Date: 2023-09-05T10:18:20+00:00

Actual source code: test5.c
slepc-3.19.2 2023-09-05
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      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 INTERPOL solver with a user-provided PEP.\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\n";

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

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

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

     25:    Discretization leads to a DDE of dimension n

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

     29:    which results in the nonlinear eigenproblem

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

     34: #include <slepcnep.h>

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

     50:   PetscFunctionBeginUser;
     51:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     52:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     53:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
     54:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
     55:   h = PETSC_PI/(PetscReal)(n+1);

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:       Create a standalone PEP and RG objects with appropriate settings
     59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     61:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
     62:   PetscCall(PEPSetType(pep,PEPTOAR));
     63:   PetscCall(PEPSetFromOptions(pep));

     65:   PetscCall(RGCreate(PETSC_COMM_WORLD,&rg));
     66:   PetscCall(RGSetType(rg,RGINTERVAL));
     67:   PetscCall(RGIntervalSetEndpoints(rg,5,20,-0.1,0.1));
     68:   PetscCall(RGSetFromOptions(rg));

     70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:      Create nonlinear eigensolver context
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

    116:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
    117:   PetscCall(FNSetType(f2,FNRATIONAL));
    118:   coeffs[0] = 1.0;
    119:   PetscCall(FNRationalSetNumerator(f2,1,coeffs));

    121:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
    122:   PetscCall(FNSetType(f3,FNEXP));
    123:   PetscCall(FNSetScale(f3,-tau,1.0));

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

    131:   /* Customize nonlinear solver; set runtime options */
    132:   PetscCall(NEPSetType(nep,NEPINTERPOL));
    133:   PetscCall(NEPSetRG(nep,rg));
    134:   PetscCall(NEPInterpolSetPEP(nep,pep));
    135:   PetscCall(NEPInterpolGetInterpolation(nep,&tol,&deg));
    136:   PetscCall(NEPInterpolSetInterpolation(nep,tol,deg+2));  /* increase degree of interpolation */
    137:   PetscCall(NEPSetFromOptions(nep));

    139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    140:                       Solve the eigensystem
    141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    143:   PetscCall(NEPSolve(nep));
    144:   PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
    145:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    148:                     Display solution and clean up
    149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    151:   /* show detailed info unless -terse option is given by user */
    152:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    153:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    154:   else {
    155:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    156:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    157:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    158:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    159:   }
    160:   PetscCall(NEPDestroy(&nep));
    161:   PetscCall(PEPDestroy(&pep));
    162:   PetscCall(RGDestroy(&rg));
    163:   PetscCall(MatDestroy(&Id));
    164:   PetscCall(MatDestroy(&A));
    165:   PetscCall(MatDestroy(&B));
    166:   PetscCall(FNDestroy(&f1));
    167:   PetscCall(FNDestroy(&f2));
    168:   PetscCall(FNDestroy(&f3));
    169:   PetscCall(SlepcFinalize());
    170:   return 0;
    171: }

    173: /*TEST

    175:    testset:
    176:       args: -nep_nev 3 -nep_target 5 -terse
    177:       output_file: output/test5_1.out
    178:       filter: sed -e "s/[+-]0\.0*i//g"
    179:       requires: !single
    180:       test:
    181:          suffix: 1
    182:       test:
    183:          suffix: 2_cuda
    184:          args: -mat_type aijcusparse
    185:          requires: cuda
    186:       test:
    187:          suffix: 3
    188:          args: -nep_view_values draw
    189:          requires: x

    191: TEST*/