Quadrature Weights on Tensor-Product Nodes for Accurate Integration of Hypersingular Functions over Some Simple 3-D Geometric Shapes
Year: 2016
Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1283–1312
Abstract
In this paper, we present accurate and economic integration quadratures for hypersingular functions over three simple geometric shapes in $\mathbb{R}^3$ (spheres, cubes, and cylinders). The quadrature nodes are made of the tensor-product of 1-D Gauss nodes on [−1,1] for non-periodic variables or uniform nodes on [0,2π] or [0,π] for periodic ones. The quadrature weights are converted from a brute-force integration of the hypersingular function through interpolating the smooth component of the integrand. Numerical results are presented to validate the accuracy and efficiency of computing hypersingular integrals, as in the computations of Cauchy principal values, with a minimum number of quadrature nodes. The pre-calculated quadrature tables can be then readily used to implement Nyström collocation methods of hypersingular volume integral equations such as the one for Maxwell equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2015-0005
Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1283–1312
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
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Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers
Chen, Duan
Cai, Wei
Zinser, Brian
Cho, Min Hyung
Journal of Computational Physics, Vol. 321 (2016), Iss. P.303
https://doi.org/10.1016/j.jcp.2016.05.042 [Citations: 10]