Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

Abstract

Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that highorder methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs. We demonstrate the reliability, efficiency, and scalability of matrix-free p-multigrid methods with algebraic multigrid coarse solvers through large deformation hyperelastic simulations of multiscale structures. We investigate accuracy, cost, and execution time on multi-node CPU and GPU systems for moderate to large models using AMD MI250X (OLCF Crusher), NVIDIA A100 (NERSC Perlmutter), and V100 (LLNL Lassen and OLCF Summit), resulting in order of magnitude efficiency improvements over a broad range of model properties and scales. We discuss efficient matrix-free representation of Jacobians and demonstrate how automatic differentiation enables rapid development of nonlinear material models without impacting debuggability and workflows targeting GPUs.

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

“…The groundwork has been laid in our contribution [29] and needs to be incorporated into the high-performance framework presented in this work. Matrix-free implementations with efficient solution strategies exist for the solid mechanics problem [77,78]. They will likely require application-specific adaptations to complement the high-performance implementation of the thermal problem presented in this work.…”