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An algebraic multigrid approach to solve extended finite element method based fracture problems
Author(s) -
Gerstenberger Axel,
Tuminaro Raymond S.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4442
Subject(s) - multigrid method , finite element method , leverage (statistics) , classification of discontinuities , mathematics , computer science , linear system , mathematical optimization , extended finite element method , convergence (economics) , mathematical analysis , engineering , partial differential equation , structural engineering , machine learning , economics , economic growth
SUMMARY This article proposes an algebraic multigrid (AMG) approach to solve linear systems arising from applications where strong discontinuities are modeled by the extended finite element method. The application of AMG methods promises optimal scalability for solving large linear systems. However, the straightforward (or ‘black‐box’) use of existing AMG techniques for extended finite element method problems is often problematic. In this paper, we highlight the reasons for this behavior and propose a relatively simple adaptation that allows one to leverage existing AMG software mostly unchanged. Numerical tests demonstrate that optimal iterative convergence rates can be attained that are comparable with AMG convergence rates associated with linear systems for standard finite element approximations without discontinuities. Published 2012. This article is a US Government work and is in the public domain in the USA.