High-order integral equation methods for problems of scattering by bumps and cavities on half-planes

Pérez‐Arancibia, Carlos; Bruno, Oscar P.

doi:10.1364/josaa.31.001738

Cited by 28 publications

(71 citation statements)

References 37 publications

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“…The ohmic absorption by the bump and trench is calculated, and compared with the intrinsic ohmic absorption of an otherwise flat surface. The HIEM code 32 was validated against analytic theory, and it was then applied to cases which defy analytic treatment. The complicated field patterns displayed in Figs.…”

Section: Discussionmentioning

confidence: 99%

“…The problems of scattering thereby formulated can be solved numerically by utilizing the HIEM introduced in Ref. 32. The HIEM is based on single-layer-potential field representations, efficient evaluation of Sommerfeld integrals, and quadrature rules which produce the single-layer potential with high-order accuracy in spite of Green-function and geometric singularities.…”

Section: A Electromagnetic Theory and High-order Integral Solvermentioning

confidence: 99%

“…In detail, according to the nomenclature established in Ref. 32, the conducting bump on the PEC plane ( Fig. 1) on one hand, and both the bump and the trench on the finitely conducing plane (Fig.…”

Section: A Electromagnetic Theory and High-order Integral Solvermentioning

confidence: 99%

“…(A9)), in terms (k/a) 2 , as a function of d/a for a number of values of k/a, for the special case l 1 ¼ l 2 ¼ l 0 and e 1r ¼ e 2 ¼ e 0 . Red dots represent the exact value computed using the Fourier-Bessel expansion 32 of the exact solution of the problem of scattering, and the black squares represent the values obtained using HIEM. maximum value of ðc E 0 =xÞðk=aÞ 2 is about 30, occurring at a value of d/a ¼ (1/2p)(k/a), as shown in Fig.…”

Section: B Analytical Model For Code Validationmentioning

confidence: 99%

“…The calculation is two-dimensional, using a high-order integral equation method (HIEM). 32 Here, we focus on the long wavelength case, where the radius of the bump (or trench), denoted by a > 0, is assumed to be smaller than the electromagnetic wavelength k > 0 exterior to the bump (or trench): a/k ( 1. The short wavelength limit, a/k > 1, together with some new features such as "pseudo resonances," will be addressed in a separate publication.…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic power absorption due to bumps and trenches on flat surfaces

Pérez‐Arancibia

Zhang

Bruno

et al. 2014

Journal of Applied Physics

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This paper presents a study of the absorption of electromagnetic power that results from the interaction of electromagnetic waves and cylindrical bumps or trenches on flat conducting surfaces. Configurations are characterized by means of adequately selected dimensionless variables and parameters so that applicability to mathematically equivalent (but physically diverse) systems can be achieved easily. Electromagnetic fields and absorption increments caused by such surface defects are evaluated by means of a high-order integral equation method which resolves fine details of the field near the surface, and which was validated by fully analytical approaches in a range of computationally challenging cases. The computational method is also applied to problems concerning bumps and trenches on imperfect conducting planes for which analytical solutions are not available. Typically, we find that absorption is enhanced by the presence of the defects considered, although, interestingly, absorption can also be significantly reduced in some cases-such as, e.g., in the case of a trench on a conducting plane where the incident electric field is perpendicular to the plane. Additionally, it is observed that, for some small-skin-depths large-wavelengths, the absorption increment is proportional to the increase in surface area. Significant physical insight is obtained on the heating that results from various types of electromagnetic incident fields. V C 2014 AIP Publishing LLC. [http://dx

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Section: Discussionmentioning

confidence: 99%

Section: A Electromagnetic Theory and High-order Integral Solvermentioning

confidence: 99%

Section: A Electromagnetic Theory and High-order Integral Solvermentioning

confidence: 99%

Section: B Analytical Model For Code Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electromagnetic power absorption due to bumps and trenches on flat surfaces

Pérez‐Arancibia

Zhang

Bruno

et al. 2014

Journal of Applied Physics

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A new hybrid integral representation for frequency domain scattering in layered media

Lai

Greengard

O’Neil

2018

Applied and Computational Harmonic Analysis

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A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and others showed that Fourier analysis combined with contour integration provides a systematic and broadly effective approach, leading to what is generally referred to as the Sommerfeld integral representation. When either the source or target is at some distance from an infinite boundary, the number of degrees of freedom needed to resolve the scattering response is very modest. When both are near an interface, however, the Sommerfeld integral involves a very large range of integration and its direct application becomes unwieldy. Historically, three schemes have been employed to overcome this difficulty: the method of images, contour deformation, and asymptotic methods of various kinds. None of these methods make use of classical layer potentials in physical space, despite their advantages in terms of adaptive resolution and high-order accuracy. The reason for this is simple: layer potentials are impractical in layered media or half-space geometries since they require the discretization of an infinite boundary. In this paper, we propose a hybrid method which combines layer potentials (physical-space) on a finite portion of the interface together with a Sommerfeldtype (Fourier) correction. We prove that our method is efficient and rapidly convergent for arbitrarily located sources and targets, and show that the scheme is particularly effective when solving scattering problems for objects which are close to the half-space boundary or even embedded across a layered media interface.

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An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation

Amlani

Chaillat

Loseille

2019

Computer Methods in Applied Mechanics and Engineering

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This paper presents an efficient algebraic preconditioner to speed up the convergence of Fast Multipole accelerated Boundary Element Methods (FM-BEMs) in the context of time-harmonic 3D wave propagation problems and in particular the case of highly non-uniform discretizations. Such configurations are produced by a recently-developed anisotropic mesh adaptation procedure that is independent of partial differential equation and integral equation. The new preconditioning methodology exploits a complement between fast BEMs by using two nested GMRES algorithms and rapid matrix-vector calculations. The fast inner iterations are evaluated by a coarse hierarchical matrix (H-matrix) representation of the BEM system. These inner iterations produce a preconditioner for FM-BEM solvers. It drastically reduces the number of outer GMRES iterations. Numerical experiments demonstrate significant speedups over non-preconditioned solvers for complex geometries and meshes specifically adapted to capture anisotropic features of a solution, including discontinuities arising from corners and edges.

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High-order integral equation methods for problems of scattering by bumps and cavities on half-planes

Cited by 28 publications

References 37 publications

Electromagnetic power absorption due to bumps and trenches on flat surfaces

Electromagnetic power absorption due to bumps and trenches on flat surfaces

A new hybrid integral representation for frequency domain scattering in layered media

An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation

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