5ld ncfl = %5ld\n\n", ncfn, ncfl);
flag = ARKBBDPrecGetWorkSpace(arkode_mem, &lenrwBBDP, &leniwBBDP);
check_flag(&flag, "ARKBBDPrecGetWorkSpace", 1, 0);
flag = ARKBBDPrecGetNumGfnEvals(arkode_mem, &ngevalsBBDP);
check_flag(&flag, "ARKBBDPrecGetNumGfnEvals", 1, 0);
printf("In ARKBBDPRE: real/integer local work space sizes = %ld, %ld\n",
lenrwBBDP, leniwBBDP);
printf(" no. flocal evals. = %ld\n",ngevalsBBDP);
}
/* 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 */
long int NEQ = 3; /* number of dependent vars. */
int Nt = ceil(Tf/dTout); /* number of output times */
int test = 2; /* test problem to run */
realtype reltol = 1.0e-6; /* tolerances */
realtype abstol = 1.0e-10;
realtype a, b, ep, u0, v0, w0;
/* 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 */
realtype rdata[3];
FILE *UFID;
realtype t, tout;
int iout;
long int nst, nst_a, nfe, nfi, nsetups, nje, nfeLS, nni, ncfn, netf;
/* set up the test problem according to the desired test */
if (test == 1) {
u0 = RCONST(3.9);
v0 = RCONST(1.1);
w0 = RCONST(2.8);
a = RCONST(1.2);
b = RCONST(2.5);
ep = RCONST(1.0e-5);
} else if (test == 3) {
u0 = RCONST(3.0);
v0 = RCONST(3.0);
w0 = RCONST(3.5);
a = RCONST(0.5);
b = RCONST(3.0);
ep = RCONST(5.0e-4);
} else {
u0 = RCONST(1.2);
v0 = RCONST(3.1);
w0 = RCONST(3.0);
a = RCONST(1.0);
b = RCONST(3.5);
ep = RCONST(5.0e-6);
}
/* Initial problem output */
printf("\nBrusselator ODE test problem:\n");
printf(" initial conditions: u0 = %g, v0 = %g, w0 = %g\n",u0,v0,w0);
printf(" problem parameters: a = %g, b = %g, ep = %g\n",a,b,ep);
printf(" reltol = %.1e, abstol = %.1e\n\n",reltol,abstol);
/* Initialize data structures */
rdata[0] = a; /* set user data */
rdata[1] = b;
rdata[2] = ep;
y = N_VNew_Serial(NEQ); /* Create serial vector for solution */
if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
NV_Ith_S(y,0) = u0; /* Set initial conditions */
NV_Ith_S(y,1) = v0;
NV_Ith_S(y,2) = w0;
arkode_mem = ARKodeCreate(); /* Create the solver memory */
if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1;
/* Call ARKodeInit to initialize the integrator memory and specify the
hand-side side function in y'=f(t,y), the inital time T0, and
the initial dependent variable vector y. Note: since this
problem is fully implicit, we set f_E to NULL and f_I to f. */
flag = ARKodeInit(arkode_mem, NULL, f, T0, y);
if (check_flag(&flag, "ARKodeInit", 1)) return 1;
/* Set routines */
flag = ARKodeSetUserData(arkode_mem, (void *) rdata); /* Pass rdata to user functions */
if (check_flag(&flag, "ARKodeSetUserData", 1)) return 1;
flag = ARKodeSStolerances(arkode_mem, reltol, abstol); /* Specify tolerances */
if (check_flag(&flag, "ARKodeSStolerances", 1)) return 1;
/* Linear solver specification */
flag = ARKDense(arkode_mem, NEQ); /* Specify dense linear solver */
if (check_flag(&flag, "ARKDense", 1)) return 1;
flag = ARKDlsSetDenseJacFn(arkode_mem, Jac); /* Set Jacobian routine */
if (check_flag(&flag, "ARKDlsSetDenseJacFn", 1)) return 1;
/* Open output stream for results, output comment line */
UFID = fopen("solution.txt","w");
fprintf(UFID,"# t u v w\n");
/* output initial condition to disk */
fprintf(UFID," %.16e %.16e %.16e %.16e\n",
T0, NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
/* Main time-stepping loop: calls ARKode to perform the integration, then
prints results. Stops when the final time has been reached */
t = T0;
tout = T0+dTout;
printf(" t u v w\n");
printf(" -------------------------------------------\n");
for (iout=0; iout<Nt; iout++) {
