A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM
This work provides a practical, publicly available parallel geometric multigrid solver for adaptive FEM, addressing scalability challenges in large-scale simulations.
The paper presents a geometric multigrid method for adaptively refined meshes on massively parallel computers, using local smoothing and space-filling curve partitioning. The method is implemented in the deal.II library and achieves efficient parallel performance, with runtime measurements matching a proposed efficiency model.
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by using a space filling curve for the leaf mesh and distributing ancestors in the hierarchy based on the leaves. We present a model of the efficiency of mesh hierarchy distribution and compare its predictions to runtime measurements. The algorithm is implemented as part of the deal.II finite element library and as such available to the public.