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High precision evaluation of the selfpatch integral for linear basis functions on flat triangles

Ignace Bogaert (UGent) and Daniël De Zutter (UGent)
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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 R-n, for all n is an element of {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 lambda/7 and lambda/10 discretizations. These analytical formulas are also very robust when applied to highly irregular triangles.
Keywords
high accuracy, linear basis functions, Analytical, self-patch, triangular domains, SINGULAR POTENTIAL INTEGRALS, ELECTROMAGNETIC SCATTERING

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Citation

Please use this url to cite or link to this publication:

Chicago
Bogaert, Ignace, and Daniël De Zutter. 2010. “High Precision Evaluation of the Selfpatch Integral for Linear Basis Functions on Flat Triangles.” Ieee Transactions on Antennas and Propagation 58 (5): 1813–1816.
APA
Bogaert, Ignace, & De Zutter, D. (2010). High precision evaluation of the selfpatch integral for linear basis functions on flat triangles. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 58(5), 1813–1816.
Vancouver
1.
Bogaert I, De Zutter D. High precision evaluation of the selfpatch integral for linear basis functions on flat triangles. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. 2010;58(5):1813–6.
MLA
Bogaert, Ignace, and Daniël De Zutter. “High Precision Evaluation of the Selfpatch Integral for Linear Basis Functions on Flat Triangles.” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 58.5 (2010): 1813–1816. Print.
@article{1161942,
  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 R-n, for all n is an element of {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 lambda/7 and lambda/10 discretizations. These analytical formulas are also very robust when applied to highly irregular triangles.},
  author       = {Bogaert, Ignace and De Zutter, Daniël},
  issn         = {0018-926X},
  journal      = {IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION},
  keywords     = {high accuracy,linear basis functions,Analytical,self-patch,triangular domains,SINGULAR POTENTIAL INTEGRALS,ELECTROMAGNETIC SCATTERING},
  language     = {eng},
  number       = {5},
  pages        = {1813--1816},
  title        = {High precision evaluation of the selfpatch integral for linear basis functions on flat triangles},
  url          = {http://dx.doi.org/10.1109/TAP.2010.2044352},
  volume       = {58},
  year         = {2010},
}

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