Actual source code: test13.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 NEPProjectOperator() function.\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";

     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:   Mat            Id,A,B,mats[3];
     40:   FN             f1,f2,f3,funs[3];
     41:   BV             V;
     42:   DS             ds;
     43:   Vec            v;
     44:   PetscScalar    coeffs[2],b,*M;
     45:   PetscInt       n=32,Istart,Iend,i,j,k,nc;
     46:   PetscReal      tau=0.001,h,a=20,xi;

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

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

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

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

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

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

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

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

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

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

    116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    117:                       Project the NEP
    118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    120:   PetscCall(NEPSetUp(nep));
    121:   PetscCall(NEPGetBV(nep,&V));
    122:   PetscCall(BVGetSizes(V,NULL,NULL,&nc));
    123:   for (i=0;i<nc;i++) {
    124:     PetscCall(BVGetColumn(V,i,&v));
    125:     PetscCall(VecSetValue(v,i,1.0,INSERT_VALUES));
    126:     PetscCall(VecAssemblyBegin(v));
    127:     PetscCall(VecAssemblyEnd(v));
    128:     PetscCall(BVRestoreColumn(V,i,&v));
    129:   }
    130:   PetscCall(NEPGetDS(nep,&ds));
    131:   PetscCall(DSSetType(ds,DSNEP));
    132:   PetscCall(DSNEPSetFN(ds,3,funs));
    133:   PetscCall(DSAllocate(ds,nc));
    134:   PetscCall(DSSetDimensions(ds,nc,0,0));
    135:   PetscCall(NEPProjectOperator(nep,0,nc));

    137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    138:                 Display projected matrices and clean up
    139:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    141:   for (k=0;k<3;k++) {
    142:     PetscCall(DSGetArray(ds,DSMatExtra[k],&M));
    143:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%" PetscInt_FMT " = \n",k));
    144:     for (i=0;i<nc;i++) {
    145:       for (j=0;j<nc;j++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  %.5g",(double)PetscRealPart(M[i+j*nc])));
    146:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    147:     }
    148:     PetscCall(DSRestoreArray(ds,DSMatExtra[k],&M));
    149:   }

    151:   PetscCall(NEPDestroy(&nep));
    152:   PetscCall(MatDestroy(&Id));
    153:   PetscCall(MatDestroy(&A));
    154:   PetscCall(MatDestroy(&B));
    155:   PetscCall(FNDestroy(&f1));
    156:   PetscCall(FNDestroy(&f2));
    157:   PetscCall(FNDestroy(&f3));
    158:   PetscCall(SlepcFinalize());
    159:   return 0;
    160: }

    162: /*TEST

    164:    test:
    165:       suffix: 1
    166:       args: -nep_ncv 5

    168: TEST*/