Title :
High Precision Evaluation of the Selfpatch Integral for Linear Basis Functions on Flat Triangles
Author :
Bogaert, Ignace ; De Zutter, Daniel
Author_Institution :
Dept. of Inf. Technol., Ghent Univ., Ghent, Belgium
fDate :
5/1/2010 12:00:00 AM
Abstract :
The application of integral equations for the frequency domain analysis of scattering problems requires the accurate evaluation of interaction integrals. Generally speaking, the most critical integral is the selfpatch. However, due to the non-smoothness of the Green function, this integral is also the toughest to calculate numerically. In previous work, the source and test integrals have been determined analytically for the 1/R singularity, i.e., the static kernel. In this work we extend this result to the terms of the form Rn, ??n ?? {0,1,2,3,4} that occur in the Taylor expansion of the Green function. Numerical testing shows that truncating the Taylor series beyond n = 4 yields a highly accurate result for ??/7 and ??/10 discretizations. These analytical formulas are also very robust when applied to highly irregular triangles.
Keywords :
Green´s function methods; computational electromagnetics; electromagnetic wave scattering; frequency-domain analysis; integral equations; Green function; Taylor expansion; flat triangles; frequency domain analysis; integral equations; linear basis functions; scattering problems; selfpatch integral; Frequency domain analysis; Green function; Information technology; Integral equations; Iron; Kernel; Moment methods; Performance evaluation; Robustness; Scattering; Taylor series; Testing; Analytical; high accuracy; linear basis functions; selfpatch; triangular domains;
Journal_Title :
Antennas and Propagation, IEEE Transactions on
DOI :
10.1109/TAP.2010.2044352