Domain decomposition methods for 3D crack propagation problems using XFEM

The extended finite element method (XFEM) has been successfully implemented in solving crack propagation problems by enriching the polynomial basis functions of standard finite elements with specialized non-smooth functions. The resulting approximation space can be used to solve problems with moving discontinuities, such as cracks, without the need of remeshing in the vicinity of the crack. The enrichment of the displacement field in XFEM inflicts a substantial increase in the ellipticity of the discretized problem. As a consequence, the resulting algebraic systems become strongly ill-conditioned, rendering the convergence of iterative solvers very slow. On the other hand, direct solvers may become inefficient in 3D problems, due to the increased bandwidth of the system matrix. In this paper, two of the most efficient domain decomposition solvers, namely the FETI-DP and P-FETI-DP, are proposed for solving the linear systems resulting from XFEM crack propagation analysis in large-scale 3D problems. Both solvers are amenable to parallelization and can be implemented in modern parallel computing environments, with multicore processors and distributed memory systems, following appropriate modifications, to achieve a drastic reduction of memory and computing time in computationally intensive problems.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The extended finite element method (XFEM) has been successfully applied to solve crack propagation problems without remeshing. However, the enrichment in XFEM leads to ill-conditioned algebraic systems and slow convergence of iterative solvers. In this paper, two efficient domain decomposition solvers, FETI-DP and P-FETI-DP, are proposed for large-scale 3D XFEM crack propagation analysis, offering parallelization and reduced computational time.