A parallel algorithm for unilateral contact problems

TL;DR

This paper presents a new parallel algorithm for solving nonlinear unilateral contact problems efficiently on supercomputers, using a coupled staggered approach with boundary condition exchange, validated through benchmarks and large-scale impact tests.

Contribution

It introduces a novel parallel contact algorithm based on partial Dirichlet-Neumann conditions and a Gauss-Seidel coupling strategy, optimized for high-performance computing environments.

Findings

Successfully validated against theoretical and numerical benchmarks.

Demonstrated scalability and efficiency in large-scale impact simulations.

Achieved effective parallel performance on supercomputing architectures.

Abstract

In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element code. The algorithm is based on the method of partial Dirichlet-Neumann boundary conditions and is capable to solve numerically a nonlinear contact problem between rigid and deformable bodies in a whole parallel framework. Its distinctive characteristic is that the contact is tackled as a coupled problem, in which the contacting bodies are treated separately, in a staggered way. Then, the coupling is performed through the exchange of boundary conditions at the contact interface following a Gauss-Seidel strategy. To validate this algorithm we conducted several benchmark tests by comparing the proposed solution against theoretical and other numerical solutions. Finally, we evaluated the parallel performance of the proposed algorithm in a real impact test to show its capabilities for large-scale applications.