Hermes,
For large systems, Krylov solvers are faster and require less memory
than direct solvers. Direct solvers scale poorly, in terms of memory
and performance, with the number of unknowns. The only problem with
Krylov solvers is that you need to use a good preconditioner. The
choice of the preconditioner depends on the system that you want to
solve.
Best,
Bruno
Le jeu. 10 mars 2022 à 02:51, Hermes Sampedro
<hermesampe...@gmail.com> a écrit :
>
> Dear Bruno,
>
> Thank you again for your answer.
>
> I managed to solve now a system of 3.5 million DOF using the same solver as I
> posted above, SparseDirectMUMPS. Now, in release mode, the assembling takes a
> few minutes instead of hours, however, the solver function takes
> approximately 1.5h (per frequency iteration) using 40 processes in parallel
> (similar to step-40).
>
> I was expecting to get faster performance when running in parallel with 40
> processes, especially because I need to run for several frequencies. I would
> like to ask if you also would expect faster performance. Would that be solved
> using the solver that you suggested (Krylov)?
>
>
> Thank you
>
> Regards,
>
> H
>
>
> El lunes, 7 de marzo de 2022 a las 15:04:19 UTC+1, bruno.t...@gmail.com
> escribió:
>>
>> Hermes,
>>
>> The problem is that you are using a direct solver. Direct solvers
>> require a lot of memory because the inverse of a sparse matrix is
>> generally not sparse. If you use a LU decomposition, which I think
>> MUMPS does, you need a dense matrix to store the LU decomposition.
>> That's a lot of memory! You will need to use a Krylov to solve a
>> problem of this size.
>>
>> Best,
>>
>> Bruno
>>
>> Le dim. 6 mars 2022 à 07:19, Hermes Sampedro <hermes...@gmail.com> a écrit :
>> >
>> > Dear Bruno,
>> >
>> > Thank you very much for the comments. The problem was that I was running
>> > in Debug mode without knowing. Now, after changing to Release the
>> > assembling time is considerably reduced.
>> >
>> > Moreover, I am experiencing another issue that I would like to ask. My
>> > mesh is done with hyper_cube() in 3D and 5 refinements. The dof is around
>> > 3 million. When running, I always get a memory issue and the program
>> > stops. I realized that the problem is in the line that executes
>> > solver.solve(system_matrix, completely_distributed_solution, system_rhs);
>> > I am using SparseMatrix and I do not fully understand where the problem
>> > could come from. The matrices are initialized beforehand, what reason do
>> > you think It could produce a memory issue in the solver?
>> >
>> > Below is the full solver function:
>> >
>> > template <int dim>
>> > void LaplaceProblem<dim>::solve()
>> > {
>> > PETScWrappers::MPI::Vector
>> > completely_distributed_solution(locally_owned_dofs,mpi_communicator);
>> > SolverControl cn;
>> > PETScWrappers::SparseDirectMUMPS solver(cn, mpi_communicator);
>> > solver.solve(system_matrix, completely_distributed_solution, system_rhs);
>> > constraints.distribute(completely_distributed_solution);
>> > locally_relevant_solution = completely_distributed_solution;
>> > }
>> >
>> >
>> > Thank you again for your help
>> > Regards
>> > H.
>> >
>> > El jueves, 3 de marzo de 2022 a las 15:13:30 UTC+1, bruno.t...@gmail.com
>> > escribió:
>> >>
>> >> Hermes,
>> >>
>> >> There is a couple of things that you could do but it probably won't give
>> >> you a significant speed up. Are you sure that you are running in Release
>> >> mode and not in Debug? Do you evaluate complicated functions in the
>> >> assembly?
>> >> A couple changes that could help:
>> >> - don't use fe.system_to_component_index(i).first and
>> >> fe.system_to_component_index(j).first everywhere. Just define const k =
>> >> ... and const m = ... and use k and m. That might help the compiler with
>> >> some optimizations
>> >> - move the two if for the cell assembly outside the for loop on the
>> >> quadrature point, similar to what you did for the boundaries. This could
>> >> potentially help quite a bit if the cpu often gets the branch prediction
>> >> wrong
>> >>
>> >> Best,
>> >>
>> >> Bruno
>> >>
>> >> On Thursday, March 3, 2022 at 4:31:04 AM UTC-5 hermes...@gmail.com wrote:
>> >>>
>> >>> Dear all,
>> >>>
>> >>> I am experiencing long times when computing the assembling and I would
>> >>> like to ask if this is common or there is something wrong with my
>> >>> implementation.
>> >>>
>> >>> My model is built in a similar way as step-29 and step-40 (using complex
>> >>> values ad solving with a direct solver using distributed parallel
>> >>> implementation).
>> >>> Now I am running larger systems with 3.5million dof and the assembling
>> >>> took 16h, while the solver function took much less.
>> >>>
>> >>> I can show the structure of my assembly_system() function to ask if
>> >>> there is something that can be done in order to speed up the process:
>> >>>
>> >>> void Problem<dim>::assemble_system()
>> >>> {
>> >>> for (unsigned int i = 0; i < dofs_per_cell; ++i) {
>> >>> for (unsigned int j = 0; j < dofs_per_cell; ++j)
>> >>> {
>> >>> for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
>> >>> {
>> >>> if (fe.system_to_component_index(i).first ==
>> >>> fe.system_to_component_index(j).first)
>> >>> {
>> >>> cell_matrix(i, j) += ....
>> >>> }
>> >>> if (fe.system_to_component_index(i).first !=
>> >>> fe.system_to_component_index(j).first)
>> >>> {
>> >>> cell_matrix(i, j) += ....
>> >>> }
>> >>> }
>> >>>
>> >>> // Boundaries
>> >>> if (fe.system_to_component_index(i).first ==
>> >>> fe.system_to_component_index(j).first)
>> >>> {
>> >>> for (unsigned int face_no : GeometryInfo<dim>::face_indices())
>> >>> if (cell->face(face_no)->at_boundary() &&
>> >>> (cell->face(face_no)->boundary_id() == 0))
>> >>> {
>> >>> fe_face_values.reinit(cell, face_no);
>> >>> for (unsigned int q_point = 0; q_point < n_face_q_points; ++q_point)
>> >>> cell_matrix(i, j) += ....
>> >>> }
>> >>> }
>> >>> if (fe.system_to_component_index(i).first !=
>> >>> fe.system_to_component_index(j).first)
>> >>> {
>> >>> for (unsigned int face_no : GeometryInfo<dim>::face_indices())
>> >>> {
>> >>> if (cell->face(face_no)->at_boundary() &&
>> >>> (cell->face(face_no)->boundary_id() == 0))
>> >>> {
>> >>> fe_face_values.reinit(cell, face_no);
>> >>> for (unsigned int q_point = 0; q_point < n_face_q_points;++q_point)
>> >>> cell_matrix(i, j) += ....
>> >>> }
>> >>> }
>> >>> }
>> >>> }
>> >>> }
>> >>>
>> >>>
>> >>> Thank you very much.
>> >>> Regards,
>> >>> Hermes
>> >
>> > --
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