Professor Bangerth:
I find that if FE_Q is replaced by FESystem in step-36 it reports that
error.
I printed all diagonal element of two matrices and they are all non-zero,
so the matrices are invertable.
My problem is a 3-dim beam eigenvalue calculation and I use FESystem just
like step-18.
And if I use FE_Q rather than FESystem, the function shape_grad_component
will report error.
I use that function to calculate stiffness_matrix, called by get_strain()
like step-18.
And the theoretical formulae are as follows:
\begin{array}{l}
K = \int {{D^{\rm{T}}}ED{\rm{d}}{V_e}} \\
\varepsilon = Du\\
\sigma = \varepsilon E
\end{array}%
I guess that here exits conflict between FESystem and SolverKrylovSchur or
just because it is a vector-value problem?
Is it a vector-value the 3-dim eigenvalue calculation?
Thanks for your help.
Best wishes
Le samedi 26 février 2022 à 09:47:34 UTC+8, Wolfgang Bangerth a écrit :
>
> Leonhard:
> have you checked that the matrix really is invertible? We use the wrappers
> as
> is for step-36, if I recall correctly. A good starting point for asking
> why
> your approach doesn't work would be to ask what is different between your
> program and step-36.
>
> Best
> W.
>
>
> On 2/25/22 07:10, Léonhard YU wrote:
> > *** Caution: EXTERNAL Sender ***
> >
> > Hello Everyone:
> >
> > I am dealing with a eigenvalue problem with SLEPc, but the program
> reports
> > this error:
> >
> > [0]PETSC ERROR: --------------------- Error Message
> > --------------------------------------------------------------
> > [0]PETSC ERROR: Zero pivot in LU factorization:
> > https://petsc.org/release/faq/#zeropivot
> > [0]PETSC ERROR: Zero pivot row 1 value 0. tolerance 2.22045e-14
> >
> > I have reviewed the documentation. It says that (Frequently Asked
> Questions
> > (FAQ) — PETSc 3.16.4 documentation
> > <
> https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Ffaq%2F%23zeropivot&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cff03e4917646439d68e908d9f868a339%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637813950590384693%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=UcAsQKuwWtUlwHjMjn8IGvLRvUbs8O592okHh6M5fuY%3D&reserved=0
> >)
> >
> > *A zero pivot in LU, ILU, Cholesky, or ICC sparse factorization does not
> > always mean that the matrix is singular. You can use*
> >
> > *-pc_factor_shift_type nonzero -pc_factor_shift_amount [amount] *
> >
> > *or*
> >
> > *-pc_factor_shift_type positive_definite -[level]_pc_factor_shift_type
> nonzero
> > -pc_factor_shift_amount [amount] *
> >
> > *or*
> >
> > *-[level]_pc_factor_shift_type positive_definite *
> >
> > *to prevent the zero pivot. [level] is “sub” when lu, ilu, cholesky, or
> icc
> > are employed in each individual block of the bjacobi or ASM
> preconditioner.
> > [level] is “mg_levels” or “mg_coarse” when lu, ilu, cholesky, or icc are
> used
> > inside multigrid smoothers or to the coarse grid solver. See
> > PCFactorSetShiftType
> > <
> https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Fdocs%2Fmanualpages%2FPC%2FPCFactorSetShiftType.html%23PCFactorSetShiftType&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cff03e4917646439d68e908d9f868a339%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637813950590384693%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=zp3oMzA5JMPuOyVmMPXG3dGx4u1m0nGLcNVh4EmOmLs%3D&reserved=0>(),
>
>
> > PCFactorSetShiftAmount
> > <
> https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Fdocs%2Fmanualpages%2FPC%2FPCFactorSetShiftAmount.html%23PCFactorSetShiftAmount&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cff03e4917646439d68e908d9f868a339%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637813950590384693%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=F85oRwsykILhaQjMn6lUfkDGQCXuHgl1ExpVllAVLAs%3D&reserved=0
> >().*
> >
> > *This error can also happen if your matrix is singular, see
> MatSetNullSpace
> > <
> https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Fdocs%2Fmanualpages%2FMat%2FMatSetNullSpace.html%23MatSetNullSpace&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cff03e4917646439d68e908d9f868a339%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637813950590384693%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=L3uPVPCwyJQF%2FqarLxETmnSrjdq5mCC2MXDXfR7bLCA%3D&reserved=0>()
> for
>
> > how to handle this. If this error occurs in the zeroth row of the
> matrix, it
> > is likely you have an error in the code that generates the matrix.*
> >
> > So I write the code as follows:
> >
> > *PETScWrappers::PreconditionBlockJacobi::AdditionalData data;
> > PETScWrappers::PreconditionBlockJacobi
> preconditioner(mpi_communicator,
> > data);
> > SolverControl linear_solver_control (dof_handler.n_dofs(),
> > 1e-9, false, false);
> > PETScWrappers::SolverCG linear_solver(linear_solver_control,
> > mpi_communicator);
> >
> > PCFactorSetShiftType(preconditioner.get_pc(), MAT_SHIFT_NONZERO);
> > // PCFactorSetShiftAmount(preconditioner.get_pc(), 3e-14);
> >
> > linear_solver.initialize(preconditioner);
> >
> > SolverControl solver_control (100, 1e-9,false,false);
> > SLEPcWrappers::SolverKrylovSchur eigensolver(solver_control,
> > mpi_communicator);
> >
> > eigensolver.set_which_eigenpairs(EPS_SMALLEST_REAL);
> >
> > eigensolver.set_problem_type(EPS_GHEP);
> >
> > SLEPcWrappers::TransformationShift
> spectral_transformation(mpi_communicator);
> > spectral_transformation.set_solver(linear_solver);
> > eigensolver.set_transformation(spectral_transformation);
> >
> > eigensolver.solve(stiffness_matrix,
> > mass_matrix,
> > eigenvalues,
> > eigenfunctions,
> > eigenfunctions.size());*
> >
> > But the error occurs as the same. I don't know how to solve it.
> >
> > Thanks for your help.
> >
> > Best Wishes.
> >
> >
> >
> > --
> > The deal.II project is located at http://www.dealii.org/
> > <
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>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>
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