CERTIFIED REDUCED BASIS METHOD FOR THE ELECTRIC FIELD INTEGRAL EQUATION

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)A1777-A1799
Number of pages23
Journal / PublicationSIAM Journal on Scientific Computing
Volume34
Issue number3
Online published28 Jun 2012
Publication statusPublished - 2012
Externally publishedYes

Abstract

[B. Fares et al., J. Comput. Phys., 230 (2011), pp. 5532-5555], a reduced basis method (RBM) for the electric field integral equation (EFIE) using the boundary element method (BEM) is developed, based on a simplified a posteriori error estimator for the greedy-based snapshot selection. In this paper, we extend this work and propose a certified RBM for the EFIE based on a mathematically rigorous a posteriori estimator. A central difficulty of the certified method is that the intrinsic solution space of the EFIE is Hdiv-1/2(Γ), inducing a relatively complicated norm. Since the measured error consists of the difference between the reduced basis solution and the boundary element solution, which is a member of the discrete boundary element space, we clarify that the intrinsic norm can be replaced by an alternative norm and in this work use the H(div)-norm, which is computable and demonstrated to not degrade the quality of the error estimator. A successive constraint method (SCM) for complex matrices is discussed in detail, and numerical tests for the SCM and then the certified RBM confirm the analysis.

Research Area(s)

  • basis methods, integral equations, electromagnetics

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