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/*
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
This file is part of SLEPc.
SLEPc is distributed under a 2-clause BSD license (see LICENSE).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
static char help[] = "Delay differential equation.\n\n"
"The command line options are:\n"
" -n <n>, where <n> = number of grid subdivisions.\n"
" -tau <tau>, where <tau> is the delay parameter.\n\n";
/*
Solve parabolic partial differential equation with time delay tau
u_t = u_xx + a*u(t) + b*u(t-tau)
u(0,t) = u(pi,t) = 0
with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
Discretization leads to a DDE of dimension n
-u' = A*u(t) + B*u(t-tau)
which results in the nonlinear eigenproblem
(-lambda*I + A + exp(-tau*lambda)*B)*u = 0
*/
#include <slepcnep.h>
int main(int argc,char **argv)
{
NEP nep; /* nonlinear eigensolver context */
Mat Id,A,B; /* problem matrices */
FN f1,f2,f3; /* functions to define the nonlinear operator */
Mat mats[3];
FN funs[3];
PetscScalar coeffs[2],b;
PetscInt n=128,nev,Istart,Iend,i;
PetscReal tau=0.001,h,a=20,xi;
PetscBool terse;
PetscFunctionBeginUser;
PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
h = PETSC_PI/(PetscReal)(n+1);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create nonlinear eigensolver context
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PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create problem matrices and coefficient functions. Pass them to NEP
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/*
Identity matrix
*/
PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));
/*
A = 1/h^2*tridiag(1,-2,1) + a*I
*/
PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
PetscCall(MatSetFromOptions(A));
PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
for (i=Istart;i<Iend;i++) {
if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
}
PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
/*
B = diag(b(xi))
*/
PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
PetscCall(MatSetFromOptions(B));
PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
for (i=Istart;i<Iend;i++) {
xi = (i+1)*h;
b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
PetscCall(MatSetValue(B,i,i,b,INSERT_VALUES));
}
PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));
/*
Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
*/
PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
PetscCall(FNSetType(f1,FNRATIONAL));
coeffs[0] = -1.0; coeffs[1] = 0.0;
PetscCall(FNRationalSetNumerator(f1,2,coeffs));
PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
PetscCall(FNSetType(f2,FNRATIONAL));
coeffs[0] = 1.0;
PetscCall(FNRationalSetNumerator(f2,1,coeffs));
PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
PetscCall(FNSetType(f3,FNEXP));
PetscCall(FNSetScale(f3,-tau,1.0));
/*
Set the split operator. Note that A is passed first so that
SUBSET_NONZERO_PATTERN can be used
*/
mats[0] = A; funs[0] = f2;
mats[1] = Id; funs[1] = f1;
mats[2] = B; funs[2] = f3;
PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize nonlinear solver; set runtime options
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PetscCall(NEPSetTolerances(nep,1e-9,PETSC_CURRENT));
PetscCall(NEPSetDimensions(nep,1,PETSC_DETERMINE,PETSC_DETERMINE));
PetscCall(NEPRIISetLagPreconditioner(nep,0));
/*
Set solver parameters at runtime
*/
PetscCall(NEPSetFromOptions(nep));
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the eigensystem
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PetscCall(NEPSolve(nep));
PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
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/* show detailed info unless -terse option is given by user */
PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
else {
PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
}
PetscCall(NEPDestroy(&nep));
PetscCall(MatDestroy(&Id));
PetscCall(MatDestroy(&A));
PetscCall(MatDestroy(&B));
PetscCall(FNDestroy(&f1));
PetscCall(FNDestroy(&f2));
PetscCall(FNDestroy(&f3));
PetscCall(SlepcFinalize());
return 0;
}
/*TEST
testset:
suffix: 1
args: -nep_type {{rii slp narnoldi}} -terse
filter: sed -e "s/[+-]0\.0*i//g"
requires: !single
test:
suffix: 1_ciss
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
requires: complex !single
test:
suffix: 2
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
filter: sed -e "s/[+-]0\.0*i//g"
requires: !single
testset:
args: -n 512 -nep_target 10 -nep_nev 3 -terse
filter: sed -e "s/[+-]0\.0*i//g"
requires: !single
output_file: output/ex22_3.out
test:
suffix: 3
args: -nep_type {{rii slp narnoldi}}
test:
suffix: 3_simpleu
args: -nep_type {{rii slp narnoldi}} -nep_deflation_simpleu
test:
suffix: 3_slp_thres
args: -nep_type slp -nep_slp_deflation_threshold 1e-8
test:
suffix: 3_rii_thres
args: -nep_type rii -nep_rii_deflation_threshold 1e-8
test:
suffix: 4
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 -nox
filter: sed -e "s/[+-]0\.0*i//g"
requires: x !single
output_file: output/ex22_2.out
TEST*/
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