flag = ARKode(arkode_mem, tout, y, &t, ARK_NORMAL); /* call integrator */
if (check_flag(&flag, "ARKode", 1)) break;
printf(" %10.6f %10.6f %10.6f %10.6f\n", /* access/print solution */
t, NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
fprintf(UFID," %.16e %.16e %.16e %.16e\n",
t, NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
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 some final statistics */
flag = ARKodeGetNumSteps(arkode_mem, &nst);
check_flag(&flag, "ARKodeGetNumSteps", 1);
flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a);
check_flag(&flag, "ARKodeGetNumStepAttempts", 1);
flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
flag = ARKDlsGetNumJacEvals(arkode_mem, &nje);
check_flag(&flag, "ARKDlsGetNumJacEvals", 1);
flag = ARKDlsGetNumRhsEvals(arkode_mem, &nfeLS);
check_flag(&flag, "ARKDlsGetNumRhsEvals", 1);
printf("\nFinal Solver Statistics:\n");
printf(" Internal solver steps = %li (attempted = %li)\n", nst, nst_a);
printf(" Total RHS evals: Fe = %li, Fi = %li\n", nfe, nfi);
printf(" Total linear solver setups = %li\n", nsetups);
printf(" Total RHS evals for setting up the linear system = %li\n", nfeLS);
printf(" Total number of Jacobian evaluations = %li\n", nje);
printf(" Total number of Newton iterations = %li\n", nni);
printf(" Total number of linear solver convergence failures = %li\n", ncfn);
printf(" Total number of error test failures = %li\n\n", netf);
/* Clean up and return with successful completion */
N_VDestroy_Serial(y); /* Free y vector */
ARKodeFree(&arkode_mem); /* Free integrator memory */
return 0;
}
static void PrintFinalStats(void *arkode_mem)
{
long int lenrw, leniw ;
long int lenrwLS, leniwLS;
long int nst, nfe, nfi, nsetups, nni, ncfn, netf;
long int nli, npe, nps, ncfl, nfeLS;
int flag;
realtype avdim;
flag = ARKodeGetWorkSpace(arkode_mem, &lenrw, &leniw);
check_flag(&flag, "ARKodeGetWorkSpace", 1);
flag = ARKodeGetNumSteps(arkode_mem, &nst);
check_flag(&flag, "ARKodeGetNumSteps", 1);
flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
flag = ARKSpilsGetWorkSpace(arkode_mem, &lenrwLS, &leniwLS);
check_flag(&flag, "ARKSpilsGetWorkSpace", 1);
flag = ARKSpilsGetNumLinIters(arkode_mem, &nli);
check_flag(&flag, "ARKSpilsGetNumLinIters", 1);
flag = ARKSpilsGetNumPrecEvals(arkode_mem, &npe);
check_flag(&flag, "ARKSpilsGetNumPrecEvals", 1);
flag = ARKSpilsGetNumPrecSolves(arkode_mem, &nps);
check_flag(&flag, "ARKSpilsGetNumPrecSolves", 1);
flag = ARKSpilsGetNumConvFails(arkode_mem, &ncfl);
check_flag(&flag, "ARKSpilsGetNumConvFails", 1);
flag = ARKSpilsGetNumRhsEvals(arkode_mem, &nfeLS);
check_flag(&flag, "ARKSpilsGetNumRhsEvals", 1);
printf("\n\n Final statistics for this run:\n\n");
printf(" ARKode real workspace length = %4ld \n", lenrw);
printf(" ARKode integer workspace length = %4ld \n", leniw);
printf(" ARKSPGMR real workspace length = %4ld \n", lenrwLS);
printf(" ARKSPGMR integer workspace length = %4ld \n", leniwLS);
printf(" Number of steps = %4ld \n", nst);
printf(" Number of f-s (explicit) = %4ld \n", nfe);
printf(" Number of f-s (implicit) = %4ld \n", nfi);
printf(" Number of f-s (SPGMR) = %4ld \n", nfeLS);
printf(" Number of f-s (TOTAL) = %4ld \n", nfe + nfeLS);
printf(" Number of setups = %4ld \n", nsetups);
printf(" Number of nonlinear iterations = %4ld \n", nni);
printf(" Number of linear iterations = %4ld \n", nli);
printf(" Number of preconditioner evaluations = %4ld \n", npe);
printf(" Number of preconditioner solves = %4ld \n", nps);
