ParaGEMS: Integrating discrete exterior calculus (DEC) into ParaFEM for geometric analysis of solid mechanics

New high-performance computing (HPC) software designed for massively parallel computers with high-speed interconnects is presented to accelerate research into geometric formulations of solid mechanics based on discrete exterior calculus (DEC). DEC is a relatively new and entirely discrete approach being developed to model non-smooth material processes, for which continuum descriptions fail. Until now, progress has been slowed by limited HPC software. The tool presented herein inte-grates the DEC library ParaGEMS into the well-established parallel finite-element (FE) code ParaFEM, leveraging ParaFEM's diverse IO routines, optimised solvers, and interfaces to third-party libraries. This is accomplished by interpreting FE elements, or their subdivision, as independent DEC simplicial complexes. The element-wise contribution to the global system matrix is then replaced with the DEC formalism, superimposing contributions from the dual mesh at element boundaries. The integrated tool is validated using five miniApps for scalar diffusion and linear elasticity on synthetic microstructures with emerging discontinuities, showing the performance for both continuum and discrete problems. Profiling indicates DEC calculations have excellent scaling and the solver achieves approximately 80% parallel efficiency using naive partitioning on similar to 8000 cores with >135 million unknowns. The tool is now being used to develop DEC formulations of more complex phenomena, such as material nonlinearity and fracture.(c) 2022 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This article presents a new high-performance computing software for accelerating research into geometric formulations of solid mechanics based on discrete exterior calculus (DEC). The software integrates the DEC library ParaGEMS into the parallel finite-element (FE) code ParaFEM, enabling efficient modeling of non-smooth material processes. The tool is validated using miniApps and exhibits excellent scaling and parallel efficiency.