Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains

Wilton, Donald R.; Rao, Sadasiva M.; Glisson, A.W.; Schaubert, D.H.; Al-Bundak, O.; Butler, C.M.

doi:10.1109/tap.1984.1143304

Cited by 599 publications

(327 citation statements)

References 8 publications

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“…In general, weakly singular integrals are treated by using mainly the singularity subtraction method [4][5][6][7][8][9][10][11][12][13][14] or the singularity cancellation method [15][16][17][18][19][20][21][22][23][24][25]. Despite their widespread usage, both singularity subtraction and singularity cancellation methods fail to meet the requirements for an accurate and efficient numerical integration of weakly singular integrals, as it will be demonstrated by the numerical examples in next sections.…”

Section: Introductionmentioning

confidence: 99%

Complete semi‐analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method

Polimeridis

Mosig

2010

Numerical Meth Engineering

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SUMMARYA complete semi-analytical treatment of the four-dimensional (4-D) weakly singular integrals over coincident, edge adjacent and vertex adjacent triangles, arising in the Galerkin discretization of mixed potential integral equation formulations, is presented. The overall analysis is based on the direct evaluation method, utilizing a series of coordinate transformations, together with a re-ordering of the integrations, in order to reduce the dimensionality of the original 4-D weakly singular integrals into, respectively, 1-D, 2-D and 3-D numerical integrations of smooth functions. The analytically obtained final formulas can be computed by using typical library routines for Gauss quadrature readily available in the literature. A comparison of the proposed method with singularity subtraction, singularity cancellation and fully numerical methods, often used to tackle the multi-dimensional singular integrals evaluation problem, is provided through several numerical examples, which clearly highlights the superior accuracy and efficiency of the direct evaluation scheme.

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Section: Introductionmentioning

confidence: 99%

Complete semi‐analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method

Polimeridis

Mosig

2010

Numerical Meth Engineering

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“…In our case we use the well-known Rao-Wilton-Glisson (RWG) vector basis/testing functions [43], together with the analytical extraction procedures of [44][45][46][47] for the accurate evaluation of singular and hypersingular integrals that appear in Equations (24) and (25). This results in a linear system of N equations and N unknowns, N being the number of surface RWG basis functions used to expand the electric and magnetic currents, that can be written as follows:…”

Section: Methods Of Moments For Surface Integral Equationsmentioning

confidence: 99%

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Solís¹,

Taboada²,

Landesa³

et al. 2015

PIER

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Abstract-The plasmonic behavior of nanostructured materials has ignited intense research for the fundamental physics of plasmonic structures and their cutting-edge applications concerning the fields of nanoscience and biosensing. The optical response of plasmonic metals is generally well-described by classical Maxwell's Equations (ME). Thus, the understanding of plasmons and the design of plasmonic nanostructures can therefore directly benefit from lastest advances achieved in classic research areas such as computational electromagnetics. In this context, this paper is devoted to review the most recent advances in nanoplasmonic modeling, related with the latest breakthroughs in surface integral equation (SIE) formulations derived from ME. These works have extended the scope of application of Maxwell's Equations, from microwave/milimeter waves to infrared and optical frequency bands, in the emerging fields of nanoscience and medical biosensing.

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“…In virtue of the results obtained in Wilton et al [1984], the integral (A4) can be expressed in terms of three line integrals. Let us consider the geometrical variables depicted in Figure A1, where we have represented a triangular cell employed when a surface is meshed using classical RWG basis functions.…”

Section: A1 Calculation Of I (Sing)mentioning

confidence: 99%

Highly efficient full‐wave electromagnetic analysis of 3‐D arbitrarily shaped waveguide microwave devices using an integral equation technique

et al. 2015

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A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented.This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RME technique. The developed tool also provides an accurate computation of the electromagnetic fields at an arbitrary observation point of the considered device, so it can be used for predicting high-power breakdown phenomena. In order to validate the accuracy and efficiency of this novel approach, several new designs of band-pass waveguides filters are presented. The obtained results (S-parameters and electromagnetic fields) are successfully compared both to experimental data and to numerical simulations provided by a commercial software based on the finite element technique. The results obtained show that the new technique is specially suitable for the efficient full-wave analysis of complex waveguide devices considering an integrated coaxial excitation, where the coaxial probes may be in contact with the metallic insets of the component.

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Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains

Cited by 599 publications

References 8 publications

Complete semi‐analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method

Complete semi‐analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Highly efficient full‐wave electromagnetic analysis of 3‐D arbitrarily shaped waveguide microwave devices using an integral equation technique

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