printf(" Number of error test failures = %4ld \n", netf);
printf(" Number of nonlinear conv. failures = %4ld \n", ncfn);
printf(" Number of linear convergence failures = %4ld \n", ncfl);
avdim = (nni > 0) ? ((realtype)nli)/((realtype)nni) : ZERO;
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf(" Average Krylov subspace dimension = %.3Lf \n", avdim);
#else
printf(" Average Krylov subspace dimension = %.3f \n", avdim);
#endif
printf("\n\n--------------------------------------------------------------");
printf("--------------\n");
printf( "--------------------------------------------------------------");
printf("--------------\n");
}
/* Main Program */
int main()
{
/* general problem parameters */
realtype T0 = RCONST(0.0); /* initial time */
realtype Tf = RCONST(10.0); /* final time */
int Nt = 100; /* total number of output times */
int Nvar = 3; /* number of solution fields */
UserData udata = NULL;
realtype *data;
long int N = 201; /* spatial mesh size */
realtype a = 0.6; /* problem parameters */
realtype b = 2.0;
realtype du = 0.025;
realtype dv = 0.025;
realtype dw = 0.025;
realtype ep = 1.0e-5; /* stiffness parameter */
realtype reltol = 1.0e-6; /* tolerances */
realtype abstol = 1.0e-10;
long int NEQ, i;
/* general problem variables */
int flag; /* reusable error-checking flag */
N_Vector y = NULL; /* empty vector for storing solution */
N_Vector umask = NULL; /* empty mask vectors for viewing solution components */
N_Vector vmask = NULL;
N_Vector wmask = NULL;
void *arkode_mem = NULL; /* empty ARKode memory structure */
realtype pi, t, dTout, tout, u, v, w;
FILE *FID, *UFID, *VFID, *WFID;
int iout;
long int nst, nst_a, nfe, nfi, nsetups, nje, nfeLS, nni, ncfn, netf;
/* allocate udata structure */
udata = (UserData) malloc(sizeof(*udata));
if (check_flag((void *) udata, "malloc", 2)) return 1;
/* store the inputs in the UserData structure */
udata->N = N;
udata->a = a;
udata->b = b;
udata->du = du;
udata->dv = dv;
udata->dw = dw;
udata->ep = ep;
/* set total allocated vector length */
NEQ = Nvar*udata->N;
/* Initial problem output */
printf("\n1D Brusselator PDE test problem:\n");
printf(" N = %li, NEQ = %li\n", udata->N, NEQ);
printf(" problem parameters: a = %g, b = %g, ep = %g\n",
udata->a, udata->b, udata->ep);
printf(" diffusion coefficients: du = %g, dv = %g, dw = %g\n",
udata->du, udata->dv, udata->dw);
printf(" reltol = %.1e, abstol = %.1e\n\n", reltol, abstol);
/* Initialize data structures */
y = N_VNew_Serial(NEQ); /* Create serial vector for solution */
if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
udata->dx = RCONST(1.0)/(N-1); /* set spatial mesh spacing */
data = N_VGetArrayPointer(y); /* Access data array for new NVector y */
if (check_flag((void *)data, "N_VGetArrayPointer", 0)) return 1;
umask = N_VNew_Serial(NEQ); /* Create serial vector masks */
if (check_flag((void *)umask, "N_VNew_Serial", 0)) return 1;
vmask = N_VNew_Serial(NEQ);
if (check_flag((void *)vmask, "N_VNew_Serial", 0)) return 1;
wmask = N_VNew_Serial(NEQ);
if (check_flag((void *)wmask, "N_VNew_Serial", 0)) return 1;
/* Set initial conditions into y */
pi = RCONST(4.0)*atan(RCONST(1.0));
for (i=0; i<N; i++) {
data[IDX(i,0)] = a + RCONST(0.1)*sin(pi*i*udata->dx); /* u */
data[IDX(i,1)] = b/a + RCONST(0.1)*sin(pi*i*udata->dx); /* v */
data[IDX(i,2)] = b + RCONST(0.1)*sin(pi*i*udata->dx); /* w */
}
/* Set mask array values for each solution component */
N_VConst(0.0, umask);
data = N_VGetArrayPointer(umask);
