The on-surface radiation condition applied to three-dimensional convex objects

Murch, R.D.

doi:10.1109/8.222284

Cited by 16 publications

(10 citation statements)

References 13 publications

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“…Section 5 provides various numerical simulations of these new MtE surface operators when they are used in the extreme context of On-Surface Radiation Condition (OSRCs) methods [40,6,47,17,55,5,14]. Let us mention that only a few results are available in the literature [28,50,3,56] when the OSRC technique is used in the framework of the full set of Maxwell's equations. Indeed, these papers only derive special canonical solutions but not a general and flexible approach as the one presented here for a general surface Γ .…”

Section: Introductionmentioning

confidence: 98%

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

Bouajaji¹,

Antoine²,

Geuzaine³

2014

Journal of Computational Physics

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The aim of this paper is to propose new local and accurate approximate magnetic-toelectric surface boundary operators for the three-dimensional time-harmonic Maxwell's equations. After their construction where their accuracy is improved through a regularization process, a localization of these operators and a full finite element approximation is introduced. Next, their numerical efficiency and accuracy is investigated in detail for different scatterers when these operators are used in the extreme situation of On-Surface Radiation Conditions methods.

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Section: Introductionmentioning

confidence: 98%

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

Bouajaji¹,

Antoine²,

Geuzaine³

2014

Journal of Computational Physics

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“…The resulting T-matrix has elements. Each element is derived from an inner product of modes which must be computed over a domain with points, where stands for points per wavelength (typically [10][11][12][13][14][15][16][17][18][19][20]. The computation of the (full) matrix elements is the most costly step.…”

Section: Discussionmentioning

confidence: 99%

A higher-order on-surface radiation condition derived from an analytic representation of a dirichlet-to-neumann map

Calvo¹,

Collins²,

Dacol³

2003

IEEE Trans. Antennas Propagat.

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On-surface radiation conditions are useful for obtaining approximate solutions to scattering problems involving compact obstacles. An analytic representation of the Dirichletto-Neumann map for a circle is derived and used to construct a higher-order on-surface radiation condition for a generally convex perfectly conducting body in two dimensions. This approach is based on a Hankel function in which a tangential operator appears in the index. In the high-frequency limit, this analytic representation approaches the square root of a differential operator which commonly arises in the application of parabolic equation techniques to propagation problems. Treating the scattered field propagation angle relative to the surface normal and the surface curvature as independent parameters, the representation is fit to a rational function to provide an accurate and efficient on-surface radiation condition that is tested for various examples.

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“…Recently, in [11], the authors proved that the convergence rates and the optimization processes for the first-and second-order formulations are the same. When developing optimized DDMs in [20], the authors used highly accurate square-root/Padé-type On-Surface Radiation Conditions (OSRCs) [21], [22], [23], [24], [12] as transmission boundary conditions, which are also GIBCs. While being easyto-use and direct to implement in a finite element environment, these GIBCs lead to the construction of fast converging nonoverlapping DDMs, most particularly when computing the solution to high-frequency three-dimensional acoustics scattering problems.…”

Section: Transmission Boundary Conditionsmentioning

confidence: 99%

An open source domain decomposition solver for time-harmonic electromagnetic wave problems

Geuzaine¹,

Thierry²,

Marsic³

et al. 2014

2014 IEEE Conference on Antenna Measurements &Amp; Applications (CAMA)

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International audienceWe present a flexible finite element solver for testing optimized Schwarz domain decomposition techniques for the time-harmonic Maxwell equations. After a review of non-overlapping Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples, is available online for further testing

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The on-surface radiation condition applied to three-dimensional convex objects

Cited by 16 publications

References 13 publications

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

A higher-order on-surface radiation condition derived from an analytic representation of a dirichlet-to-neumann map

An open source domain decomposition solver for time-harmonic electromagnetic wave problems

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