Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle

Ronald D. Haynes, Wing Hong Felix KWOK

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Moving mesh methods based on the equidistribution principle are powerful techniques for the space-time adaptive solution of evolution problems. Solving the resulting coupled system of equations, namely the original PDE and the mesh PDE, however, is challenging in parallel. Recently several Schwarz domain decomposition algorithms were proposed for this task and analyzed at the continuous level. However, after discretization, the resulting problems may not even be well posed, so the discrete algorithms require a different analysis, which is the subject of this paper. We prove that when the number of grid points is large enough, the classical parallel and alternating Schwarz methods converge to the unique rnonodomain solution. Thus, such methods can be used in place of Newton's method, which can suffer from convergence difficulties for challenging problems. The analysis for the nonlinear domain decomposition algorithms is based on ./W-function theory and is valid for an arbitrary number of subdomains. An asymptotic convergence rate is provided and numerical experiments illustrate the results.

Original languageEnglish
Pages (from-to)233-273
Number of pages41
JournalMathematics of Computation
Volume86
Issue number303
DOIs
Publication statusPublished - Jan 2017

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • A/-functions
  • Discretization
  • Domain decomposition
  • Equidistribution
  • Moving meshes
  • Schwarz methods

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