Date: 2022-10-01T06:40:39+00:00

Actual source code: test13.c
slepc-3.18.0 2022-10-01
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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 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;

     49:   SlepcInitialize(&argc,&argv,(char*)0,help);
     50:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     51:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     52:   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:   NEPCreate(PETSC_COMM_WORLD,&nep);

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

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

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

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

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

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

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

    118:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    119:                       Project the NEP
    120:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    140:                 Display projected matrices and clean up
    141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    143:   for (k=0;k<3;k++) {
    144:     DSGetArray(ds,DSMatExtra[k],&M);
    145:     PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%" PetscInt_FMT " = \n",k);
    146:     for (i=0;i<nc;i++) {
    147:       for (j=0;j<nc;j++) PetscPrintf(PETSC_COMM_WORLD,"  %.5g",(double)PetscRealPart(M[i+j*nc]));
    148:       PetscPrintf(PETSC_COMM_WORLD,"\n");
    149:     }
    150:     DSRestoreArray(ds,DSMatExtra[k],&M);
    151:   }

    153:   NEPDestroy(&nep);
    154:   MatDestroy(&Id);
    155:   MatDestroy(&A);
    156:   MatDestroy(&B);
    157:   FNDestroy(&f1);
    158:   FNDestroy(&f2);
    159:   FNDestroy(&f3);
    160:   SlepcFinalize();
    161:   return 0;
    162: }

    164: /*TEST

    166:    test:
    167:       suffix: 1
    168:       args: -nep_ncv 5

    170: TEST*/