The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Thomas Jaroszewicz - One of the best experts on this subject based on the ideXlab platform.
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Reduction of Singular Surface integrals to non-Singular line integrals in integral equations involving non-parallel Surface elements
2017 11th European Conference on Antennas and Propagation (EUCAP), 2017Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of integrals involving Singular Green function and Rao-Wilton-Glisson basis functions with arbitrary mutual non-planar geometrical configuration which appear in Surface integral equations representation of Maxwell equations. The proposed procedure constitutes a generalization of our previously reported result valid for planar geometries. The method employs a suitably constructed representation of the Helmholtz equation Green function in terms of an differential operator acting on an auxiliary function which allows one to reduce four-dimensional Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. Advantages of our approach include simplicity and high accuracy at a computational cost considerably lower than for previously considered methods, such as the Singularity subtraction technique.
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reduction of Singular Surface integrals to nonSingular line integrals in integral equations for planar geometries
IEEE Transactions on Antennas and Propagation, 2016Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao–Wilton–Glisson basis functions appearing in Surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, or geometries composed of parallel planar sheets, reduces 4-D Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy achieved at a computational cost significantly lower than for previously considered techniques, in particular the conventional Singularity subtraction method.
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Reduction of Singular Surface integrals of tensor Green function to non-Singular line integrals in integral equations for planar geometries
2016 10th European Conference on Antennas and Propagation (EuCAP), 2016Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao-Wilton-Glisson basis functions appearing in Surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, reduces four-dimensional Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy without the need of using numerical Singularity extraction methods.
Elizabeth Bleszynski - One of the best experts on this subject based on the ideXlab platform.
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Reduction of Singular Surface integrals to non-Singular line integrals in integral equations involving non-parallel Surface elements
2017 11th European Conference on Antennas and Propagation (EUCAP), 2017Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of integrals involving Singular Green function and Rao-Wilton-Glisson basis functions with arbitrary mutual non-planar geometrical configuration which appear in Surface integral equations representation of Maxwell equations. The proposed procedure constitutes a generalization of our previously reported result valid for planar geometries. The method employs a suitably constructed representation of the Helmholtz equation Green function in terms of an differential operator acting on an auxiliary function which allows one to reduce four-dimensional Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. Advantages of our approach include simplicity and high accuracy at a computational cost considerably lower than for previously considered methods, such as the Singularity subtraction technique.
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reduction of Singular Surface integrals to nonSingular line integrals in integral equations for planar geometries
IEEE Transactions on Antennas and Propagation, 2016Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao–Wilton–Glisson basis functions appearing in Surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, or geometries composed of parallel planar sheets, reduces 4-D Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy achieved at a computational cost significantly lower than for previously considered techniques, in particular the conventional Singularity subtraction method.
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Reduction of Singular Surface integrals of tensor Green function to non-Singular line integrals in integral equations for planar geometries
2016 10th European Conference on Antennas and Propagation (EuCAP), 2016Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao-Wilton-Glisson basis functions appearing in Surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, reduces four-dimensional Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy without the need of using numerical Singularity extraction methods.
R Klees - One of the best experts on this subject based on the ideXlab platform.
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numerical calculation of weakly Singular Surface integrals
Journal of Geodesy, 1996Co-Authors: R KleesAbstract:We consider semi-analytical and purely numerical integration methods for weakly Singular integrals with point Singularities on curved smooth Surfaces. The methods can be applied to many practical computations in Geodesy, e.g. terrain corrections, Stokes' and Hotines' integral, Surface potentials, and the solution of geodetic boundary value problems using integral equations. Current numerical integration techniques are reviewed. The most important semi-analytical and purely numerical techniques are described. Test calcualtions are done and the techniques are compared as regards accuracy and computational efficiency. Semi-analytical methods, which are based on some regularizing parameter transformations, are superior to purely numerical techniques. The best choice are modified polar coordinates defined in the parameter domain with the Singularity as pole. Triangular coordinates show similar performance if carefully tuned. Extrapolation techniques and adaptive subdivision techniques behave poorly as regards accuracy and numerical efficiency. Standard integration techniques, which ignore the Singularity, completely fail.
Weng Cho Chew - One of the best experts on this subject based on the ideXlab platform.
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a novel approach for evaluating hyperSingular and strongly Singular Surface integrals in electromagnetics
IEEE Transactions on Antennas and Propagation, 2010Co-Authors: Mei Song Tong, Weng Cho ChewAbstract:Solving electromagnetic (EM) problems by integral equation methods requires an accurate and efficient treatment for the Singular integral kernels related to the Green's function. For Surface integral equations (SIEs), there are L and K operators which include hyperSingular integrals (HSIs) and strongly Singular integrals (SSIs), respectively. The HSIs are generated from the double gradient of the Green's function while the SSIs come from the single gradient of the Green's function. Although the HSIs could be reduced to weakly Singular integrals (WSIs) in the method of moments (MoM) implementation with divergence conforming basis function such as the Rao-Wilton-Glisson (RWG) basis function, they do appear in Nystrom method (NM) or boundary element method (BEM) and one has to tackle them. The SSIs always exist in the K operator and could also exist in the L operator when the testing function is not the RWG-like basis function. The treatment for the HSIs and SSIs is essential because they have a significant influence on the numerical solutions. There have been many publications dealing with the Singular integrals, but they mainly focus on the WISs or SSIs, and the HSIs were seldom addressed. In this work, we develop a novel approach for evaluating those HSIs and SSIs based on the Stokes' theorem. The derived formulas are much simpler and more friendly in implementation since no polar coordinates or extra coordinate transformation are involved. Numerical experiments are presented to demonstrate the effectiveness of the approach.
Marek Bleszynski - One of the best experts on this subject based on the ideXlab platform.
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Reduction of Singular Surface integrals to non-Singular line integrals in integral equations involving non-parallel Surface elements
2017 11th European Conference on Antennas and Propagation (EUCAP), 2017Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of integrals involving Singular Green function and Rao-Wilton-Glisson basis functions with arbitrary mutual non-planar geometrical configuration which appear in Surface integral equations representation of Maxwell equations. The proposed procedure constitutes a generalization of our previously reported result valid for planar geometries. The method employs a suitably constructed representation of the Helmholtz equation Green function in terms of an differential operator acting on an auxiliary function which allows one to reduce four-dimensional Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. Advantages of our approach include simplicity and high accuracy at a computational cost considerably lower than for previously considered methods, such as the Singularity subtraction technique.
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reduction of Singular Surface integrals to nonSingular line integrals in integral equations for planar geometries
IEEE Transactions on Antennas and Propagation, 2016Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao–Wilton–Glisson basis functions appearing in Surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, or geometries composed of parallel planar sheets, reduces 4-D Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy achieved at a computational cost significantly lower than for previously considered techniques, in particular the conventional Singularity subtraction method.
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Reduction of Singular Surface integrals of tensor Green function to non-Singular line integrals in integral equations for planar geometries
2016 10th European Conference on Antennas and Propagation (EuCAP), 2016Co-Authors: Elizabeth Bleszynski, Marek Bleszynski, Thomas JaroszewiczAbstract:A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao-Wilton-Glisson basis functions appearing in Surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, reduces four-dimensional Surface integrals with Singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy without the need of using numerical Singularity extraction methods.