Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

Tzanio V. Kolev; Jinchao Xu; Yunrong Zhu

doi:10.1007/s10915-015-0083-7

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

Tzanio V. Kolev, Jinchao Xu, Yunrong Zhu

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 language	English (US)
Pages (from-to)	324-350
Number of pages	27
Journal	Journal of Scientific Computing
Volume	67
Issue number	1
DOIs	https://doi.org/10.1007/s10915-015-0083-7
State	Published - Apr 1 2016
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Computational Theory and Mathematics
Theoretical Computer Science
Software
General Engineering

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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.",

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AU - Kolev, Tzanio V.

AU - Xu, Jinchao

AU - Zhu, Yunrong

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PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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.

AB - 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.

UR - http://link.springer.com/10.1007/s10915-015-0083-7

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JO - Journal of Scientific Computing

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IS - 1

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Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

Abstract

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ASJC Scopus subject areas

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