Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

Tzanio V. Kolev, Jinchao Xu, Yunrong Zhu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we extend some of the multilevel convergence results obtained by Xu and Zhu in [Xu and Zhu, M3AS 2008], to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Original languageEnglish (US)
Pages (from-to)324-350
Number of pages27
JournalJournal of Scientific Computing
Volume67
Issue number1
DOIs
StatePublished - Apr 1 2016

Fingerprint

Multilevel Preconditioners
Reaction-diffusion Problems
Discontinuous Coefficients
Constant function
Linear Approximation
Finite Element Approximation
Reaction-diffusion Equations
Preconditioner
Convergence Results
Diffusion Coefficient
Linear equation
Linear Systems
Cycle
Linear systems
Coefficient
Influence

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients. / Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong.

In: Journal of Scientific Computing, Vol. 67, No. 1, 01.04.2016, p. 324-350.

Research output: Contribution to journalArticle

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