if (check_flag((void *)data, "N_VGetArrayPointer", 0)) return 1;
for (i=0; i<N; i++) data[IDX(i,0)] = RCONST(1.0);
N_VConst(0.0, vmask);
data = N_VGetArrayPointer(vmask);
if (check_flag((void *)data, "N_VGetArrayPointer", 0)) return 1;
for (i=0; i<N; i++) data[IDX(i,1)] = RCONST(1.0);
N_VConst(0.0, wmask);
data = N_VGetArrayPointer(wmask);
if (check_flag((void *)data, "N_VGetArrayPointer", 0)) return 1;
for (i=0; i<N; i++) data[IDX(i,2)] = RCONST(1.0);
/* Create the solver memory */
arkode_mem = ARKodeCreate();
if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1;
/* Call ARKodeInit to initialize the integrator memory and specify the
right-hand side function in y'=f(t,y), the inital time T0, and
the initial dependent variable vector y. Note: since this
problem is fully implicit, we set f_E to NULL and f_I to f. */
flag = ARKodeInit(arkode_mem, NULL, f, T0, y);
if (check_flag(&flag, "ARKodeInit", 1)) return 1;
/* Set routines */
flag = ARKodeSetUserData(arkode_mem, (void *) udata); /* Pass udata to user functions */
if (check_flag(&flag, "ARKodeSetUserData", 1)) return 1;
flag = ARKodeSStolerances(arkode_mem, reltol, abstol); /* Specify tolerances */
if (check_flag(&flag, "ARKodeSStolerances", 1)) return 1;
/* Linear solver specification */
flag = ARKBand(arkode_mem, NEQ, 4, 4); /* Specify the band linear solver */
if (check_flag(&flag, "ARKBand", 1)) return 1;
flag = ARKDlsSetBandJacFn(arkode_mem, Jac); /* Set the Jacobian routine */
if (check_flag(&flag, "ARKDlsSetBandJacFn", 1)) return 1;
/* output spatial mesh to disk */
FID = fopen("bruss_mesh.txt","w");
for (i=0; i<N; i++) fprintf(FID," %.16e\n", udata->dx*i);
fclose(FID);
/* Open output streams for results, access data array */
UFID=fopen("bruss_u.txt","w");
VFID=fopen("bruss_v.txt","w");
WFID=fopen("bruss_w.txt","w");
/* output initial condition to disk */
data = N_VGetArrayPointer(y);
if (check_flag((void *)data, "N_VGetArrayPointer", 0)) return 1;
for (i=0; i<N; i++) fprintf(UFID," %.16e", data[IDX(i,0)]);
for (i=0; i<N; i++) fprintf(VFID," %.16e", data[IDX(i,1)]);
for (i=0; i<N; i++) fprintf(WFID," %.16e", data[IDX(i,2)]);
fprintf(UFID,"\n");
fprintf(VFID,"\n");
fprintf(WFID,"\n");
/* Main time-stepping loop: calls ARKode to perform the integration, then
prints results. Stops when the final time has been reached */
t = T0;
dTout = (Tf-T0)/Nt;
tout = T0+dTout;
printf(" t ||u||_rms ||v||_rms ||w||_rms\n");
printf(" ----------------------------------------------\n");
for (iout=0; iout<Nt; iout++) {
flag = ARKode(arkode_mem, tout, y, &t, ARK_NORMAL); /* call integrator */
if (check_flag(&flag, "ARKode", 1)) break;
u = N_VWL2Norm(y,umask); /* access/print solution statistics */
u = SUNRsqrt(u*u/N);
v = N_VWL2Norm(y,vmask);
v = SUNRsqrt(v*v/N);
w = N_VWL2Norm(y,wmask);
w = SUNRsqrt(w*w/N);
printf(" %10.6f %10.6f %10.6f %10.6f\n", t, u, v, w);
if (flag >= 0) { /* successful solve: update output time */
tout += dTout;
tout = (tout > Tf) ? Tf : tout;
} else { /* unsuccessful solve: break */
fprintf(stderr,"Solver failure, stopping integration\n");
break;
}
/* output results to disk */
for (i=0; i<N; i++) fprintf(UFID," %.16e", data[IDX(i,0)]);
for (i=0; i<N; i++) fprintf(VFID," %.16e", data[IDX(i,1)]);
for (i=0; i<N; i++) fprintf(WFID," %.16e", data[IDX(i,2)]);
fprintf(UFID,"\n");
fprintf(VFID,"\n");
fprintf(WFID,"\n");
}
printf(" ----------------------------------------------\n");
fclose(UFID);
fclose(VFID);
fclose(WFID);
/* Print some final statistics */
flag = ARKodeGetNumSteps(arkode_mem, &nst);
