A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM

Abstract

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.

References in corpus (4)

• The deal.II finite element library: design, features, and insights
• Fast matrix-free evaluation of discontinuous Galerkin finite element operators
• A performance comparison of continuous and discontinuous Galerkin methods with fast multigrid solvers
• Hybrid multigrid methods for high-order discontinuous Galerkin discretizations

Cited by in corpus (5)

• On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations
• A matrix-free high-order solver for the numerical solution of cardiac electrophysiology
• Propagating geometry information to finite element computations
• Smoothers with localized residual computations for geometric multigrid methods
• Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems