/* Fortran interface to C routine ARKPcg and it's associated "set" routines; see farkode.h for further details */ void FARK_PCG(int *pretype, int *maxl, realtype *delt, int *ier) { *ier = ARKPcg(ARK_arkodemem, *pretype, *maxl); if (*ier != ARKSPILS_SUCCESS) return; *ier = ARKSpilsSetEpsLin(ARK_arkodemem, *delt); if (*ier != ARKSPILS_SUCCESS) return; ARK_ls = ARK_LS_PCG; return; }
/* 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; }