Date: 2021-02-01T14:42:17+00:00

Actual source code: test13.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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() operator.\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);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,(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);
    124:   NEPSetType(nep,NEPNARNOLDI);
    125:   NEPSetFromOptions(nep);

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:                       Project the NEP
    129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    131:   NEPSetUp(nep);
    132:   NEPGetBV(nep,&V);
    133:   BVGetSizes(V,NULL,NULL,&nc);
    134:   for (i=0;i<nc;i++) {
    135:     BVGetColumn(V,i,&v);
    136:     VecSetValue(v,i,1.0,INSERT_VALUES);
    137:     VecAssemblyBegin(v);
    138:     VecAssemblyEnd(v);
    139:     BVRestoreColumn(V,i,&v);
    140:   }
    141:   NEPGetDS(nep,&ds);
    142:   DSSetType(ds,DSNEP);
    143:   DSNEPSetFN(ds,3,funs);
    144:   DSAllocate(ds,nc);
    145:   DSSetDimensions(ds,nc,0,0,0);
    146:   NEPProjectOperator(nep,0,nc);

    148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    149:                 Display projected matrices and clean up
    150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    152:   for (k=0;k<3;k++) {
    153:     DSGetArray(ds,DSMatExtra[k],&M);
    154:     PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%d = \n",k);
    155:     for (i=0;i<nc;i++) {
    156:       for (j=0;j<nc;j++) {
    157:         PetscPrintf(PETSC_COMM_WORLD,"  %.5g",(double)PetscRealPart(M[i+j*nc]));
    158:       }
    159:       PetscPrintf(PETSC_COMM_WORLD,"\n");
    160:     }
    161:     DSRestoreArray(ds,DSMatExtra[k],&M);
    162:   }

    164:   NEPDestroy(&nep);
    165:   MatDestroy(&Id);
    166:   MatDestroy(&A);
    167:   MatDestroy(&B);
    168:   FNDestroy(&f1);
    169:   FNDestroy(&f2);
    170:   FNDestroy(&f3);
    171:   SlepcFinalize();
    172:   return ierr;
    173: }

    175: /*TEST

    177:    test:
    178:       suffix: 1
    179:       args: -nep_ncv 5

    181: TEST*/