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Title: Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

Abstract

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, 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.

Authors:
 [1];  [2];  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Penn State Univ., University Park, PA (United States)
  3. Idaho State Univ., Pocatello, ID (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1440717
Report Number(s):
LLNL-JRNL-663816
Journal ID: ISSN 0885-7474; 785179
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Volume: 67; Journal Issue: 1; Journal ID: ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Reaction-diffusion equations; Multigrid; BPX; Discontinuous coefficients; Robust solver; Multilevel preconditioners

Citation Formats

Kolev, Tzanio V., Xu, Jinchao, and Zhu, Yunrong. Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients. United States: N. p., 2015. Web. doi:10.1007/s10915-015-0083-7.
Kolev, Tzanio V., Xu, Jinchao, & Zhu, Yunrong. Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients. United States. doi:10.1007/s10915-015-0083-7.
Kolev, Tzanio V., Xu, Jinchao, and Zhu, Yunrong. Sun . "Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients". United States. doi:10.1007/s10915-015-0083-7. https://www.osti.gov/servlets/purl/1440717.
@article{osti_1440717,
title = {Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients},
author = {Kolev, Tzanio V. and Xu, Jinchao and Zhu, Yunrong},
abstractNote = {In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, 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.},
doi = {10.1007/s10915-015-0083-7},
journal = {Journal of Scientific Computing},
number = 1,
volume = 67,
place = {United States},
year = {2015},
month = {8}
}

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