check_flag(&flag, "ARKodeGetNumSteps", 1);
flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a);
check_flag(&flag, "ARKodeGetNumStepAttempts", 1);
flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
flag = ARKDlsGetNumJacEvals(arkode_mem, &nje);
check_flag(&flag, "ARKDlsGetNumJacEvals", 1);
flag = ARKDlsGetNumRhsEvals(arkode_mem, &nfeLS);
check_flag(&flag, "ARKDlsGetNumRhsEvals", 1);
printf("\nFinal Solver Statistics:\n");
printf(" Internal solver steps = %li (attempted = %li)\n", nst, nst_a);
printf(" Total RHS evals: Fe = %li, Fi = %li\n", nfe, nfi);
printf(" Total linear solver setups = %li\n", nsetups);
printf(" Total RHS evals for setting up the linear system = %li\n", nfeLS);
printf(" Total number of Jacobian evaluations = %li\n", nje);
printf(" Total number of Newton iterations = %li\n", nni);
printf(" Total number of nonlinear solver convergence failures = %li\n", ncfn);
printf(" Total number of error test failures = %li\n\n", netf);
/* Clean up and return with successful completion */
N_VDestroy_Serial(y); /* Free vectors */
N_VDestroy_Serial(umask);
N_VDestroy_Serial(vmask);
N_VDestroy_Serial(wmask);
free(udata); /* Free user data */
ARKodeFree(&arkode_mem); /* Free integrator memory */
return 0;
}
/* Main Program */
int main()
{
/* general problem parameters */
realtype T0 = RCONST(0.0); /* initial time */
realtype T1 = RCONST(0.4); /* first output time */
realtype TMult = RCONST(10.0); /* output time multiplication factor */
int Nt = 12; /* total number of output times */
long int NEQ = 3; /* number of dependent vars. */
realtype reltol;
int rootsfound[2];
long int nst, nst_a, nfe, nfi, nsetups;
long int nje, nfeLS, nni, ncfn, netf, nge;
int flag, rtflag; /* reusable error-checking flags */
FILE *UFID;
realtype t, tout;
int iout;
/* general problem variables */
N_Vector y = NULL; /* empty vector for storing solution */
N_Vector atols = NULL; /* empty vector for absolute tolerances */
void *arkode_mem = NULL; /* empty ARKode memory structure */
/* set up the initial conditions */
realtype u0 = RCONST(1.0);
realtype v0 = RCONST(0.0);
realtype w0 = RCONST(0.0);
/* Initial problem output */
printf("\nRobertson ODE test problem (with rootfinding):\n");
printf(" initial conditions: u0 = %g, v0 = %g, w0 = %g\n",u0,v0,w0);
/* Initialize data structures */
y = N_VNew_Serial(NEQ); /* Create serial vector for solution */
if (check_flag((void *) y, "N_VNew_Serial", 0)) return 1;
atols = N_VNew_Serial(NEQ); /* Create serial vector absolute tolerances */
if (check_flag((void *) atols, "N_VNew_Serial", 0)) return 1;
NV_Ith_S(y,0) = u0; /* Set initial conditions into y */
NV_Ith_S(y,1) = v0;
NV_Ith_S(y,2) = w0;
arkode_mem = ARKodeCreate(); /* Create the solver memory */
if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1;
/* Call ARKodeInit to initialize the integrator memory and specify the
hand-side side function in y'=f(t,y), the inital time T0, and
the initial dependent variable vector y. Note: since this
problem is fully implicit, we set f_E to NULL and f_I to f. */
flag = ARKodeInit(arkode_mem, NULL, f, T0, y);
if (check_flag(&flag, "ARKodeInit", 1)) return 1;
/* Set tolerances */
reltol = RCONST(1.0e-4);
NV_Ith_S(atols,0) = RCONST(1.0e-8);
NV_Ith_S(atols,1) = RCONST(1.0e-11);
NV_Ith_S(atols,2) = RCONST(1.0e-8);
/* Set routines */
flag = ARKodeSetMaxErrTestFails(arkode_mem, 20); /* Increase max error test fails */
if (check_flag(&flag, "ARKodeSetMaxErrTestFails", 1)) return 1;
flag = ARKodeSetMaxNonlinIters(arkode_mem, 8); /* Increase max nonlinear iterations */
