Questions Regarding mesh_loop and Multigrid

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HC Zhang

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May 16, 2025, 3:02:39 AM5/16/25

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Dear all,

I am new to using deal.II and have recently been focusing on learning the mesh_loop framework, which I understand is the recommended modern way to assemble matrices in deal.II.

I would like to ask for your advice regarding the integration of multigrid methods as preconditioners when using the mesh_loop framework. I have studied step-74 and step-16, and have been able to implement an IPDG method for solving the Poisson equation using mesh_loop on globally refined meshes.

However, I have encountered two key issues where I am uncertain:

When using global refinement, is it necessary to call
mg.set_edge_flux_matrices(mg_matrix_down, mg_matrix_up); in the solver, or can this step be omitted?
For adaptive refinement, I am unsure how to implement the code—specifically how to correctly define the CopyData and CopyFaceData structures and how to assemble mg_matrix_down and mg_matrix_up in the assemble_multigrid function.

I have looked into step-39 for guidance, but it uses the older loop function instead of mesh_loop, and I am unsure how to properly translate its approach into the mesh_loop context. I think it is two different ways to loop cells.