Evaluation of 4-D Reaction Integrals Via Double Application of the Divergence Theorem

Rivero, J.; Vipiana, F.; Wilton, Donald R.; Johnson, William A.

doi:10.1109/tap.2018.2882589

Cited by 22 publications

(6 citation statements)

References 16 publications

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“…In [14], the authors use a series of variable transformations and integration reordering to integrate the four-dimensional integrals. In [15], the authors present an approach for coplanar source and test elements, extended in [16] to general element orientations. In [17], for the CFIE, the authors avoid the singularity in the test-element integral by modifying the integrand.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Characterization and Integration of the Singular Test Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation

Freno,

Johnson,

Zinser

et al. 2019

Preprint

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In this paper, we present two approaches for designing geometrically symmetric quadrature rules to address the logarithmic singularities arising in the method of moments from the Green's function in integrals over the test domain. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma-Rokhlin-Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

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Section: Acknowledgmentsmentioning

confidence: 99%

Characterization and Integration of the Singular Test Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation

Freno,

Johnson,

Zinser

et al. 2019

Preprint

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“…Several approaches in literature aim to manipulate the integrals so that their computation is faster and their solution is still accurate. In [25], the authors solve the surface integrals by resorting to the surface divergence theorem, together with a reordering of the integration order. However, the results are tailored for triangular surfaces, as further investigated in [18], where the authors propose a similar approach for general-case surfaces but limiting the analysis to the electrostatic case.…”

Section: Introductionmentioning

confidence: 99%

On the rectangular mesh and the decomposition of a Green’s-function-based quadruple integral into elementary integrals

Lauretis¹,

Haller

Murro

et al. 2022

Engineering Analysis with Boundary Elements

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Computational electromagnetic problems require evaluating the electric and magnetic fields of the physical object under investigation, divided into elementary cells with a mesh. The partial element equivalent circuit (PEEC) method has recently received attention from academic and industry communities because it provides a circuit representation of the electromagnetic problem. The surface formulation, known as S-PEEC, requires computing quadruple integrals for each mesh patch. Several techniques have been developed to simplify the computational complexity of quadruple integrals but limited to triangular meshes as used in well-known methods such as the Method of Moments (MoM). However, in the S-PEEC method, the mesh can be rectangular and orthogonal, and new approaches must be investigated to simplify the quadruple integrals. This work proposes a numerical approach that treats the singularity and reduces the computational complexity of one of the two quadruple integrals used in the S-PEEC method. The accuracy and computational time are tested for representative parallel and orthogonal meshes.✩ This document is the results of the research project funded by the Swedish Research Council, grant no. 2018-05252.

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“…However, the presence of a Green's function in these equations yields singularities when the test and source elements share one or more edges or vertices and near-singularities when they are otherwise close. Many approaches have been developed to address the singularity and near-singularity for the inner, source-element integral [1][2][3][4][5][6][7][8][9][10], as well as for the outer, test-element integral [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Characterization and integration of the singular test integrals in the method‐of‐moments implementation of the electric‐field integral equation

Freno

Johnson

Zinser

et al. 2021

Engineering Analysis with Boundary Elements

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The method-of-moments implementation of the electric-field integral equation yields many code-verification challenges due to the different sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. In this paper, we provide approaches to separately assess the numerical errors arising from the use of basis functions to approximate the solution and the use of quadrature to approximate the integration. Through these approaches, we are able to verify the code and compare the error from different quadrature options.

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Evaluation of 4-D Reaction Integrals Via Double Application of the Divergence Theorem

Cited by 22 publications

References 16 publications

Characterization and Integration of the Singular Test Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation

Characterization and Integration of the Singular Test Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation

On the rectangular mesh and the decomposition of a Green’s-function-based quadruple integral into elementary integrals

Characterization and integration of the singular test integrals in the method‐of‐moments implementation of the electric‐field integral equation

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