A Parallel Scalable Domain Decomposition Preconditioner for Elastic Crack Simulation Using XFEM

TL;DR

This paper introduces a parallel domain decomposition preconditioner for XFEM that effectively accelerates elastic crack simulations, achieving high scalability and efficiency on thousands of processor cores.

Contribution

It proposes a novel parallel overlapping domain decomposition preconditioner tailored for XFEM elastic crack problems, improving convergence and scalability.

Findings

Reduces iteration count and total computation time significantly.

Achieves over 70% parallel efficiency on 8192 cores.

Handles problems with over 200 million degrees of freedom.

Abstract

In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the computational mesh into two types of subdomains: the regular subdomains and the crack tip subdomains based on the observation that the crack tips have a significant impact on the convergence of the iterative method while the impact of the crack lines is not that different from those of regular mesh points. The tip subdomains consist of mesh points at crack tips and all neighboring points where the branch enrichment functions are applied. The regular subdomains consist of all other mesh points, including those on the crack lines. To overcome the mismatch between the number of subdomains and the number of processor cores, the proposed method is divided into two steps: solve the crack tip problem and then the regular subdomain problem during each iteration. The proposed method was used to develop a parallel XFEM package which is able to test different types of iterative methods. To achieve good parallel efficiency, additional methods were introduced to reduce communication and to maintain the load balance between processors. Numerical experiments indicate that the proposed method significantly reduces the number of iterations and the total computation time compared to the classical methods. In addition, the method scales up to 8192 processor cores with over 70\% parallel efficiency to solve problems with more than $2\times10^8$ degrees of freedom.