if (check_flag(&flag, "ARKodeSetMaxNonlinIters", 1)) return 1;
flag = ARKodeSetNonlinConvCoef(arkode_mem, 1.e-7); /* Update nonlinear solver convergence coeff. */
if (check_flag(&flag, "ARKodeSetNonlinConvCoef", 1)) return 1;
flag = ARKodeSetMaxNumSteps(arkode_mem, 100000); /* Increase max number of steps */
if (check_flag(&flag, "ARKodeSetMaxNumSteps", 1)) return 1;
flag = ARKodeSVtolerances(arkode_mem, reltol, atols); /* Specify tolerances */
if (check_flag(&flag, "ARKodeSStolerances", 1)) return 1;
/* Specify the root-finding function, having 2 equations */
flag = ARKodeRootInit(arkode_mem, 2, g);
if (check_flag(&flag, "ARKodeRootInit", 1)) return 1;
/* Linear solver specification */
flag = ARKDense(arkode_mem, NEQ); /* Specify dense linear solver */
if (check_flag(&flag, "ARKDense", 1)) return 1;
flag = ARKDlsSetDenseJacFn(arkode_mem, Jac); /* Set the Jacobian routine */
if (check_flag(&flag, "ARKDlsSetDenseJacFn", 1)) return 1;
/* Open output stream for results, output comment line */
UFID = fopen("solution.txt","w");
fprintf(UFID,"# t u v w\n");
/* output initial condition to disk */
fprintf(UFID," %.16e %.16e %.16e %.16e\n",
T0, NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
/* Main time-stepping loop: calls ARKode to perform the integration, then
prints results. Stops when the final time has been reached */
t = T0;
printf(" t u v w\n");
printf(" -----------------------------------------------------\n");
printf(" %12.5e %12.5e %12.5e %12.5e\n",
t, NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
tout = T1;
iout = 0;
while(1) {
flag = ARKode(arkode_mem, tout, y, &t, ARK_NORMAL); /* call integrator */
if (check_flag(&flag, "ARKode", 1)) break;
printf(" %12.5e %12.5e %12.5e %12.5e\n", t, /* access/print solution */
NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
fprintf(UFID," %.16e %.16e %.16e %.16e\n",
t, NV_Ith_S(y,0), NV_Ith_S(y,1), NV_Ith_S(y,2));
if (flag == ARK_ROOT_RETURN) { /* check if a root was found */
rtflag = ARKodeGetRootInfo(arkode_mem, rootsfound);
if (check_flag(&rtflag, "ARKodeGetRootInfo", 1)) return 1;
printf(" rootsfound[] = %3d %3d\n",
rootsfound[0], rootsfound[1]);
}
if (flag >= 0) { /* successful solve: update output time */
iout++;
tout *= TMult;
} else { /* unsuccessful solve: break */
fprintf(stderr,"Solver failure, stopping integration\n");
break;
}
if (iout == Nt) break; /* stop after enough outputs */
}
printf(" -----------------------------------------------------\n");
fclose(UFID);
/* Print some final statistics */
flag = ARKodeGetNumSteps(arkode_mem, &nst);
check_flag(&flag, "ARKodeGetNumSteps", 1);
flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a);
check_flag(&flag, "ARKodeGetNumStepAttempts", 1);
flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
flag = ARKDlsGetNumJacEvals(arkode_mem, &nje);
check_flag(&flag, "ARKDlsGetNumJacEvals", 1);
flag = ARKDlsGetNumRhsEvals(arkode_mem, &nfeLS);
check_flag(&flag, "ARKDlsGetNumRhsEvals", 1);
flag = ARKodeGetNumGEvals(arkode_mem, &nge);
check_flag(&flag, "ARKodeGetNumGEvals", 1);
printf("\nFinal Solver Statistics:\n");
printf(" Internal solver steps = %li (attempted = %li)\n",
nst, nst_a);
printf(" Total RHS evals: Fe = %li, Fi = %li\n", nfe, nfi);
printf(" Total linear solver setups = %li\n", nsetups);
printf(" Total RHS evals for setting up the linear system = %li\n", nfeLS);
printf(" Total number of Jacobian evaluations = %li\n", nje);
printf(" Total number of Newton iterations = %li\n", nni);
