Smoothers with localized residual computations for geometric multigrid methods

Abstract

We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence rates with respect to the finite element degree for various equations, in the setting of multiplicative subspace correction for numerical efficiency. By combining the computation of local residuals with local solvers, we increase the locality of the problem and thus reduce data transfers. The thread-parallel implementation of this algorithm is based on coloring, which contradicts cache efficiency. We improve data locality by rearranging the loop into batches so that more data can be reused. The organization of consecutive batches prioritizes data locality.

References in corpus (10)

• The deal.II finite element library: design, features, and insights
• Fast matrix-free evaluation of discontinuous Galerkin finite element operators
• A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM
• Hybrid multigrid methods for high-order discontinuous Galerkin discretizations
• PCPATCH: software for the topological construction of multigrid relaxation methods
• Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
• Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods
• A scalable and robust vertex-star relaxation for high-order FEM
• Exploiting high-contrast Stokes preconditioners to efficiently solve incompressible fluid-structure interaction problems
• Matrix-free GPU-accelerated saddle-point solvers for high-order problems in $H(\mathrm{div})$

Cited by in corpus (1)

• Multilevel Interior Penalty Methods on GPUs