Date: 2022-03-31T15:29:33+00:00

Actual source code: test15.c
slepc-3.17.0 2022-03-31
Report Typos and Errors

      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[] = "Illustrates the use of a user-defined stopping test.\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\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: /*
     37:    User-defined routines
     38: */
     39: PetscErrorCode MyStoppingTest(NEP,PetscInt,PetscInt,PetscInt,PetscInt,NEPConvergedReason*,void*);

     41: typedef struct {
     42:   PetscInt    lastnconv;      /* last value of nconv; used in stopping test */
     43:   PetscInt    nreps;          /* number of repetitions of nconv; used in stopping test */
     44: } CTX_DELAY;

     46: int main(int argc,char **argv)
     47: {
     48:   NEP            nep;
     49:   Mat            Id,A,B;
     50:   FN             f1,f2,f3;
     51:   RG             rg;
     52:   CTX_DELAY      *ctx;
     53:   Mat            mats[3];
     54:   FN             funs[3];
     55:   PetscScalar    coeffs[2],b;
     56:   PetscInt       n=128,Istart,Iend,i,mpd;
     57:   PetscReal      tau=0.001,h,a=20,xi;
     58:   PetscBool      terse;
     59:   PetscViewer    viewer;

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

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:      Create nonlinear eigensolver context
     69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     71:   NEPCreate(PETSC_COMM_WORLD,&nep);

     73:   /* Identity matrix */
     74:   MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
     75:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

     77:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     78:   MatCreate(PETSC_COMM_WORLD,&A);
     79:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     80:   MatSetFromOptions(A);
     81:   MatSetUp(A);
     82:   MatGetOwnershipRange(A,&Istart,&Iend);
     83:   for (i=Istart;i<Iend;i++) {
     84:     if (i>0) MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);
     85:     if (i<n-1) MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);
     86:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
     87:   }
     88:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     89:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     90:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

     92:   /* B = diag(b(xi)) */
     93:   MatCreate(PETSC_COMM_WORLD,&B);
     94:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
     95:   MatSetFromOptions(B);
     96:   MatSetUp(B);
     97:   MatGetOwnershipRange(B,&Istart,&Iend);
     98:   for (i=Istart;i<Iend;i++) {
     99:     xi = (i+1)*h;
    100:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    101:     MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
    102:   }
    103:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    104:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    105:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

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

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

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

    122:   /* Set the split operator */
    123:   mats[0] = A;  funs[0] = f2;
    124:   mats[1] = Id; funs[1] = f1;
    125:   mats[2] = B;  funs[2] = f3;
    126:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

    128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    129:                 Customize nonlinear solver; set runtime options
    130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    132:   NEPSetType(nep,NEPNLEIGS);
    133:   NEPGetRG(nep,&rg);
    134:   RGSetType(rg,RGINTERVAL);
    135: #if defined(PETSC_USE_COMPLEX)
    136:   RGIntervalSetEndpoints(rg,5,20,-0.001,0.001);
    137: #else
    138:   RGIntervalSetEndpoints(rg,5,20,-0.0,0.0);
    139: #endif
    140:   NEPSetTarget(nep,15.0);
    141:   NEPSetWhichEigenpairs(nep,NEP_TARGET_MAGNITUDE);

    143:   /*
    144:      Set solver options. In particular, we must allocate sufficient
    145:      storage for all eigenpairs that may converge (ncv). This is
    146:      application-dependent.
    147:   */
    148:   mpd = 40;
    149:   NEPSetDimensions(nep,2*mpd,3*mpd,mpd);
    150:   NEPSetTolerances(nep,PETSC_DEFAULT,2000);
    151:   PetscNew(&ctx);
    152:   ctx->lastnconv = 0;
    153:   ctx->nreps     = 0;
    154:   NEPSetStoppingTestFunction(nep,MyStoppingTest,(void*)ctx,NULL);

    156:   NEPSetFromOptions(nep);

    158:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    159:                       Solve the eigensystem
    160:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    162:   NEPSolve(nep);

    164:   /* show detailed info unless -terse option is given by user */
    165:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    166:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    167:   NEPConvergedReasonView(nep,viewer);
    168:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    169:   if (!terse) NEPErrorView(nep,NEP_ERROR_BACKWARD,viewer);
    170:   PetscViewerPopFormat(viewer);

    172:   NEPDestroy(&nep);
    173:   MatDestroy(&Id);
    174:   MatDestroy(&A);
    175:   MatDestroy(&B);
    176:   FNDestroy(&f1);
    177:   FNDestroy(&f2);
    178:   FNDestroy(&f3);
    179:   PetscFree(ctx);
    180:   SlepcFinalize();
    181:   return 0;
    182: }

    184: /*
    185:     Function for user-defined stopping test.

    187:     Ignores the value of nev. It only takes into account the number of
    188:     eigenpairs that have converged in recent outer iterations (restarts);
    189:     if no new eigenvalues have converged in the last few restarts,
    190:     we stop the iteration, assuming that no more eigenvalues are present
    191:     inside the region.
    192: */
    193: PetscErrorCode MyStoppingTest(NEP nep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,NEPConvergedReason *reason,void *ptr)
    194: {
    195:   CTX_DELAY      *ctx = (CTX_DELAY*)ptr;

    198:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    199:   NEPStoppingBasic(nep,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
    200:   if (*reason==NEP_CONVERGED_ITERATING) {
    201:     /* check if nconv is the same as before */
    202:     if (nconv==ctx->lastnconv) ctx->nreps++;
    203:     else {
    204:       ctx->lastnconv = nconv;
    205:       ctx->nreps     = 0;
    206:     }
    207:     /* check if no eigenvalues converged in last 10 restarts */
    208:     if (nconv && ctx->nreps>10) *reason = NEP_CONVERGED_USER;
    209:   }
    210:   PetscFunctionReturn(0);
    211: }

    213: /*TEST

    215:    test:
    216:       suffix: 1
    217:       args: -terse

    219: TEST*/