예제 #1
0
/* Fortran interface to C routine ARKode (the main integrator); 
   see farkode.h for further details */
void FARK_ARKODE(realtype *tout, realtype *t, realtype *y, 
		 int *itask, int *ier) {

  /* attach user solution array to solver memory */
  N_VSetArrayPointer(y, F2C_ARKODE_vec);

  /* call ARKode solver */
  *ier = ARKode(ARK_arkodemem, *tout, F2C_ARKODE_vec, t, *itask);

  /* detach user solution array from solver memory */
  N_VSetArrayPointer(NULL, F2C_ARKODE_vec);

  /* Load optional outputs in iout & rout */
  ARKodeGetWorkSpace(ARK_arkodemem,
		     &ARK_iout[0],          /* LENRW   */
		     &ARK_iout[1]);         /* LENIW   */
  ARKodeGetIntegratorStats(ARK_arkodemem, 
			   &ARK_iout[2],    /* NST     */
			   &ARK_iout[3],    /* NST_STB */
			   &ARK_iout[4],    /* NST_ACC */ 
			   &ARK_iout[5],    /* NST_ATT */ 
			   &ARK_iout[6],    /* NFE     */ 
			   &ARK_iout[7],    /* NFI     */ 
			   &ARK_iout[8],    /* NSETUPS */ 
			   &ARK_iout[9],    /* NETF    */ 
			   &ARK_rout[0],    /* H0U     */
			   &ARK_rout[1],    /* HU      */ 
			   &ARK_rout[2],    /* HCUR    */ 
			   &ARK_rout[3]);   /* TCUR    */ 
  ARKodeGetTolScaleFactor(ARK_arkodemem, 
			  &ARK_rout[4]);    /* TOLSFAC */
  ARKodeGetNonlinSolvStats(ARK_arkodemem,
                          &ARK_iout[10],    /* NNI     */
                          &ARK_iout[11]);   /* NCFN    */
  
  /* If root finding is on, load those outputs as well */
  if (ARK_nrtfn != 0)
    ARKodeGetNumGEvals(ARK_arkodemem, &ARK_iout[12]);  /* NGE */

  /* Attach linear solver outputs */
  switch(ARK_ls) {
  case ARK_LS_DENSE:
  case ARK_LS_BAND:
  case ARK_LS_LAPACKDENSE:
  case ARK_LS_LAPACKBAND:
    ARKDlsGetWorkSpace(ARK_arkodemem, &ARK_iout[13], &ARK_iout[14]);  /* LENRWLS, LENIWLS */
    ARKDlsGetLastFlag(ARK_arkodemem, &ARK_iout[15]);                  /* LSTF  */
    ARKDlsGetNumRhsEvals(ARK_arkodemem, &ARK_iout[16]);               /* NFELS */
    ARKDlsGetNumJacEvals(ARK_arkodemem, &ARK_iout[17]);               /* NJE   */
    break;
  case ARK_LS_KLU:
  case ARK_LS_SUPERLUMT:
    ARKSlsGetLastFlag(ARK_arkodemem, &ARK_iout[15]);                  /* LSTF  */
    ARKSlsGetNumJacEvals(ARK_arkodemem, &ARK_iout[17]);               /* NJE   */
    break;
  case ARK_LS_SPGMR:
  case ARK_LS_SPBCG:
  case ARK_LS_SPTFQMR:
  case ARK_LS_SPFGMR:
  case ARK_LS_PCG:
    ARKSpilsGetWorkSpace(ARK_arkodemem, &ARK_iout[13], &ARK_iout[14]); /* LENRWLS, LENIWLS */
    ARKSpilsGetLastFlag(ARK_arkodemem, &ARK_iout[15]);                 /* LSTF  */
    ARKSpilsGetNumRhsEvals(ARK_arkodemem, &ARK_iout[16]);              /* NFELS */
    ARKSpilsGetNumJtimesEvals(ARK_arkodemem, &ARK_iout[17]);           /* NJTV  */
    ARKSpilsGetNumPrecEvals(ARK_arkodemem, &ARK_iout[18]);             /* NPE   */
    ARKSpilsGetNumPrecSolves(ARK_arkodemem, &ARK_iout[19]);            /* NPS   */
    ARKSpilsGetNumLinIters(ARK_arkodemem, &ARK_iout[20]);              /* NLI   */
    ARKSpilsGetNumConvFails(ARK_arkodemem, &ARK_iout[21]);             /* NCFL  */
  }

  /* Attach mass matrix linear solver outputs */
  switch(ARK_mass_ls) {
  case ARK_LS_DENSE:
  case ARK_LS_BAND:
  case ARK_LS_LAPACKDENSE:
  case ARK_LS_LAPACKBAND:
    ARKDlsGetMassWorkSpace(ARK_arkodemem, &ARK_iout[22], &ARK_iout[23]);  /* LENRWMS, LENIWMS */
    ARKDlsGetLastMassFlag(ARK_arkodemem, &ARK_iout[24]);                  /* LSTMF */
    ARKDlsGetNumMassEvals(ARK_arkodemem, &ARK_iout[25]);                  /* NME   */
    break;
  case ARK_LS_KLU:
  case ARK_LS_SUPERLUMT:
    ARKSlsGetLastMassFlag(ARK_arkodemem, &ARK_iout[24]);                  /* LSTMF */
    ARKSlsGetNumMassEvals(ARK_arkodemem, &ARK_iout[25]);                  /* NME   */
    break;
  case ARK_LS_SPGMR:
  case ARK_LS_SPBCG:
  case ARK_LS_SPTFQMR:
  case ARK_LS_SPFGMR:
  case ARK_LS_PCG:
    ARKSpilsGetMassWorkSpace(ARK_arkodemem, &ARK_iout[22], &ARK_iout[23]); /* LENRWMS, LENIWMS */
    ARKSpilsGetLastMassFlag(ARK_arkodemem, &ARK_iout[24]);                 /* LSTMF */
    ARKSpilsGetNumMassPrecEvals(ARK_arkodemem, &ARK_iout[25]);             /* NMPE  */
    ARKSpilsGetNumMassPrecSolves(ARK_arkodemem, &ARK_iout[26]);            /* NMPS  */
    ARKSpilsGetNumMassIters(ARK_arkodemem, &ARK_iout[27]);                 /* NMLI  */
    ARKSpilsGetNumMassConvFails(ARK_arkodemem, &ARK_iout[28]);             /* NMCFL */
  }
  return;
}
예제 #2
0
/* 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;
}
예제 #3
0
/* 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;
}
예제 #4
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;
}