scholarly journals Review of singular potential integrals for method of moments solutions of surface integral equations

2005 ◽  
Vol 2 ◽  
pp. 93-99 ◽  
Author(s):  
A. Tzoulis ◽  
T. F. Eibert
Keyword(s):  
Integral Equations ◽  
Method Of Moments ◽  
Singular Potential ◽  
Logarithmic Singularity ◽  
Boundary Integral ◽  
Surface Integral ◽  
Hybrid Finite Element ◽  
Convergence Results ◽  
Surface Integral Equations ◽  
Element Boundary

Abstract. Accurate evaluation of singular potential integrals is essential for successful method of moments (MoM) solutions of surface integral equations. In mixed potential formulations for metallic and dielectric scatterers, kernels with 1/R and r1/R singularities must be considered. Several techniques for the treatment of these singularities will be reviewed. The most common approach solves the MoM source integrals analytically for specific observation points, thus regularizing the integral. However, in the case of r1/R a logarithmic singularity remains for which numerical evaluation of the testing integral is still difficult. A recently by Yl¨a-Oijala and Taskinen proposed remedy to this issue is discussed and evaluated within a hybrid finite element – boundary integral technique. Convergence results for the MoM coupling integrals are presented where also higher-order singularity extraction is considered.

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