A two-scale solver for linear elasticity problems in the context of parallel message passing

TL;DR

This paper develops a distributed MPI-based global-local solver for linear elasticity problems, enhancing the GFEM$^{gl}$ approach with new scheduling, convergence measurement, and matrix-based implementation, demonstrating scalability and efficiency through numerical tests.

Contribution

Introduces a distributed MPI implementation of the GFEM$^{gl}$ global-local approach with novel scheduling and convergence strategies for linear elasticity problems.

Findings

The distributed solver scales well with problem size.

It outperforms other parallel solvers in elapsed time.

Effective handling of complex micro-structures and crack problems.

Abstract

This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local problems. Regarding local problems, a specific scheduling strategy is introduced. Then, to measure correctly the convergence of the iterative process, we introduce a reference solution that revisits the product of classical and enriched functions. As a consequence, we are able to propose a purely matrix-based implementation of the global-local problem. The distributed approach is then compared to other parallel solvers either direct or iterative with domain decomposition. The comparison addresses the scalability as well as the elapsed time. Numerical examples deal with linear elastic problems: a polynomial exact solution problem, a complex micro-structure, and, finally, a pull-out test (with different crack extent). 1: C. A. Duarte, D.-J. Kim, and I. Babu\v{s}ka. A global-local approach for the construction of enrichment functions for the generalized fem and its application to three-dimensional cracks. In Advances in Meshfree Techniques, Dordrecht, 2007. Springer