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Journal of Scientific Computing

, Volume 67, Issue 1, pp 324–350 | Cite as

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

  • Tzanio V. Kolev
  • Jinchao Xu
  • Yunrong Zhu
Article

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.

Keywords

Reaction-diffusion equations Multigrid BPX Discontinuous coefficients Robust solver Multilevel preconditioners 

Mathematics Subject Classification

65F10 65N20 65N30 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Department of MathematicsPenn. State UniversityUniversity ParkUSA
  3. 3.Department of MathematicsIdaho State UniversityPocatelloUSA

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