Effective Two-Level Domain Decomposition Preconditioners for Elastic Crack Problems Modeled by Extended Finite Element Method
Year: 2020
Author: Xingding Chen, Xiao-Chuan Cai
Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1561–1584
Abstract
In this paper, we propose some effective one- and two-level domain decomposition preconditioners for elastic crack problems modeled by extended finite element method. To construct the preconditioners, the physical domain is decomposed into the "crack tip" subdomain, which contains all the degrees of freedom (dofs) of the branch enrichment functions, and the "regular" subdomains, which contain the standard dofs and the dofs of the Heaviside enrichment function. In the one-level additive Schwarz and restricted additive Schwarz preconditioners, the "crack tip" subproblem is solved directly and the "regular" subproblems are solved by some inexact solvers, such as ILU. In the two-level domain decomposition preconditioners, traditional interpolations between the coarse and the fine meshes destroy the good convergence property. Therefore, we propose an unconventional approach in which the coarse mesh is exactly the same as the fine mesh along the crack line, and adopt the technique of a non-matching grid interpolation between the fine and the coarse meshes. Numerical experiments demonstrate the effectiveness of the two-level domain decomposition preconditioners applied to elastic crack problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0009
Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1561–1584
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Extended finite element method domain decomposition two-level preconditioners elastic crack problem non-matching grid.