TY - GEN
T1 - New formulations for evaluating hypersingular and strongly singular integrals in electromagnetic integral equations
AU - Tong, Mei Song
AU - Chew, Weng Cho
PY - 2010
Y1 - 2010
N2 - Electromagnetic (EM) integral equations include the singular integral kernels related to the Green's function. For surface integral equations (SIEs), there are two kinds of kernels, i.e. the L operator and K operator. The L operator is the dyadic Green's function which includes a double gradient operation on the scalar Green's function that results in 1/R3 hypersingular integrals (HSIs), where R is the distance between a source point and an observation point or field point. However, the HSIs could be reduced to 1/R weakly singular integrals (WSIs) in the method of moments (MoM) solutions if divergence conforming basis function like the Rao-Wilton-Glisson (RWG) basis function is used as an expansion and testing function. Without the help of these basis functions, we must carefully handle the HSIs and this happens in the implementation of Nystr̈om method (NM) or boundary element method (BEM). The K operator includes a single gradient operation on the scalar Green's function, yielding 1/R2 strongly singular integrals (SSIs) in the matrix elements. The SSIs also exist in the L operator in the MoM when the RWG-like basis functions cannot be used as a testing function. The accurate and efficient evaluation for the HSIs and SSIs is essential in solving the SIEs because they have a significant impact on the numerical solutions.
AB - Electromagnetic (EM) integral equations include the singular integral kernels related to the Green's function. For surface integral equations (SIEs), there are two kinds of kernels, i.e. the L operator and K operator. The L operator is the dyadic Green's function which includes a double gradient operation on the scalar Green's function that results in 1/R3 hypersingular integrals (HSIs), where R is the distance between a source point and an observation point or field point. However, the HSIs could be reduced to 1/R weakly singular integrals (WSIs) in the method of moments (MoM) solutions if divergence conforming basis function like the Rao-Wilton-Glisson (RWG) basis function is used as an expansion and testing function. Without the help of these basis functions, we must carefully handle the HSIs and this happens in the implementation of Nystr̈om method (NM) or boundary element method (BEM). The K operator includes a single gradient operation on the scalar Green's function, yielding 1/R2 strongly singular integrals (SSIs) in the matrix elements. The SSIs also exist in the L operator in the MoM when the RWG-like basis functions cannot be used as a testing function. The accurate and efficient evaluation for the HSIs and SSIs is essential in solving the SIEs because they have a significant impact on the numerical solutions.
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U2 - 10.1109/APS.2010.5561064
DO - 10.1109/APS.2010.5561064
M3 - Conference contribution
AN - SCOPUS:78349253501
SN - 9781424449682
T3 - 2010 IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting - Leading the Wave, AP-S/URSI 2010
BT - 2010 IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting - Leading the Wave, AP-S/URSI 2010
T2 - 2010 IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting - Leading the Wave, AP-S/URSI 2010
Y2 - 11 July 2010 through 17 July 2010
ER -