Discretization error due to the identity operator in surface integral equations


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Ergul O. , Gurel L.

COMPUTER PHYSICS COMMUNICATIONS, vol.180, no.10, pp.1746-1752, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 180 Issue: 10
  • Publication Date: 2009
  • Doi Number: 10.1016/j.cpc.2009.04.020
  • Title of Journal : COMPUTER PHYSICS COMMUNICATIONS
  • Page Numbers: pp.1746-1752
  • Keywords: Surface integral equations, Low-order basis functions, First-kind integral equations, Second-kind integral equations, Identity operator, Accuracy analysis, CONFORMING BASIS FUNCTIONS, ELECTROMAGNETIC SCATTERING, MAGNETIC-FIELD, FORMULATION

Abstract

We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving well-tested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao-Wilton-Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the identity operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly. (C) 2009 Elsevier B.V. All rights reserved.