Date: 2022-10-01T06:40:40+00:00

Actual source code: test15.c
slepc-3.18.0 2022-10-01
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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[] = "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;

     62:   SlepcInitialize(&argc,&argv,(char*)0,help);
     63:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     64:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     65:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", 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:   /* Identity matrix */
     75:   MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
     76:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

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

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

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

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

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

    123:   /* Set the split operator */
    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:   NEPSetType(nep,NEPNLEIGS);
    134:   NEPGetRG(nep,&rg);
    135:   RGSetType(rg,RGINTERVAL);
    136: #if defined(PETSC_USE_COMPLEX)
    137:   RGIntervalSetEndpoints(rg,5,20,-0.001,0.001);
    138: #else
    139:   RGIntervalSetEndpoints(rg,5,20,-0.0,0.0);
    140: #endif
    141:   NEPSetTarget(nep,15.0);
    142:   NEPSetWhichEigenpairs(nep,NEP_TARGET_MAGNITUDE);

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

    157:   NEPSetFromOptions(nep);

    159:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    160:                       Solve the eigensystem
    161:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    163:   NEPSolve(nep);

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

    173:   NEPDestroy(&nep);
    174:   MatDestroy(&Id);
    175:   MatDestroy(&A);
    176:   MatDestroy(&B);
    177:   FNDestroy(&f1);
    178:   FNDestroy(&f2);
    179:   FNDestroy(&f3);
    180:   PetscFree(ctx);
    181:   SlepcFinalize();
    182:   return 0;
    183: }

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

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

    199:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    200:   NEPStoppingBasic(nep,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
    201:   if (*reason==NEP_CONVERGED_ITERATING) {
    202:     /* check if nconv is the same as before */
    203:     if (nconv==ctx->lastnconv) ctx->nreps++;
    204:     else {
    205:       ctx->lastnconv = nconv;
    206:       ctx->nreps     = 0;
    207:     }
    208:     /* check if no eigenvalues converged in last 10 restarts */
    209:     if (nconv && ctx->nreps>10) *reason = NEP_CONVERGED_USER;
    210:   }
    211:   return 0;
    212: }

    214: /*TEST

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

    220: TEST*/