Date: 2021-02-01T14:42:17+00:00

Actual source code: test15.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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);if (ierr) return ierr;
     63:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     64:   PetscOptionsGetReal(NULL,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:   /* Identity matrix */
     75:   MatCreate(PETSC_COMM_WORLD,&Id);
     76:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
     77:   MatSetFromOptions(Id);
     78:   MatSetUp(Id);
     79:   MatGetOwnershipRange(Id,&Istart,&Iend);
     80:   for (i=Istart;i<Iend;i++) {
     81:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
     82:   }
     83:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
     85:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

     87:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     88:   MatCreate(PETSC_COMM_WORLD,&A);
     89:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     90:   MatSetFromOptions(A);
     91:   MatSetUp(A);
     92:   MatGetOwnershipRange(A,&Istart,&Iend);
     93:   for (i=Istart;i<Iend;i++) {
     94:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
     95:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
     96:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
     97:   }
     98:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     99:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    100:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

    102:   /* B = diag(b(xi)) */
    103:   MatCreate(PETSC_COMM_WORLD,&B);
    104:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
    105:   MatSetFromOptions(B);
    106:   MatSetUp(B);
    107:   MatGetOwnershipRange(B,&Istart,&Iend);
    108:   for (i=Istart;i<Iend;i++) {
    109:     xi = (i+1)*h;
    110:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    111:     MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
    112:   }
    113:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    114:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    115:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

    117:   /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
    118:   FNCreate(PETSC_COMM_WORLD,&f1);
    119:   FNSetType(f1,FNRATIONAL);
    120:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    121:   FNRationalSetNumerator(f1,2,coeffs);

    123:   FNCreate(PETSC_COMM_WORLD,&f2);
    124:   FNSetType(f2,FNRATIONAL);
    125:   coeffs[0] = 1.0;
    126:   FNRationalSetNumerator(f2,1,coeffs);

    128:   FNCreate(PETSC_COMM_WORLD,&f3);
    129:   FNSetType(f3,FNEXP);
    130:   FNSetScale(f3,-tau,1.0);

    132:   /* Set the split operator */
    133:   mats[0] = A;  funs[0] = f2;
    134:   mats[1] = Id; funs[1] = f1;
    135:   mats[2] = B;  funs[2] = f3;
    136:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:                 Customize nonlinear solver; set runtime options
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    142:   NEPSetType(nep,NEPNLEIGS);
    143:   NEPGetRG(nep,&rg);
    144:   RGSetType(rg,RGINTERVAL);
    145: #if defined(PETSC_USE_COMPLEX)
    146:   RGIntervalSetEndpoints(rg,5,20,-0.001,0.001);
    147: #else
    148:   RGIntervalSetEndpoints(rg,5,20,-0.0,0.0);
    149: #endif
    150:   NEPSetTarget(nep,15.0);
    151:   NEPSetWhichEigenpairs(nep,NEP_TARGET_MAGNITUDE);

    153:   /*
    154:      Set solver options. In particular, we must allocate sufficient
    155:      storage for all eigenpairs that may converge (ncv). This is
    156:      application-dependent.
    157:   */
    158:   mpd = 40;
    159:   NEPSetDimensions(nep,2*mpd,3*mpd,mpd);
    160:   NEPSetTolerances(nep,PETSC_DEFAULT,2000);
    161:   PetscNew(&ctx);
    162:   ctx->lastnconv = 0;
    163:   ctx->nreps     = 0;
    164:   NEPSetStoppingTestFunction(nep,MyStoppingTest,(void*)ctx,NULL);

    166:   NEPSetFromOptions(nep);

    168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169:                       Solve the eigensystem
    170:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    172:   NEPSolve(nep);

    174:   /* show detailed info unless -terse option is given by user */
    175:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    176:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    177:   NEPConvergedReasonView(nep,viewer);
    178:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    179:   if (!terse) {
    180:     NEPErrorView(nep,NEP_ERROR_BACKWARD,viewer);
    181:   }
    182:   PetscViewerPopFormat(viewer);

    184:   NEPDestroy(&nep);
    185:   MatDestroy(&Id);
    186:   MatDestroy(&A);
    187:   MatDestroy(&B);
    188:   FNDestroy(&f1);
    189:   FNDestroy(&f2);
    190:   FNDestroy(&f3);
    191:   PetscFree(ctx);
    192:   SlepcFinalize();
    193:   return ierr;
    194: }

    196: /*
    197:     Function for user-defined stopping test.

    199:     Ignores the value of nev. It only takes into account the number of
    200:     eigenpairs that have converged in recent outer iterations (restarts);
    201:     if no new eigenvalues have converged in the last few restarts,
    202:     we stop the iteration, assuming that no more eigenvalues are present
    203:     inside the region.
    204: */
    205: PetscErrorCode MyStoppingTest(NEP nep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,NEPConvergedReason *reason,void *ptr)
    206: {
    208:   CTX_DELAY      *ctx = (CTX_DELAY*)ptr;

    211:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    212:   NEPStoppingBasic(nep,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
    213:   if (*reason==NEP_CONVERGED_ITERATING) {
    214:     /* check if nconv is the same as before */
    215:     if (nconv==ctx->lastnconv) ctx->nreps++;
    216:     else {
    217:       ctx->lastnconv = nconv;
    218:       ctx->nreps     = 0;
    219:     }
    220:     /* check if no eigenvalues converged in last 10 restarts */
    221:     if (nconv && ctx->nreps>10) *reason = NEP_CONVERGED_USER;
    222:   }
    223:   return(0);
    224: }

    226: /*TEST

    228:    test:
    229:       suffix: 1
    230:       args: -terse

    232: TEST*/