A New Efie Method Based on Coulomb Gauge for the Low-Frequency Electromagnetic Analysis

Xiong, Xiang; Jiang, Li Jun; Sha, Wei E. I.; Lo, Yat Hei

doi:10.2528/pier13040303

Cited by 5 publications

(4 citation statements)

References 33 publications

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“…However, a salient feature of the IGA-basis is that constructing a well behaved system is tantamount to using a diagonal preconditioning sans constructing the complementary system that is required for a loop-tree/star (Hodge) decomposition. It should be noted that Helmholtz decomposition is not the only way to solve low frequency breakdown, and other techniques [30,38,39,40,41] exist. The isogeometric basis functions presented herein could help construct those methods.…”

Section: Low-frequency Stable Efiementioning

confidence: 99%

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Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures

Dault

Liu

et al. 2016

Journal of Computational Physics

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The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but not differentiable. The need to define physical quantities on this geometric representation has led to development of sets of basis functions that need to satisfy constraints at the boundaries of the elements/tesselations (viz., continuity of normal or tangential components across element boundaries). For electromagnetics, these result in either curl/div-conforming basis sets. The geometric representation used for analysis is in stark contrast with that used for design, wherein the surface representation is higher order differentiable. Using this representation for both geometry and physics on geometry has several advantages, and is eludicated in Hughes et al., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering 194 (39-41) (2005). Until now, a bulk of the literature on isogeometric methods have been limited to solid mechanics, with some effort to create NURBS based basis functions for electromagnetic analysis. In this paper, we present the first complete isogeometry solution methodology for the electric field integral equation as applied to simply connected structures. This paper systematically proceeds through surface representation using subdivision, definition of vector basis functions on this surface, to fidelity in the solution of integral equations. We also present techniques to stabilize the solution at low frequencies, and impose a Calderón preconditioner. Several results presented serve to validate the proposed approach as well as demonstrate some of its capabilities.

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Section: Low-frequency Stable Efiementioning

confidence: 99%

“…It should be noted that Helmholtz decomposition is not the only way to solve low frequency breakdown, and other techniques [30,38,39,40,41] exist. The isogeometric basis functions presented herein could help construct those methods.…”

Section: Low-frequency Stable Efiementioning

confidence: 99%

Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures

Dault

Liu

et al. 2016

Journal of Computational Physics

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show abstract

“…However, by and large, the problem has remained the same: how does one develop integral formulations that are well behaved across frequencies of interest especially when high discretization density is required to capture geometric features. To this end, several new SIE formulations and numerical techniques have been proposed; a partial listing of these includes the current and charge integral equation (CCIE) [9], augmented EFIE (A-EFIE) [13], Calderón preconditioner [14], multi-resolution analysis [15] and introducing loop-tree/star basis functions [7], [8], [16]- [18], and Debye sources [19]- [21]. Recently, a decoupled potential integral equation (DPIE) based on Lorentz gauge has been proposed in [22] that leads to a second-kind and stable formulation over a wide frequency band.…”

Section: Introductionmentioning

confidence: 99%

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

Jiang

et al. 2017

IEEE Trans. Antennas Propagat.

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Abstract-The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while. Two recent papers motivate the effort presented in this paper. Unlike traditional work that uses equivalent currents defined on surfaces, recent research proposes a technique that results in well conditioned systems by employing generalized Debye sources (GDS) as unknowns. In a complementary effort, some of us developed a method that exploits the same representation for both the geometry (subdivision surface representations) and functions defined on the geometry, also known as isogeometric analysis (IGA). The challenge in generalizing GDS method to a discretized geometry is the complexity of the intermediate operators. However, thanks to our earlier work on subdivision surfaces, the additional smoothness of geometric representation permits discretizing these intermediate operations. In this paper, we employ both ideas to present a well conditioned GDS-EFIE. Here, the intermediate surface Laplacian is well discretized by using subdivision basis. Likewise, using subdivision basis to represent the sources, results in an efficient and accurate IGA framework. Numerous results are presented to demonstrate the efficacy of the approach.

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Section: Introductionmentioning

confidence: 99%

Generalized Debye Sources Based EFIE Solver on Subdivision Surfaces

Fu,

Li,

Jiang

et al. 2017

Preprint

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The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while. Two recent papers motivate the effort presented in this paper. Unlike traditional work that uses equivalent currents defined on surfaces, recent research proposes a technique that results in well conditioned systems by employing generalized Debye sources (GDS) as unknowns. In a complementary effort, some of us developed a method that exploits the same representation for both the geometry (subdivision surface representations) and functions defined on the geometry, also known as isogeometric analysis (IGA). The challenge in generalizing GDS method to a discretized geometry is the complexity of the intermediate operators. However, thanks to our earlier work on subdivision surfaces, the additional smoothness of geometric representation permits discretizing these intermediate operations. In this paper, we employ both ideas to present a well conditioned GDS-EFIE. Here, the intermediate surface Laplacian is well discretized by using subdivision basis. Likewise, using subdivision basis to represent the sources, results in an efficient and accurate IGA framework. Numerous results are presented to demonstrate the efficacy of the approach.

show abstract

A New Efie Method Based on Coulomb Gauge for the Low-Frequency Electromagnetic Analysis

Cited by 5 publications

References 33 publications

Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures

Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

Generalized Debye Sources Based EFIE Solver on Subdivision Surfaces

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