Scalable computational kernels for mortar finite element methods

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling conditions at high accuracy, but come with considerable numerical effort and cost for the evaluation of the mortar integrals to compute the coupling operators. In this paper, we identify bottlenecks in parallel data layout and domain decomposition that hinder an efficient evaluation of the mortar integrals. We then propose a set of computational strategies to restore optimal parallel communication and scalability for the core kernels devoted to the evaluation of mortar terms. We exemplarily study the proposed algorithmic components in the context of three-dimensional large-deformation contact mechanics, both for cases with fixed and dynamically varying interface topology, yet these concepts can naturally and easily be transferred to other mortar applications, e.g. classical meshtying problems. To restore parallel scalability, we employ overlapping domain decompositions of the interface discretization independent from the underlying volumes and then tackle parallel communication for the mortar evaluation by a geometrically motivated reduction of ghosting data. Using three-dimensional contact examples, we demonstrate strong and weak scalability of the proposed algorithms up to 480 parallel processes as well as study and discuss improvements in parallel communication related to mortar finite element methods. For the first time, dynamic load balancing is applied to mortar contact problems with evolving contact zones, such that the computational work is well balanced among all parallel processors independent of the current state of the simulation.

Automated summary

This paper presents computational kernels for efficient computations in mortar finite element methods on parallel hardware architectures. By addressing bottlenecks in parallel data layout and domain decomposition, the paper proposes computational strategies to optimize parallel communication and scalability for the evaluation of mortar terms. The proposed algorithms have been demonstrated to have strong and weak scalability in three-dimensional contact mechanics simulations, and improvements in parallel communication related to mortar finite element methods have been studied and discussed. Additionally, dynamic load balancing has been successfully applied to mortar contact problems with evolving contact zones to achieve balanced computational work among parallel processors.