Date: 2016-03-29T14:59:26+00:00

Actual source code: ex22.c
slepc-3.6.3 2016-03-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Delay differential equation.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     25:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

     27: /*
     28:    Solve parabolic partial differential equation with time delay tau

     30:             u_t = u_xx + a*u(t) + b*u(t-tau)
     31:             u(0,t) = u(pi,t) = 0

     33:    with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).

     35:    Discretization leads to a DDE of dimension n

     37:             -u' = A*u(t) + B*u(t-tau)

     39:    which results in the nonlinear eigenproblem

     41:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
     42: */

     44: #include <slepcnep.h>

     48: int main(int argc,char **argv)
     49: {
     50:   NEP            nep;             /* nonlinear eigensolver context */
     51:   Mat            Id,A,B;          /* problem matrices */
     52:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
     53:   Mat            mats[3];
     54:   FN             funs[3];
     55:   NEPType        type;
     56:   PetscScalar    coeffs[2],b;
     57:   PetscInt       n=128,nev,Istart,Iend,i,its;
     58:   PetscReal      tau=0.001,h,a=20,xi;
     59:   PetscBool      terse;

     62:   SlepcInitialize(&argc,&argv,(char*)0,help);
     63:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     64:   PetscOptionsGetReal(NULL,"-tau",&tau,NULL);
     65:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
     66:   h = PETSC_PI/(PetscReal)(n+1);

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

     72:   NEPCreate(PETSC_COMM_WORLD,&nep);

     74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     75:      Create problem matrices and coefficient functions. Pass them to NEP
     76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     78:   /*
     79:      Identity matrix
     80:   */
     81:   MatCreate(PETSC_COMM_WORLD,&Id);
     82:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
     83:   MatSetFromOptions(Id);
     84:   MatSetUp(Id);
     85:   MatGetOwnershipRange(Id,&Istart,&Iend);
     86:   for (i=Istart;i<Iend;i++) {
     87:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
     88:   }
     89:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
     90:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
     91:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

     93:   /*
     94:      A = 1/h^2*tridiag(1,-2,1) + a*I
     95:   */
     96:   MatCreate(PETSC_COMM_WORLD,&A);
     97:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     98:   MatSetFromOptions(A);
     99:   MatSetUp(A);
    100:   MatGetOwnershipRange(A,&Istart,&Iend);
    101:   for (i=Istart;i<Iend;i++) {
    102:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
    103:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
    104:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
    105:   }
    106:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    107:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    108:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

    110:   /*
    111:      B = diag(b(xi))
    112:   */
    113:   MatCreate(PETSC_COMM_WORLD,&B);
    114:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
    115:   MatSetFromOptions(B);
    116:   MatSetUp(B);
    117:   MatGetOwnershipRange(B,&Istart,&Iend);
    118:   for (i=Istart;i<Iend;i++) {
    119:     xi = (i+1)*h;
    120:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    121:     MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
    122:   }
    123:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    124:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    125:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

    127:   /*
    128:      Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
    129:   */
    130:   FNCreate(PETSC_COMM_WORLD,&f1);
    131:   FNSetType(f1,FNRATIONAL);
    132:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    133:   FNRationalSetNumerator(f1,2,coeffs);

    135:   FNCreate(PETSC_COMM_WORLD,&f2);
    136:   FNSetType(f2,FNRATIONAL);
    137:   coeffs[0] = 1.0;
    138:   FNRationalSetNumerator(f2,1,coeffs);

    140:   FNCreate(PETSC_COMM_WORLD,&f3);
    141:   FNSetType(f3,FNEXP);
    142:   FNSetScale(f3,-tau,1.0);

    144:   /*
    145:      Set the split operator. Note that A is passed first so that
    146:      SUBSET_NONZERO_PATTERN can be used
    147:   */
    148:   mats[0] = A;  funs[0] = f2;
    149:   mats[1] = Id; funs[1] = f1;
    150:   mats[2] = B;  funs[2] = f3;
    151:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

    153:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    154:              Customize nonlinear solver; set runtime options
    155:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    157:   NEPSetTolerances(nep,PETSC_DEFAULT,1e-9,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    158:   NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);
    159:   NEPSetLagPreconditioner(nep,0);

    161:   /*
    162:      Set solver parameters at runtime
    163:   */
    164:   NEPSetFromOptions(nep);

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:                       Solve the eigensystem
    168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    170:   NEPSolve(nep);
    171:   NEPGetIterationNumber(nep,&its);
    172:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

    174:   /*
    175:      Optional: Get some information from the solver and display it
    176:   */
    177:   NEPGetType(nep,&type);
    178:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
    179:   NEPGetDimensions(nep,&nev,NULL,NULL);
    180:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    183:                     Display solution and clean up
    184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    186:   /* show detailed info unless -terse option is given by user */
    187:   PetscOptionsHasName(NULL,"-terse",&terse);
    188:   if (terse) {
    189:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    190:   } else {
    191:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    192:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    193:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    194:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    195:   }
    196:   NEPDestroy(&nep);
    197:   MatDestroy(&Id);
    198:   MatDestroy(&A);
    199:   MatDestroy(&B);
    200:   FNDestroy(&f1);
    201:   FNDestroy(&f2);
    202:   FNDestroy(&f3);
    203:   SlepcFinalize();
    204:   return 0;
    205: }