Date: 2018-10-23T10:32:49+00:00

Actual source code: test11.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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:   PetscScalar    coeffs[2],b;
     44:   PetscInt       n=128,Istart,Iend,i,nsolve;
     45:   PetscReal      tau=0.001,h,a=20,xi;
     46:   PetscBool      terse;

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

     55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     56:      Create nonlinear eigensolver context
     57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     59:   NEPCreate(PETSC_COMM_WORLD,&nep);

     61:   /* Identity matrix */
     62:   MatCreate(PETSC_COMM_WORLD,&Id);
     63:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
     64:   MatSetFromOptions(Id);
     65:   MatSetUp(Id);
     66:   MatGetOwnershipRange(Id,&Istart,&Iend);
     67:   for (i=Istart;i<Iend;i++) {
     68:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
     69:   }
     70:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
     71:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
     72:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

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

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

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

    110:   FNCreate(PETSC_COMM_WORLD,&f2);
    111:   FNSetType(f2,FNRATIONAL);
    112:   coeffs[0] = 1.0;
    113:   FNRationalSetNumerator(f2,1,coeffs);

    115:   FNCreate(PETSC_COMM_WORLD,&f3);
    116:   FNSetType(f3,FNEXP);
    117:   FNSetScale(f3,-tau,1.0);

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

    125:   /* Customize nonlinear solver; set runtime options */
    126:   NEPSetType(nep,NEPCISS);
    127:   NEPSetDimensions(nep,1,24,PETSC_DEFAULT);
    128:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
    129:   NEPGetRG(nep,&rg);
    130:   RGSetType(rg,RGELLIPSE);
    131:   RGEllipseSetParameters(rg,10.0,9.5,0.1);
    132:   NEPCISSSetSizes(nep,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1,PETSC_DEFAULT,PETSC_TRUE);
    133:   NEPCISSGetKSPs(nep,&nsolve,&ksp);
    134:   for (i=0;i<nsolve;i++) {
    135:     KSPSetTolerances(ksp[i],1e-12,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    136:     KSPSetType(ksp[i],KSPBCGS);
    137:     KSPGetPC(ksp[i],&pc);
    138:     PCSetType(pc,PCSOR);
    139:   }
    140:   NEPSetFromOptions(nep);

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:                       Solve the eigensystem
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    146:   PetscPrintf(PETSC_COMM_WORLD," Running CISS with %D KSP solvers\n",nsolve);
    147:   NEPSolve(nep);

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:                     Display solution and clean up
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    153:   /* show detailed info unless -terse option is given by user */
    154:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    155:   if (terse) {
    156:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    157:   } else {
    158:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    159:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    160:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    161:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    162:   }
    163:   NEPDestroy(&nep);
    164:   MatDestroy(&Id);
    165:   MatDestroy(&A);
    166:   MatDestroy(&B);
    167:   FNDestroy(&f1);
    168:   FNDestroy(&f2);
    169:   FNDestroy(&f3);
    170:   SlepcFinalize();
    171:   return ierr;
    172: }

    174: /*TEST

    176:    build:
    177:       requires: complex

    179:    test:
    180:       suffix: 1
    181:       args: -terse
    182:       requires: complex

    184: TEST*/