Yes.
Peter
On 07.10.22 07:44, 'yy.wayne' via deal.II User Group wrote:
I see. So that's why we create a new dof_handlers in solve_with_gmg()
function instead of continue using dof_handler as other tutorials. If
I want to build mg_matrices and their SparsityPattern, they should
based on dof_handlers as well, is it correct?
Thank you
在2022年10月7日星期五 UTC+8 13:35:16<[email protected]> 写道：
Hej,
> One thing I'm confused is that why we use
"make_hanging_node_constraints" and "interpolate_boundary_values"
for a new constraints in solve_with_gmg in step-75, instead of the
boundary_constraints as done in previous MG tutorials.
Your observation is correct. It is related to the fact that
p-multigrid in deal.II uses the new global-coarsening
infrastructure (it was introduced in release 7.3). In the other
tutorials, the local-smoothing infrastructure is used.
In a nutshell, the difference is that local smoothing is working
on refinement levels, while global coarsening works on the
complete active levels of multiple Triangulation/DoFHandler
objects. In the case of h-multigrid, one works on multiple meshes,
which are created by globally coarsening the finest mesh (this is
the reason for the name "global coarsening"); in the case of
p-multigrid, one would work with the same Triangulation but would
distribute different FEs on different DoFHandler objects. Since
you work on the active level, you can simple use the functions you
would use if you don't work on refinement levels.
For more details see our publication: https://arxiv.org/abs/2203.12292
Hope this help,
Peter
On Wednesday, 5 October 2022 at 14:17:03 UTC+2 yy.wayne wrote:
Hello sir,
One thing I'm confused is that why we use
"make_hanging_node_constraints" and
"interpolate_boundary_values" for a new constraints in
solve_with_gmg in step-75, instead of the boundary_constraints
as done in previous MG tutorials.
在2022年10月4日星期二 UTC+8 00:11:49<[email protected]> 写道：
Hi!
The "Possibilities for extensions" section of step-75
gives you a few hints on how to achieve p-multigrid
preconditioning with matrix-based methods:
https://www.dealii.org/current/doxygen/deal.II/step_75.html#Solvewithmatrixbasedmethods
If you look for an example implementation, the "hpbox"
tool demonstrates both matrix-based and matrix-free
implementations of the p-multigrid method.
https://zenodo.org/record/6425947
https://github.com/marcfehling/hpbox/
Best,
Marc
On Monday, October 3, 2022 at 3:39:51 AM UTC-6 yy.wayne wrote:
Hello,
I plan to test the converge of polynomial multigrid
preconditioning on a problem, with matrix-based
framework. However, step-75 is a bit confusing since I
cannot clearly separate classses contributed by
matrix-free and p-multigrid.
Specifically, in step-16 (with MeshWorker) and step-56
(assemble cell_matrix by hand) there are
assemble_system() and assemble_multigrid(), while in
step-75 there are solve_system() which calls
solve_with_gmg and mg_solve. It is due to matrix-free
or p-multigrid? By the way, is there a code gallery
for matrix-based polynomial-multigrid ?
Thanks
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