Multigrid methods for two-dimensional Maxwell's equations on graded meshes

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Abstract

In this paper we investigate the numerical solution for two-dimensional Maxwell's equations on graded meshes. The approach is based on the Hodge decomposition. The solution u of Maxwell's equations is approximated by solving standard second order elliptic problems. Quasi-optimal error estimates for both u and ×u in the L2 norm are obtained on graded meshes. We prove the uniform convergence of the W-cycle and full multigrid algorithms for the resulting discrete problem. The performance of these methods is illustrated by numerical results.
Original languageEnglish
Pages (from-to)231-247
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume255
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Graded meshes
  • Hodge decomposition
  • Maxwell's equations
  • Multigrid methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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