Actual source code: test11.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 CISS solver with the problem of ex22.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     14:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

     16: /*
     17:    Solve parabolic partial differential equation with time delay tau

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

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

     24:    Discretization leads to a DDE of dimension n

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

     28:    which results in the nonlinear eigenproblem

     30:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
     31: */

     33: #include <slepcnep.h>

     35: int main(int argc,char **argv)
     36: {
     37:   NEP               nep;
     38:   Mat               Id,A,B,mats[3];
     39:   FN                f1,f2,f3,funs[3];
     40:   RG                rg;
     41:   KSP               *ksp;
     42:   PC                pc;
     43:   NEPCISSExtraction ext;
     44:   PetscScalar       coeffs[2],b;
     45:   PetscInt          n=128,Istart,Iend,i,nsolve;
     46:   PetscReal         tau=0.001,h,a=20,xi;
     47:   PetscBool         flg,terse;

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

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:      Create nonlinear eigensolver context
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     62:   /* Identity matrix */
     63:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
     64:   PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));

     66:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     67:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     68:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
     69:   PetscCall(MatSetFromOptions(A));
     70:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     71:   for (i=Istart;i<Iend;i++) {
     72:     if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
     73:     if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
     74:     PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     75:   }
     76:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     77:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
     78:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));

     80:   /* B = diag(b(xi)) */
     81:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
     82:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
     83:   PetscCall(MatSetFromOptions(B));
     84:   PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
     85:   for (i=Istart;i<Iend;i++) {
     86:     xi = (i+1)*h;
     87:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
     88:     PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES));
     89:   }
     90:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
     91:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
     92:   PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));

     94:   /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
     95:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
     96:   PetscCall(FNSetType(f1,FNRATIONAL));
     97:   coeffs[0] = -1.0; coeffs[1] = 0.0;
     98:   PetscCall(FNRationalSetNumerator(f1,2,coeffs));

    100:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
    101:   PetscCall(FNSetType(f2,FNRATIONAL));
    102:   coeffs[0] = 1.0;
    103:   PetscCall(FNRationalSetNumerator(f2,1,coeffs));

    105:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
    106:   PetscCall(FNSetType(f3,FNEXP));
    107:   PetscCall(FNSetScale(f3,-tau,1.0));

    109:   /* Set the split operator */
    110:   mats[0] = A;  funs[0] = f2;
    111:   mats[1] = Id; funs[1] = f1;
    112:   mats[2] = B;  funs[2] = f3;
    113:   PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));

    115:   /* Customize nonlinear solver; set runtime options */
    116:   PetscCall(NEPSetType(nep,NEPCISS));
    117:   PetscCall(NEPSetDimensions(nep,1,24,PETSC_DETERMINE));
    118:   PetscCall(NEPSetTolerances(nep,1e-9,PETSC_CURRENT));
    119:   PetscCall(NEPGetRG(nep,&rg));
    120:   PetscCall(RGSetType(rg,RGELLIPSE));
    121:   PetscCall(RGEllipseSetParameters(rg,10.0,9.5,0.1));
    122:   PetscCall(NEPCISSSetSizes(nep,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_DETERMINE,1,PETSC_DETERMINE,PETSC_TRUE));
    123:   PetscCall(NEPCISSGetKSPs(nep,&nsolve,&ksp));
    124:   for (i=0;i<nsolve;i++) {
    125:     PetscCall(KSPSetTolerances(ksp[i],1e-12,PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
    126:     PetscCall(KSPSetType(ksp[i],KSPBCGS));
    127:     PetscCall(KSPGetPC(ksp[i],&pc));
    128:     PetscCall(PCSetType(pc,PCSOR));
    129:   }
    130:   PetscCall(NEPSetFromOptions(nep));

    132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    133:                       Solve the eigensystem
    134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    136:   PetscCall(PetscObjectTypeCompare((PetscObject)nep,NEPCISS,&flg));
    137:   if (flg) {
    138:     PetscCall(NEPCISSGetExtraction(nep,&ext));
    139:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Running CISS with %" PetscInt_FMT " KSP solvers (%s extraction)\n",nsolve,NEPCISSExtractions[ext]));
    140:   }
    141:   PetscCall(NEPSolve(nep));

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:                     Display solution and clean up
    145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    147:   /* show detailed info unless -terse option is given by user */
    148:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    149:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    150:   else {
    151:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    152:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    153:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    154:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    155:   }
    156:   PetscCall(NEPDestroy(&nep));
    157:   PetscCall(MatDestroy(&Id));
    158:   PetscCall(MatDestroy(&A));
    159:   PetscCall(MatDestroy(&B));
    160:   PetscCall(FNDestroy(&f1));
    161:   PetscCall(FNDestroy(&f2));
    162:   PetscCall(FNDestroy(&f3));
    163:   PetscCall(SlepcFinalize());
    164:   return 0;
    165: }

    167: /*TEST

    169:    build:
    170:       requires: complex

    172:    testset:
    173:       args: -nep_ciss_extraction {{ritz hankel caa}} -terse
    174:       requires: complex !single
    175:       output_file: output/test11_1.out
    176:       filter: sed -e "s/([A-Z]* extraction)//"
    177:       test:
    178:          suffix: 1
    179:          args: -nep_ciss_delta 1e-10
    180:       test:
    181:          suffix: 2
    182:          nsize: 2
    183:          args: -nep_ciss_partitions 2
    184:       test:
    185:          suffix: 3
    186:          args: -nep_ciss_moments 6 -nep_ciss_blocksize 4 -nep_ciss_refine_inner 1 -nep_ciss_refine_blocksize 2

    188:    test:
    189:       suffix: 4
    190:       args: -terse -nep_view
    191:       requires: complex !single
    192:       filter: grep -v tolerance | grep -v threshold

    194: TEST*/