Evaluation of Static Potential Integrals on Triangular Domains

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

doi:10.1109/access.2020.2997287

Cited by 13 publications

(3 citation statements)

References 21 publications

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“…After the fast decay of the exponential has been handled, the near-singularity of the right hand side and matrix self-or near-elements require special treatment as they cannot be obtained accurately using standard Gaussian quadrature. In this work, we have opted for singularity extraction approaches [40], [41] but other schemes such as singularity cancellation [42] can be employed.…”

Section: S S B Q -H Pmentioning

confidence: 99%

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Chhim

Merlini

Rahmouni

et al. 2020

IEEE Open J. Antennas Propag.

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Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell's equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full-wave solvers such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation become highly ill-conditioned and inaccurate in eddy current settings. This work presents a new well-conditioned and stable full-wave formulation which encompasses the simulation of eddy currents. Our method is built upon the PMCHWT equation and thus remains valid over the entire frequency range. Moreover, our scheme is also compatible with structures containing holes and handles (multiply connected geometries). The effectiveness of quasi-Helmholtz projectors is leveraged to obtain a versatile solver, which is computationally efficient and allows for a seamless transition between low and high frequencies. The stability and accuracy of the new method are demonstrated both theoretically and through numerical experiments on canonical and realistic structures.

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Section: S S B Q -H Pmentioning

confidence: 99%

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Chhim

Merlini

Rahmouni

et al. 2020

IEEE Open J. Antennas Propag.

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“…3 suggest. The techniques shown in [2] and [28] may allow one to derive the singularities for completely general source and test triangle configurations.…”

Section: Numerical Experiments For Singular Near-singular and Far Int...mentioning

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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“…If the surface-equivalence principle is adopted, the full-wave Green's function within homogeneous lossy dielectric/magnetic materials is to be used along with its curl [11] in the computation of interaction integrals describing the electric and magnetic field coupling. Potential integrals over triangular domains in the static limit (k → 0) have recently been analyzed in [12].…”

Section: Introductionmentioning

confidence: 99%

Cagniard-DeHoop Technique-Based Computation of Retarded Partial Coefficients: The Coplanar Case

2020

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Efficient computation of partial elements plays a key role in the Partial Element Equivalent Circuit (PEEC) Method. A novel analytical method for computing retarded partial coefficients based on the Cagniard-DeHoop (CdH) technique is proposed. The methodology is first theoretically developed and then illustrated on the computation of a surface retarded partial coefficient pertaining to two coplanar rectangular surface elements. An efficient way for incorporating loss mechanisms in the time domain (TD) via the Schouten-Van der Pol theorem is proposed. Illustrative numerical examples demonstrating the validity of the introduced solution are given.

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Evaluation of Static Potential Integrals on Triangular Domains

Cited by 13 publications

References 21 publications

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

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

Cagniard-DeHoop Technique-Based Computation of Retarded Partial Coefficients: The Coplanar Case

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