A massively parallel explicit solver for elasto-dynamic problems exploiting octree meshes

TL;DR

This paper introduces a parallel explicit solver for elasto-dynamic problems using octree meshes and SBFEM, achieving high efficiency and scalability for large-scale simulations with complex geometries.

Contribution

It presents a novel parallel explicit solver leveraging octree meshes and SBFEM, with pre-computed matrices and extended mass lumping for improved performance.

Findings

Achieved significant speedup on large problems with up to one billion degrees of freedom.

Demonstrated scalability up to 16,384 cores in distributed computing environments.

Validated the method with complex geometries and practical impact applications.

Abstract

Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and transient solvers are required. To this end, a parallel explicit solver exploiting the advantages of balanced octree meshes is introduced. To avoid the hanging nodes problem encountered in standard finite element analysis (FEA), the scaled boundary finite element method (SBFEM) is deployed as a spatial discretization scheme. Consequently, arbitrarily shaped star-convex polyhedral elements are straightforwardly generated. Considering the scaling and transformation of octree cells, the stiffness and mass matrices of a limited number of unique cell patterns are pre-computed. A recently proposed mass lumping technique is extended to 3D yielding a well-conditioned diagonal mass matrix. This enables us to leverage the advantages of explicit time integrator, i.e., it is possible to efficiently compute the nodal displacements without the need for solving a system of linear equations. We implement the proposed scheme together with a central difference method (CDM) in a distributed computing environment. The performance of our parallel explicit solver is evaluated by means of several numerical benchmark examples, including complex geometries and various practical applications. A significant speedup is observed for these examples with up to one billion of degrees of freedom and running on up to 16,384 computing cores.