printf(" Total root-function g evals = %li\n", nge);
printf(" Total number of nonlinear solver convergence failures = %li\n", ncfn);
printf(" Total number of error test failures = %li\n", netf);
/* Clean up and return with successful completion */
N_VDestroy_Serial(y); /* Free y vector */
ARKodeFree(&arkode_mem); /* Free integrator memory */
return 0;
}
/* Main Program */
int main() {
/* general problem parameters */
realtype T0 = RCONST(0.0); /* initial time */
realtype Tf = RCONST(1.0); /* final time */
realtype rtol = 1.e-3; /* relative tolerance */
realtype atol = 1.e-10; /* absolute tolerance */
realtype hscale = 1.0; /* time step change factor on resizes */
UserData udata = NULL;
realtype *data;
long int N = 21; /* initial spatial mesh size */
realtype refine = 3.e-3; /* adaptivity refinement tolerance */
realtype k = 0.5; /* heat conductivity */
long int i, nni, nni_cur=0, nni_tot=0, nli, nli_tot=0;
int iout=0;
/* general problem variables */
int flag; /* reusable error-checking flag */
N_Vector y = NULL; /* empty vector for storing solution */
N_Vector y2 = NULL; /* empty vector for storing solution */
N_Vector yt = NULL; /* empty vector for swapping */
void *arkode_mem = NULL; /* empty ARKode memory structure */
FILE *XFID, *UFID;
realtype t, olddt, newdt;
realtype *xnew = NULL;
long int Nnew;
/* allocate and fill initial udata structure */
udata = (UserData) malloc(sizeof(*udata));
udata->N = N;
udata->k = k;
udata->refine_tol = refine;
udata->x = malloc(N * sizeof(realtype));
for (i=0; i<N; i++) udata->x[i] = 1.0*i/(N-1);
/* Initial problem output */
printf("\n1D adaptive Heat PDE test problem:\n");
printf(" diffusion coefficient: k = %g\n", udata->k);
printf(" initial N = %li\n", udata->N);
/* Initialize data structures */
y = N_VNew_Serial(N); /* Create initial serial vector for solution */
if (check_flag((void *) y, "N_VNew_Serial", 0)) return 1;
N_VConst(0.0, y); /* Set initial conditions */
/* output mesh to disk */
XFID=fopen("heat_mesh.txt","w");
/* output initial mesh to disk */
for (i=0; i<udata->N; i++) fprintf(XFID," %.16e", udata->x[i]);
fprintf(XFID,"\n");
/* Open output stream for results, access data array */
UFID=fopen("heat1D.txt","w");
/* output initial condition to disk */
data = N_VGetArrayPointer(y);
for (i=0; i<udata->N; i++) fprintf(UFID," %.16e", data[i]);
fprintf(UFID,"\n");
/* Create the solver memory */
arkode_mem = ARKodeCreate();
if (check_flag((void *) arkode_mem, "ARKodeCreate", 0)) return 1;
/* Initialize the integrator memory */
flag = ARKodeInit(arkode_mem, NULL, f, T0, y);
if (check_flag(&flag, "ARKodeInit", 1)) return 1;
/* Set routines */
flag = ARKodeSetUserData(arkode_mem, (void *) udata); /* Pass udata to user functions */
if (check_flag(&flag, "ARKodeSetUserData", 1)) return 1;
flag = ARKodeSetMaxNumSteps(arkode_mem, 10000); /* Increase max num steps */
if (check_flag(&flag, "ARKodeSetMaxNumSteps", 1)) return 1;
flag = ARKodeSStolerances(arkode_mem, rtol, atol); /* Specify tolerances */
if (check_flag(&flag, "ARKodeSStolerances", 1)) return 1;
flag = ARKodeSetAdaptivityMethod(arkode_mem, 2, 1, 0, NULL); /* Set adaptivity method */
if (check_flag(&flag, "ARKodeSetAdaptivityMethod", 1)) return 1;
flag = ARKodeSetPredictorMethod(arkode_mem, 0); /* Set predictor method */
if (check_flag(&flag, "ARKodeSetPredictorMethod", 1)) return 1;
/* Linear solver specification */
flag = ARKPcg(arkode_mem, 0, N);
if (check_flag(&flag, "ARKPcg", 1)) return 1;
flag = ARKSpilsSetJacTimesVecFn(arkode_mem, Jac);
