Singularity subtraction technique for high-order polynomial vector basis functions on planar triangles

In this paper a singularity subtraction technique is developed for computing the impedance matrix elements of various electromagnetic surface integral equation formulations with the Galerkin method and high-order basis functions. Analytical closed form formulas for computing surface integrals with |r - r'|/sup n/, n/spl ges/-3, singularities times polynomial nodal shape functions of arbitrary order on a planar triangle are presented.

[1]  J. P. Webb,et al.  Hierarchal vector boundary elements and p-adaption for 3-D electromagnetic scattering , 1997 .

[2]  D. Wilton,et al.  Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains , 1984 .

[3]  P. Yla-Oijala,et al.  Calculation of CFIE impedance matrix elements with RWG and n/spl times/RWG functions , 2003 .

[4]  Werner Wiesbeck,et al.  Methods for the Evaluation of Regular, Weakly Singular and Strongly Singular Surface Reaction Integrals Arising in Method of Moments , 2002 .

[5]  M. G. Duffy,et al.  Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex , 1982 .

[6]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[7]  B. Kolundžija,et al.  Entire-domain Galerkin method for analysis of metallic antennas and scatterers , 1993 .

[8]  P. J. Cullen,et al.  On the fully numerical evaluation of the linear-shape function times the 3D Green's function on a plane triangle , 1999 .

[9]  Seppo Järvenpää,et al.  Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra , 2003 .

[10]  E. Jorgensen,et al.  Higher order hierarchical Legendre basis functions for electromagnetic modeling , 2004, IEEE Transactions on Antennas and Propagation.

[11]  Roberto D. Graglia,et al.  Higher order interpolatory vector bases for computational electromagnetics," Special Issue on "Advanced Numerical Techniques in Electromagnetics , 1997 .

[12]  C. Schwab,et al.  On numerical cubatures of singular surface integrals in boundary element methods , 1992 .

[13]  Wei Cai,et al.  High-order mixed RWG basis functions for electromagnetic applications , 2001 .

[14]  H. Kardestuncer,et al.  Finite element handbook , 1987 .

[15]  Jian-Ming Jin,et al.  A novel grid-robust higher order vector basis function for the method of moments , 2000 .

[16]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[17]  D. A. Dunavant.  High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[18]  Yijun Yu,et al.  Singularity treatment and high‐order RWG basis functions for integral equations of electromagnetic scattering , 2001 .

[19]  A. Peterson,et al.  High Accuracy Calculation of the Magnetic Vector Potential On Surfaces , 2004 .

[20]  M.A. Khayat,et al.  Numerical evaluation of singular and near-singular potential Integrals , 2005, IEEE Transactions on Antennas and Propagation.