Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media

AbstractThis work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

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STRONG AND WEAK FORMS OF THE METHOD OF MOMENTS AND THE COUPLED DIPOLE METHOD FOR SCATTERING OF TIME-HARMONIC ELECTROMAGNETIC FIELDS

International Journal of Modern Physics C ◽

10.1142/s0129183192000385 ◽

1992 ◽

Vol 03 (03) ◽

pp. 583-603 ◽

Cited By ~ 93

Author(s):

AKHLESH LAKHTAKIA

Keyword(s):

Electromagnetic Fields ◽

Method Of Moments ◽

Electromagnetic Scattering ◽

Final Section ◽

The Other ◽

Numerical Techniques ◽

Scattering Problems ◽

Time Harmonic

Algorithms based on the method of moments (MOM) and the coupled dipole method (CDM) are commonly used to solve electromagnetic scattering problems. In this paper, the strong and the weak forms of both numerical techniques are derived for bianisotropic scatterers. The two techniques are shown to be fully equivalent to each other, thereby defusing claims of superiority often made for the charms of one technique over the other. In the final section, reductions of the algorithms for isotropic dielectric scatterers are explicitly given.

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On the edge element boundary element method/finite element method coupling for time harmonic electromagnetic scattering problems

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6675 ◽

2021 ◽

Author(s):

Hrvoje Dodig ◽

Dragan Poljak ◽

Mario Cvetković

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Boundary Element Method ◽

Boundary Element ◽

Electromagnetic Scattering ◽

Scattering Problems ◽

Edge Element ◽

Time Harmonic ◽

Element Boundary ◽

Element Method

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Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part I: the free space case

Engineering Computations ◽

10.1108/ec-06-2021-0327 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Frédérique Le Louër ◽

María-Luisa Rapún

Keyword(s):

Free Space ◽

Order Term ◽

Harmonic Wave ◽

Dirichlet Condition ◽

Point Sources ◽

Neumann Condition ◽

Scattering Problems ◽

Content Type ◽

Time Harmonic ◽

Topological Gradient

PurposeIn this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.Design/methodology/approachFrom the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.FindingsAs the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

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Scattering of a Plane Elastic Wave From Objects Near an Interface

Journal of Applied Mechanics ◽

10.1115/1.3422822 ◽

1972 ◽

Vol 39 (4) ◽

pp. 1019-1026 ◽

Cited By ~ 2

Author(s):

Stephen B. Bennett

Keyword(s):

Elastic Wave ◽

Electromagnetic Waves ◽

Three Dimensions ◽

Circular Cylinders ◽

Scattering Problems ◽

Reflection And Refraction ◽

Time Harmonic ◽

Incident Plane ◽

Boundary Curves ◽

Consistent Formulation

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.

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