@Article{CiCP-28-4,
author = {Xingding, Chen and Xiao-Chuan, Cai},
title = {Effective Two-Level Domain Decomposition Preconditioners for Elastic Crack Problems Modeled by Extended Finite Element Method},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {4},
pages = {1561--1584},
abstract = {<p style="text-align: justify;">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 &quot;crack tip&quot; subdomain, which contains all the degrees of freedom (dofs) of the
branch enrichment functions, and the &quot;regular&quot; 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 &quot;crack tip&quot; subproblem
is solved directly and the &quot;regular&quot; 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0009},
url = {https://global-sci.com/article/79731/effective-two-level-domain-decomposition-preconditioners-for-elastic-crack-problems-modeled-by-extended-finite-element-method}
}