Journal
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
Volume 51, Issue 7, Pages 1630-1637Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAP.2003.813623
Keywords
Galerkin method; impedance matrix; integro-differential equation
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A Galerkin descretization of the electric field integral equation for perfectly conducting surfaces using Rao-Wilton-Glisson basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions. These singularities have been traditionally handled by utilizing a singularity extraction procedure to produce a regular integral and an analytic function to replace the original singular integral. A new approach is presented here in which the four-dimensional (4-D) weakly singular integrals unique to the Galerkin Rao-Wilton-Glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands. The transformations allow some of the integrations to be performed analytically, in some cases reducing the original 4-D integral into a 1-D numerical integration. The accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle.
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