Date: 2023-09-05T10:18:22+00:00

Actual source code: ex22.c
slepc-3.19.2 2023-09-05
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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:   PetscFunctionBeginUser;
     48:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     49:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     50:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
     51:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
     52:   h = PETSC_PI/(PetscReal)(n+1);

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:      Create nonlinear eigensolver context
     56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:      Create problem matrices and coefficient functions. Pass them to NEP
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

     87:   /*
     88:      B = diag(b(xi))
     89:   */
     90:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
     91:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
     92:   PetscCall(MatSetFromOptions(B));
     93:   PetscCall(MatSetUp(B));
     94:   PetscCall(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:     PetscCall(MatSetValue(B,i,i,b,INSERT_VALUES));
     99:   }
    100:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    101:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    102:   PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));

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

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

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

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

    130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    131:              Customize nonlinear solver; set runtime options
    132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:                       Solve the eigensystem
    145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:                     Display solution and clean up
    153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    155:   /* show detailed info unless -terse option is given by user */
    156:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    157:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    158:   else {
    159:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    160:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    161:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    162:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    163:   }
    164:   PetscCall(NEPDestroy(&nep));
    165:   PetscCall(MatDestroy(&Id));
    166:   PetscCall(MatDestroy(&A));
    167:   PetscCall(MatDestroy(&B));
    168:   PetscCall(FNDestroy(&f1));
    169:   PetscCall(FNDestroy(&f2));
    170:   PetscCall(FNDestroy(&f3));
    171:   PetscCall(SlepcFinalize());
    172:   return 0;
    173: }

    175: /*TEST

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

    183:    test:
    184:       suffix: 1_ciss
    185:       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
    186:       requires: complex !single

    188:    test:
    189:       suffix: 2
    190:       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
    191:       filter: sed -e "s/[+-]0\.0*i//g"
    192:       requires: !single

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

    212:    test:
    213:       suffix: 4
    214:       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
    215:       filter: sed -e "s/[+-]0\.0*i//g"
    216:       requires: x !single
    217:       output_file: output/ex22_2.out

    219: TEST*/