Actual source code: test6.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Test the NArnoldi solver with a user-provided KSP.\n\n"
     12:   "This is based on ex22.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     15:   "  -tau <tau>, where <tau> is the delay parameter.\n"
     16:   "  -initv ... set an initial vector.\n\n";

     18: /*
     19:    Solve parabolic partial differential equation with time delay tau

     21:             u_t = u_xx + a*u(t) + b*u(t-tau)
     22:             u(0,t) = u(pi,t) = 0

     24:    with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).

     26:    Discretization leads to a DDE of dimension n

     28:             -u' = A*u(t) + B*u(t-tau)

     30:    which results in the nonlinear eigenproblem

     32:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
     33: */

     35: #include <slepcnep.h>

     37: int main(int argc,char **argv)
     38: {
     39:   NEP            nep;
     40:   KSP            ksp;
     41:   PC             pc;
     42:   Mat            Id,A,B,mats[3];
     43:   FN             f1,f2,f3,funs[3];
     44:   Vec            v0;
     45:   PetscScalar    coeffs[2],b,*pv;
     46:   PetscInt       n=128,nev,Istart,Iend,i,lag;
     47:   PetscReal      tau=0.001,h,a=20,xi;
     48:   PetscBool      terse,initv=PETSC_FALSE;
     49:   const char     *prefix;

     51:   PetscFunctionBeginUser;
     52:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     53:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     54:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
     55:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-initv",&initv,NULL));
     56:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
     57:   h = PETSC_PI/(PetscReal)(n+1);

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:       Create a standalone KSP with appropriate settings
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   PetscCall(KSPCreate(PETSC_COMM_WORLD,&ksp));
     64:   PetscCall(KSPSetType(ksp,KSPBCGS));
     65:   PetscCall(KSPGetPC(ksp,&pc));
     66:   PetscCall(PCSetType(pc,PCBJACOBI));
     67:   PetscCall(KSPSetFromOptions(ksp));

     69:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     70:      Create nonlinear eigensolver context
     71:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     73:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));

     75:   /* Identity matrix */
     76:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
     77:   PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));

     79:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     80:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     81:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
     82:   PetscCall(MatSetFromOptions(A));
     83:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     84:   for (i=Istart;i<Iend;i++) {
     85:     if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
     86:     if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
     87:     PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     88:   }
     89:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     90:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
     91:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));

     93:   /* B = diag(b(xi)) */
     94:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
     95:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
     96:   PetscCall(MatSetFromOptions(B));
     97:   PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
     98:   for (i=Istart;i<Iend;i++) {
     99:     xi = (i+1)*h;
    100:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    101:     PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES));
    102:   }
    103:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    104:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    105:   PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));

    107:   /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
    108:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
    109:   PetscCall(FNSetType(f1,FNRATIONAL));
    110:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    111:   PetscCall(FNRationalSetNumerator(f1,2,coeffs));

    113:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
    114:   PetscCall(FNSetType(f2,FNRATIONAL));
    115:   coeffs[0] = 1.0;
    116:   PetscCall(FNRationalSetNumerator(f2,1,coeffs));

    118:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
    119:   PetscCall(FNSetType(f3,FNEXP));
    120:   PetscCall(FNSetScale(f3,-tau,1.0));

    122:   /* Set the split operator */
    123:   mats[0] = A;  funs[0] = f2;
    124:   mats[1] = Id; funs[1] = f1;
    125:   mats[2] = B;  funs[2] = f3;
    126:   PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));

    128:   /* Customize nonlinear solver; set runtime options */
    129:   PetscCall(NEPSetOptionsPrefix(nep,"check_"));
    130:   PetscCall(NEPAppendOptionsPrefix(nep,"myprefix_"));
    131:   PetscCall(NEPGetOptionsPrefix(nep,&prefix));
    132:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"NEP prefix is currently: %s\n\n",prefix));
    133:   PetscCall(NEPSetType(nep,NEPNARNOLDI));
    134:   PetscCall(NEPNArnoldiSetKSP(nep,ksp));
    135:   if (initv) { /* initial vector */
    136:     PetscCall(MatCreateVecs(A,&v0,NULL));
    137:     PetscCall(VecGetArray(v0,&pv));
    138:     for (i=Istart;i<Iend;i++) pv[i-Istart] = PetscSinReal((4.0*PETSC_PI*i)/n);
    139:     PetscCall(VecRestoreArray(v0,&pv));
    140:     PetscCall(NEPSetInitialSpace(nep,1,&v0));
    141:     PetscCall(VecDestroy(&v0));
    142:   }
    143:   PetscCall(NEPSetFromOptions(nep));

    145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:                       Solve the eigensystem
    147:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    149:   PetscCall(NEPSolve(nep));
    150:   PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
    151:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
    152:   PetscCall(NEPNArnoldiGetLagPreconditioner(nep,&lag));
    153:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," N-Arnoldi lag parameter: %" PetscInt_FMT "\n",lag));

    155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    156:                     Display solution and clean up
    157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    159:   /* show detailed info unless -terse option is given by user */
    160:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    161:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    162:   else {
    163:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    164:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    165:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    166:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    167:   }
    168:   PetscCall(NEPDestroy(&nep));
    169:   PetscCall(KSPDestroy(&ksp));
    170:   PetscCall(MatDestroy(&Id));
    171:   PetscCall(MatDestroy(&A));
    172:   PetscCall(MatDestroy(&B));
    173:   PetscCall(FNDestroy(&f1));
    174:   PetscCall(FNDestroy(&f2));
    175:   PetscCall(FNDestroy(&f3));
    176:   PetscCall(SlepcFinalize());
    177:   return 0;
    178: }

    180: /*TEST

    182:    test:
    183:       suffix: 1
    184:       args: -check_myprefix_nep_view -check_myprefix_nep_monitor_conv -initv -terse
    185:       filter: grep -v "tolerance" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g" -e "s/+0i//g"
    186:       requires: double

    188: TEST*/