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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Discrete Fredholm properties and convergence estimates for the electric field integral equation
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by Snorre H. Christiansen;
Math. Comp. 73 (2004), 143-167
DOI: https://doi.org/10.1090/S0025-5718-03-01581-3
Published electronically: July 1, 2003

Abstract:

The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies, using orthogonal splittings of the Galerkin space. At resonant frequencies we show that the spurious electric currents radiate only weakly in the exterior domain. This is achieved through the study of some finitely degenerated problems in terms of LBB Inf-Sup estimates and the use of discrete Helmholtz decompositions.
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Bibliographic Information
  • Snorre H. Christiansen
  • Affiliation: Matematisk Institutt, P.B. 1053 Blindern, N-0316 Oslo, Norway
  • MR Author ID: 663397
  • Email: snorrec@math.uio.no
  • Received by editor(s): December 26, 2000
  • Received by editor(s) in revised form: April 10, 2002
  • Published electronically: July 1, 2003
  • Additional Notes: This work received financial support from Thales Airborne Systems
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 143-167
  • MSC (2000): Primary 65N12, 65N38, 78M15
  • DOI: https://doi.org/10.1090/S0025-5718-03-01581-3
  • MathSciNet review: 2034114