Numerical study of surface integral formulations for homogeneous bodies

Lloyd, T.W.; Song, Jiming; Kang, G.; Lu, Cai‐Cheng

doi:10.1109/aps.2004.1330200

Cited by 7 publications

(8 citation statements)

References 9 publications

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“…where the choices (10) and (11) lead to NMF [13] and CNF [14], respectively. Using a Galerkin scheme, matrix equations obtained by using the N formulations are usually better conditioned than those obtained with the T formulations.…”

Section: Surface Formulations Of Dielectric Problemsmentioning

confidence: 99%

“…In this class of formulations, Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) [1], [4], [5] and Müller [3] formulations are well known and commonly used in the literature. Both T and N versions of these formulations are possible, but only the tangential PMCHWT (T-PMCHWT) formulation and the normal Müller formulation (NMF) are stable, whereas the normal PMCHWT and the tangential Müller formulations are usually unstable [11], [13]. Recently, remarkable efforts have been made to further improve the dielectric formulations by devising novel combinations of the integral equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

Ergül

Gürel

2009

IEEE Trans. Antennas Propagat.

124

103

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We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations.Index Terms-Dielectrics, iterative solutions, multilevel fast multipole algorithm (MLFMA), surface integral equations.

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Section: Surface Formulations Of Dielectric Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

Ergül

Gürel

2009

IEEE Trans. Antennas Propagat.

124

103

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“…The classical PMCHWT technique [4], [6] is defined by choosing (14) This is equivalent to adding (8) with (9) and (10) with (11). This leads to (15) (16) It is observed that the diagonal terms cancel.…”

Section: A the Pmchwt Formulationmentioning

confidence: 97%

“…This is motivated in part by the advancement of fast iterative solution methods, which can be accelerated with the use of well-conditioned operators. Inverse scattering problems are also benefited by well-conditioned operators [9]. Furthermore, it has been found that the rate of error convergence of high-order methods can be affected, by the properties of the integral operator.…”

Section: Introductionmentioning

confidence: 99%

A study of combined field formulations for material scattering for a locally corrected Nystro/spl uml/m discretization

Zhu

Gedney

Visher³

2005

IEEE Trans. Antennas Propagat.

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A study of the error convergence and condition number of three integral-equation formulations derived for penetrable material scattering objects-the Poggio, Miller, Chang, Harrington, Wu and Tsai (PMCHWT), the Müller, and the PM-CHWT(-) formulations-is presented for a variety of problems when discretized via a locally corrected Nyström method. The PMCHWT formulation is a first-kind integral equation with a hypersingular operator. The Müller formulation leads to a second-kind equation consisting of a diagonal term plus a compact operator. This form is both frequency and mesh stable. However, unlike the PMCHWT formulation, the error grows with the refractive index. The PMCHWT(-) formulation is in the form of a second-kind equation, but has a hypersingular term.Index Terms-Boundary integral equations, convergence of numerical methods, electromagnetic scattering, locally corrected Nystrom method, radar cross section.

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“…The integral equation formulation continues with the imposition of the boundary conditions for the fields inside the structure. First, the tangential electric field on conducting surfaces is null (EFIE), and second, the total tangential electric and magnetic fields must be continuous across the dielectric post surfaces (PMCHWT formulation [Lloyd et al, 2004]). In that reference, it was shown that the PMCHWT formulation is one of the most robust from the numerical point of view, since it is free from internal resonances.…”

Section: Theoretical Outlinementioning

confidence: 99%

Efficient integral equation formulation for inductive waveguide components with posts touching the waveguide walls

et al. 2007

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[1] In this paper a surface integral equation technique is employed for the analysis of inductive waveguide problems containing metallic or dielectric objects of arbitrary shape, focusing on the case where these objects are connected to the waveguide walls. Using the extinction theorem, the main problem is split into two problems. In the first one the parallel plate waveguide Green's functions are used. Because of the choice of these functions, the side of the object touching the waveguide wall is not considered for discretization in a method of moments analysis. The second problem is applied inside the dielectric object, and uses the free space Green's functions. It is shown that an additional spatial image is needed to impose the proper boundary conditions for the fields on the side touching the waveguide wall in the original problem. Results show the importance of including this additional image in the formulation for the correct behavior of the fields. With the proposed technique, the paper explores some alternatives for designing specific filter responses using dielectric posts inside cavity filters. Comparisons with a commercial finite elements tool demonstrate the accuracy of the proposed integral equation formulation.

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Numerical study of surface integral formulations for homogeneous bodies

Cited by 7 publications

References 9 publications

Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

A study of combined field formulations for material scattering for a locally corrected Nystro/spl uml/m discretization

Efficient integral equation formulation for inductive waveguide components with posts touching the waveguide walls

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