article

A Quasi-algebraic Multigrid Approach to Fracture Problems Based on Extended Finite Elements

Authors:

D.E. KeyesAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 34, Issue 2

Pages 603 - 626

https://doi.org/10.1137/110819913

Published: 01 March 2012 Publication History

Abstract

The modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges. The extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine spatial resolution in the vicinity of discontinuities nor do they require repeated remeshing to properly address propagation of cracks. They do, however, give rise to linear systems requiring special care within an iterative solver method. An algebraic multigrid method is proposed that is suitable for the linear systems associated with modeling fracture via extended finite elements. The new method follows naturally from an energy minimizing algebraic multigrid framework. The key idea is the modification of the prolongator sparsity pattern to prevent interpolation across cracks. This is accomplished by accessing the standard levelset functions used during the discretization process. Numerical experiments illustrate that the resulting method converges in a fashion that is relatively insensitive to mesh resolution and to the number of cracks or their location.

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Cited By

Grigorovitch MGal EWaisman H(2021)Embedded unit cell homogenization model for localized non-periodic elasto-plastic zonesComputational Mechanics10.1007/s00466-021-02077-368:6(1437-1456)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s00466-021-02077-3
de Prenter FVerhoosel Cvan Brummelen EEvans JMesse CBenzaken JMaute K(2019)Multigrid solvers for immersed finite element methods and immersed isogeometric analysisComputational Mechanics10.1007/s00466-019-01796-y65:3(807-838)Online publication date: 26-Nov-2019
https://dl.acm.org/doi/10.1007/s00466-019-01796-y
Zhang SOskay C(2015)Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problemsComputational Mechanics10.1007/s00466-015-1135-455:4(771-787)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1007/s00466-015-1135-4

A Quasi-algebraic Multigrid Approach to Fracture Problems Based on Extended Finite Elements
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 34, Issue 2

April 2012

829 pages

ISSN:1064-8275

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 March 2012

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Cited By

Grigorovitch MGal EWaisman H(2021)Embedded unit cell homogenization model for localized non-periodic elasto-plastic zonesComputational Mechanics10.1007/s00466-021-02077-368:6(1437-1456)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s00466-021-02077-3
de Prenter FVerhoosel Cvan Brummelen EEvans JMesse CBenzaken JMaute K(2019)Multigrid solvers for immersed finite element methods and immersed isogeometric analysisComputational Mechanics10.1007/s00466-019-01796-y65:3(807-838)Online publication date: 26-Nov-2019
https://dl.acm.org/doi/10.1007/s00466-019-01796-y
Zhang SOskay C(2015)Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problemsComputational Mechanics10.1007/s00466-015-1135-455:4(771-787)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1007/s00466-015-1135-4

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