Date: 2022-08-09T09:05:56+00:00

Actual source code: ex22.c
slepc-3.17.2 2022-08-09
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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[] = "Delay differential equation.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     14:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

     16: /*
     17:    Solve parabolic partial differential equation with time delay tau

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

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

     24:    Discretization leads to a DDE of dimension n

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

     28:    which results in the nonlinear eigenproblem

     30:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
     31: */

     33: #include <slepcnep.h>

     35: int main(int argc,char **argv)
     36: {
     37:   NEP            nep;             /* nonlinear eigensolver context */
     38:   Mat            Id,A,B;          /* problem matrices */
     39:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
     40:   Mat            mats[3];
     41:   FN             funs[3];
     42:   PetscScalar    coeffs[2],b;
     43:   PetscInt       n=128,nev,Istart,Iend,i;
     44:   PetscReal      tau=0.001,h,a=20,xi;
     45:   PetscBool      terse;

     47:   SlepcInitialize(&argc,&argv,(char*)0,help);
     48:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     49:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     50:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau);
     51:   h = PETSC_PI/(PetscReal)(n+1);

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:      Create nonlinear eigensolver context
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   NEPCreate(PETSC_COMM_WORLD,&nep);

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:      Create problem matrices and coefficient functions. Pass them to NEP
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   /*
     64:      Identity matrix
     65:   */
     66:   MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
     67:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

     69:   /*
     70:      A = 1/h^2*tridiag(1,-2,1) + a*I
     71:   */
     72:   MatCreate(PETSC_COMM_WORLD,&A);
     73:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     74:   MatSetFromOptions(A);
     75:   MatSetUp(A);
     76:   MatGetOwnershipRange(A,&Istart,&Iend);
     77:   for (i=Istart;i<Iend;i++) {
     78:     if (i>0) MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);
     79:     if (i<n-1) MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);
     80:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
     81:   }
     82:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     83:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     84:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

     86:   /*
     87:      B = diag(b(xi))
     88:   */
     89:   MatCreate(PETSC_COMM_WORLD,&B);
     90:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
     91:   MatSetFromOptions(B);
     92:   MatSetUp(B);
     93:   MatGetOwnershipRange(B,&Istart,&Iend);
     94:   for (i=Istart;i<Iend;i++) {
     95:     xi = (i+1)*h;
     96:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
     97:     MatSetValue(B,i,i,b,INSERT_VALUES);
     98:   }
     99:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    100:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    101:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

    103:   /*
    104:      Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
    105:   */
    106:   FNCreate(PETSC_COMM_WORLD,&f1);
    107:   FNSetType(f1,FNRATIONAL);
    108:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    109:   FNRationalSetNumerator(f1,2,coeffs);

    111:   FNCreate(PETSC_COMM_WORLD,&f2);
    112:   FNSetType(f2,FNRATIONAL);
    113:   coeffs[0] = 1.0;
    114:   FNRationalSetNumerator(f2,1,coeffs);

    116:   FNCreate(PETSC_COMM_WORLD,&f3);
    117:   FNSetType(f3,FNEXP);
    118:   FNSetScale(f3,-tau,1.0);

    120:   /*
    121:      Set the split operator. Note that A is passed first so that
    122:      SUBSET_NONZERO_PATTERN can be used
    123:   */
    124:   mats[0] = A;  funs[0] = f2;
    125:   mats[1] = Id; funs[1] = f1;
    126:   mats[2] = B;  funs[2] = f3;
    127:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:              Customize nonlinear solver; set runtime options
    131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    133:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
    134:   NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);
    135:   NEPRIISetLagPreconditioner(nep,0);

    137:   /*
    138:      Set solver parameters at runtime
    139:   */
    140:   NEPSetFromOptions(nep);

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:                       Solve the eigensystem
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    146:   NEPSolve(nep);
    147:   NEPGetDimensions(nep,&nev,NULL,NULL);
    148:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

    150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    151:                     Display solution and clean up
    152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    154:   /* show detailed info unless -terse option is given by user */
    155:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    156:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    157:   else {
    158:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    159:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    160:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    161:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    162:   }
    163:   NEPDestroy(&nep);
    164:   MatDestroy(&Id);
    165:   MatDestroy(&A);
    166:   MatDestroy(&B);
    167:   FNDestroy(&f1);
    168:   FNDestroy(&f2);
    169:   FNDestroy(&f3);
    170:   SlepcFinalize();
    171:   return 0;
    172: }

    174: /*TEST

    176:    testset:
    177:       suffix: 1
    178:       args: -nep_type {{rii slp narnoldi}} -terse
    179:       filter: sed -e "s/[+-]0\.0*i//g"
    180:       requires: !single

    182:    test:
    183:       suffix: 1_ciss
    184:       args: -nep_type ciss -nep_ciss_extraction {{ritz hankel caa}} -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -nep_ncv 24 -terse
    185:       requires: complex !single

    187:    test:
    188:       suffix: 2
    189:       args: -nep_type interpol -nep_interpol_pep_extract {{none norm residual}} -rg_type interval -rg_interval_endpoints 5,20,-.1,.1 -nep_nev 3 -nep_target 5 -terse
    190:       filter: sed -e "s/[+-]0\.0*i//g"
    191:       requires: !single

    193:    testset:
    194:       args: -n 512 -nep_target 10 -nep_nev 3 -terse
    195:       filter: sed -e "s/[+-]0\.0*i//g"
    196:       requires: !single
    197:       output_file: output/ex22_3.out
    198:       test:
    199:          suffix: 3
    200:          args: -nep_type {{rii slp narnoldi}}
    201:       test:
    202:          suffix: 3_simpleu
    203:          args: -nep_type {{rii slp narnoldi}} -nep_deflation_simpleu
    204:       test:
    205:          suffix: 3_slp_thres
    206:          args: -nep_type slp -nep_slp_deflation_threshold 1e-8
    207:       test:
    208:          suffix: 3_rii_thres
    209:          args: -nep_type rii -nep_rii_deflation_threshold 1e-8

    211:    test:
    212:       suffix: 4
    213:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,20,-.1,.1 -nep_nev 3 -nep_target 5 -terse -nep_monitor draw::draw_lg
    214:       filter: sed -e "s/[+-]0\.0*i//g"
    215:       requires: x !single
    216:       output_file: output/ex22_2.out

    218: TEST*/