Research Article

Preconditioners for the discretized time-harmonic Maxwell equations in mixed form

  1. Chen Greif1,*,
  2. Dominik Schötzau2

Article first published online: 9 JAN 2007

DOI: 10.1002/nla.515

Issue

Numerical Linear Algebra with Applications

Numerical Linear Algebra with Applications

Special Issue: Mathematical Modelling and Mathematical Methods in Energy

Volume 14, Issue 4, pages 281–297, May 2007

Additional Information

How to Cite

Greif, C. and Schötzau, D. (2007), Preconditioners for the discretized time-harmonic Maxwell equations in mixed form. Numer. Linear Algebra Appl., 14: 281–297. doi: 10.1002/nla.515

Author Information

  1. 1

    Department of Computer Science, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4

  2. 2

    Mathematics Department, The University of British Columbia, Vancouver, BC, Canada V6T 1Z2

*Department of Computer Science, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4

Publication History

  1. Issue published online: 2 APR 2007
  2. Article first published online: 9 JAN 2007
  3. Manuscript Accepted: 10 JUN 2006
  4. Manuscript Revised: 29 MAY 2006
  5. Manuscript Received: 30 OCT 2005

Funded by

  • Natural Sciences and Engineering Research Council of Canada

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Keywords:

  • time-harmonic Maxwell equations;
  • finite element methods;
  • saddle point linear systems;
  • block preconditioners;
  • Krylov subspace solvers

Abstract

We introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the discrete operators, but are augmentation free and Schur complement free. We provide a complete spectral analysis, and show that the eigenvalues of the preconditioned saddle point matrix are strongly clustered. The analytical observations are accompanied by numerical results that demonstrate the scalability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

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