A simple preconditioner for the SIPG discretization of linear elasticity equations

B. Ayuso, I. Georgiev, J. Kraus, Ludmil Tomov Zikatanov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We deal with the solution of the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The main focus of the paper is on constructing a uniform preconditioner which is based on a natural splitting of the space of piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.

Original languageEnglish (US)
Title of host publicationNumerical Methods and Applications - 7th International Conference, NMA 2010, Revised Papers
Pages353-361
Number of pages9
DOIs
Publication statusPublished - Mar 1 2011
Event7th International Conference on Numerical Methods and Applications, NMA 2010 - Borovets, Bulgaria
Duration: Aug 20 2010Aug 24 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6046 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on Numerical Methods and Applications, NMA 2010
CountryBulgaria
CityBorovets
Period8/20/108/24/10

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ayuso, B., Georgiev, I., Kraus, J., & Zikatanov, L. T. (2011). A simple preconditioner for the SIPG discretization of linear elasticity equations. In Numerical Methods and Applications - 7th International Conference, NMA 2010, Revised Papers (pp. 353-361). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6046 LNCS). https://doi.org/10.1007/978-3-642-18466-6_42