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Numerical Algorithms

, Volume 69, Issue 1, pp 109–144 | Cite as

Optimized Schwarz methods for a diffusion problem with discontinuous coefficient

  • Martin J. Gander
  • Olivier Dubois
Original Paper

Abstract

We study non-overlapping Schwarz methods for solving a steady-state diffusion problem in heterogeneous media. Various optimized transmission conditions are determined by solving the corresponding min-max problems; we consider different choices of Robin conditions and second order conditions. To compare the resulting methods, we analyze the convergence in two separate asymptotic regimes: when the mesh size is small, and when the jump in the coefficient is large. It is shown that optimized two-sided Robin transmission conditions are very effective in both regimes; in particular they give mesh independent convergence. Numerical experiments are presented to illustrate and confirm the theoretical results.

Keywords

Optimized Schwarz methods Optimized transmission conditions Domain decomposition Parallel preconditioning 

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Section de mathématiquesUniversité de GenèveGenève 4Suisse
  2. 2.Department of MathematicsJohn Abbott CollegeSainte-Anne-de-Bellevue, H9X 3L9, QuébecCanada

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