An iterative substructuring method for maxwell's equations in two dimensions

Andrea Toselli, Olof B. Widlund, Barbara I. Wohlmuth

Research output: Contribution to journalArticle

Abstract

Iterative substructuring methods, also known as Schur complement methods, form an important family of domain decomposition algorithms. They are preconditioned conjugate gradient methods where solvers on local subregions and a solver on a coarse mesh are used to construct the preconditioner. For conforming finite element approximations of H1, it is known that the number of conjugate gradient steps required to reduce the residual norm by a fixed factor is independent of the number of substructures, and that it grows only as the logarithm of the dimension of the local problem associated with an individual substructure. In this paper, the same result is established for similar iterative methods for low-order Nédélec finite elements, which approximate H(curl; Ω) in two dimensions. Results of numerical experiments are also provided.

Original languageEnglish (US)
Pages (from-to)935-949
Number of pages15
JournalMathematics of Computation
Volume70
Issue number235
DOIs
StatePublished - Jul 2001

Fingerprint

Iterative Substructuring
Maxwell equations
Substructure
Iterative methods
Maxwell's equations
Two Dimensions
Preconditioned Conjugate Gradient Method
Conjugate gradient method
Schur Complement
Curl
Conjugate Gradient
Decomposition Algorithm
Domain Decomposition
Finite Element Approximation
Logarithm
Preconditioner
Numerical Experiment
Mesh
Finite Element
Decomposition

Keywords

  • Domain decomposition
  • Iterative substructuring methods
  • Maxwell's equations
  • Nédélec finite elements

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Computational Mathematics

Cite this

An iterative substructuring method for maxwell's equations in two dimensions. / Toselli, Andrea; Widlund, Olof B.; Wohlmuth, Barbara I.

In: Mathematics of Computation, Vol. 70, No. 235, 07.2001, p. 935-949.

Research output: Contribution to journalArticle

Toselli, Andrea ; Widlund, Olof B. ; Wohlmuth, Barbara I. / An iterative substructuring method for maxwell's equations in two dimensions. In: Mathematics of Computation. 2001 ; Vol. 70, No. 235. pp. 935-949.
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