if (check_flag(&flag, "ARKSpilsSetJacTimesVecFn", 1)) return 1;
/* Main time-stepping loop: calls ARKode to perform the integration, then
prints results. Stops when the final time has been reached */
t = T0;
olddt = 0.0;
newdt = 0.0;
printf(" iout dt_old dt_new ||u||_rms N NNI NLI\n");
printf(" ----------------------------------------------------------------------------------------\n");
printf(" %4i %19.15e %19.15e %19.15e %li %2i %3i\n",
iout, olddt, newdt, sqrt(N_VDotProd(y,y)/udata->N), udata->N, 0, 0);
while (t < Tf) {
/* "set" routines */
flag = ARKodeSetStopTime(arkode_mem, Tf);
if (check_flag(&flag, "ARKodeSetStopTime", 1)) return 1;
flag = ARKodeSetInitStep(arkode_mem, newdt);
if (check_flag(&flag, "ARKodeSetInitStep", 1)) return 1;
/* call integrator */
flag = ARKode(arkode_mem, Tf, y, &t, ARK_ONE_STEP);
if (check_flag(&flag, "ARKode", 1)) return 1;
/* "get" routines */
flag = ARKodeGetLastStep(arkode_mem, &olddt);
if (check_flag(&flag, "ARKodeGetLastStep", 1)) return 1;
flag = ARKodeGetCurrentStep(arkode_mem, &newdt);
if (check_flag(&flag, "ARKodeGetCurrentStep", 1)) return 1;
flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
if (check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1)) return 1;
flag = ARKSpilsGetNumLinIters(arkode_mem, &nli);
if (check_flag(&flag, "ARKSpilsGetNumLinIters", 1)) return 1;
/* print current solution stats */
iout++;
printf(" %4i %19.15e %19.15e %19.15e %li %2li %3li\n",
iout, olddt, newdt, sqrt(N_VDotProd(y,y)/udata->N), udata->N, nni-nni_cur, nli);
nni_cur = nni;
nni_tot = nni;
nli_tot += nli;
/* output results and current mesh to disk */
data = N_VGetArrayPointer(y);
for (i=0; i<udata->N; i++) fprintf(UFID," %.16e", data[i]);
fprintf(UFID,"\n");
for (i=0; i<udata->N; i++) fprintf(XFID," %.16e", udata->x[i]);
fprintf(XFID,"\n");
/* adapt the spatial mesh */
xnew = adapt_mesh(y, &Nnew, udata);
if (check_flag(xnew, "ark_adapt", 0)) return 1;
/* create N_Vector of new length */
y2 = N_VNew_Serial(Nnew);
if (check_flag((void *) y2, "N_VNew_Serial", 0)) return 1;
/* project solution onto new mesh */
flag = project(udata->N, udata->x, y, Nnew, xnew, y2);
if (check_flag(&flag, "project", 1)) return 1;
/* delete old vector, old mesh */
N_VDestroy_Serial(y);
free(udata->x);
/* swap x and xnew so that new mesh is stored in udata structure */
udata->x = xnew;
xnew = NULL;
udata->N = Nnew; /* store size of new mesh */
/* swap y and y2 so that y holds new solution */
yt = y;
y = y2;
y2 = yt;
/* call ARKodeResize to notify integrator of change in mesh */
flag = ARKodeResize(arkode_mem, y, hscale, t, NULL, NULL);
if (check_flag(&flag, "ARKodeResize", 1)) return 1;
/* destroy and re-allocate linear solver memory */
flag = ARKPcg(arkode_mem, 0, udata->N);
if (check_flag(&flag, "ARKPcg", 1)) return 1;
flag = ARKSpilsSetJacTimesVecFn(arkode_mem, Jac);
if (check_flag(&flag, "ARKSpilsSetJacTimesVecFn", 1)) return 1;
}
printf(" ----------------------------------------------------------------------------------------\n");
/* Free integrator memory */
ARKodeFree(&arkode_mem);
/* print some final statistics */
printf(" Final solver statistics:\n");
printf(" Total number of time steps = %i\n", iout);
printf(" Total nonlinear iterations = %li\n", nni_tot);
printf(" Total linear iterations = %li\n\n", nli_tot);
/* Clean up and return with successful completion */
fclose(UFID);
fclose(XFID);
N_VDestroy_Serial(y); /* Free vectors */
free(udata->x); /* Free user data */
free(udata);
return 0;
}
