Date: 2018-10-23T10:32:47+00:00

Actual source code: test6.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 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;
     47:   PetscReal      tau=0.001,h,a=20,xi;
     48:   PetscBool      terse,initv=PETSC_FALSE;

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

     58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:       Create a standalone KSP with appropriate settings
     60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69:      Create nonlinear eigensolver context
     70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     72:   NEPCreate(PETSC_COMM_WORLD,&nep);

     74:   /* Identity matrix */
     75:   MatCreate(PETSC_COMM_WORLD,&Id);
     76:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
     77:   MatSetFromOptions(Id);
     78:   MatSetUp(Id);
     79:   MatGetOwnershipRange(Id,&Istart,&Iend);
     80:   for (i=Istart;i<Iend;i++) {
     81:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
     82:   }
     83:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
     85:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

     87:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     88:   MatCreate(PETSC_COMM_WORLD,&A);
     89:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     90:   MatSetFromOptions(A);
     91:   MatSetUp(A);
     92:   MatGetOwnershipRange(A,&Istart,&Iend);
     93:   for (i=Istart;i<Iend;i++) {
     94:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
     95:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
     96:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
     97:   }
     98:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     99:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    100:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

    102:   /* B = diag(b(xi)) */
    103:   MatCreate(PETSC_COMM_WORLD,&B);
    104:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
    105:   MatSetFromOptions(B);
    106:   MatSetUp(B);
    107:   MatGetOwnershipRange(B,&Istart,&Iend);
    108:   for (i=Istart;i<Iend;i++) {
    109:     xi = (i+1)*h;
    110:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    111:     MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
    112:   }
    113:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    114:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    115:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

    117:   /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
    118:   FNCreate(PETSC_COMM_WORLD,&f1);
    119:   FNSetType(f1,FNRATIONAL);
    120:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    121:   FNRationalSetNumerator(f1,2,coeffs);

    123:   FNCreate(PETSC_COMM_WORLD,&f2);
    124:   FNSetType(f2,FNRATIONAL);
    125:   coeffs[0] = 1.0;
    126:   FNRationalSetNumerator(f2,1,coeffs);

    128:   FNCreate(PETSC_COMM_WORLD,&f3);
    129:   FNSetType(f3,FNEXP);
    130:   FNSetScale(f3,-tau,1.0);

    132:   /* Set the split operator */
    133:   mats[0] = A;  funs[0] = f2;
    134:   mats[1] = Id; funs[1] = f1;
    135:   mats[2] = B;  funs[2] = f3;
    136:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

    138:   /* Customize nonlinear solver; set runtime options */
    139:   NEPSetOptionsPrefix(nep,"myprefix_");
    140:   NEPSetType(nep,NEPNARNOLDI);
    141:   NEPNArnoldiSetKSP(nep,ksp);
    142:   if (initv) { /* initial vector */
    143:     MatCreateVecs(A,&v0,NULL);
    144:     VecGetArray(v0,&pv);
    145:     for (i=Istart;i<Iend;i++) pv[i-Istart] = PetscSinReal((4.0*PETSC_PI*i)/n);
    146:     VecRestoreArray(v0,&pv);
    147:     NEPSetInitialSpace(nep,1,&v0);
    148:     VecDestroy(&v0);
    149:   }
    150:   NEPSetFromOptions(nep);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:                       Solve the eigensystem
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   NEPSolve(nep);
    157:   NEPGetDimensions(nep,&nev,NULL,NULL);
    158:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    161:                     Display solution and clean up
    162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    164:   /* show detailed info unless -terse option is given by user */
    165:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    166:   if (terse) {
    167:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    168:   } else {
    169:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    170:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    171:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    172:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    173:   }
    174:   NEPDestroy(&nep);
    175:   KSPDestroy(&ksp);
    176:   MatDestroy(&Id);
    177:   MatDestroy(&A);
    178:   MatDestroy(&B);
    179:   FNDestroy(&f1);
    180:   FNDestroy(&f2);
    181:   FNDestroy(&f3);
    182:   SlepcFinalize();
    183:   return ierr;
    184: }

    186: /*TEST

    188:    test:
    189:       suffix: 1
    190:       args: -myprefix_nep_view -myprefix_nep_monitor_conv -initv -terse
    191:       filter: grep -v "tolerance" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    192:       requires: double !complex !define(PETSC_USE_64BIT_INDICES)

    194: TEST*/