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

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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Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part II: recursive computations by the boundary integral equation method

Engineering Computations ◽

10.1108/ec-06-2021-0341 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Frédérique Le Louër ◽

María-Luisa Rapún

Keyword(s):

Acoustic Waves ◽

Boundary Integral Equations ◽

Order Term ◽

Elliptic Boundary ◽

Harmonic Wave ◽

Boundary Integral ◽

Neumann Condition ◽

Content Type ◽

Time Harmonic ◽

Topological Gradient

PurposeThe purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).Design/methodology/approachThe elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.FindingsAs the shape gradients 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 in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.

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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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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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Solutions of the Time-Harmonic Wave Equation in Periodic Waveguides: Asymptotic Behaviour and Radiation Condition

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-015-0897-3 ◽

2015 ◽

Vol 219 (1) ◽

pp. 349-386 ◽

Cited By ~ 18

Author(s):

Sonia Fliss ◽

Patrick Joly

Keyword(s):

Wave Equation ◽

Asymptotic Behaviour ◽

Harmonic Wave ◽

Radiation Condition ◽

Time Harmonic

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Phylogenetic structure of Shiga toxin-producing Escherichia coli O157:H7 from sub-lineage to SNPs

Microbial Genomics ◽

10.1099/mgen.0.000544 ◽

2021 ◽

Author(s):

Timothy J. Dallman ◽

David R. Greig ◽

Saheer E. Gharbia ◽

Claire Jenkins

Keyword(s):

Escherichia Coli ◽

Shiga Toxin ◽

Sequence Similarity ◽

Evidence Base ◽

Point Sources ◽

Single Linkage ◽

Phylogenetic Structure ◽

Content Type ◽

Geographically Dispersed ◽

Cluster Threshold

Sequence similarity of pathogen genomes can infer the relatedness between isolates as the fewer genetic differences identified between pairs of isolates, the less time since divergence from a common ancestor. Clustering based on hierarchical single linkage clustering of pairwise SNP distances has been employed to detect and investigate outbreaks. Here, we evaluated the evidence-base for the interpretation of phylogenetic clusters of Shiga toxin-producing Escherichia coli (STEC) O157:H7. Whole genome sequences of 1193 isolates of STEC O157:H7 submitted to Public Health England between July 2015 and December 2016 were mapped to the Sakai reference strain. Hierarchical single linkage clustering was performed on the pairwise SNP difference between all isolates at descending distance thresholds. Cases with known epidemiological links fell within 5-SNP single linkage clusters. Five-SNP single linkage community clusters where an epidemiological link was not identified were more likely to be temporally and/or geographically related than sporadic cases. Ten-SNP single linkage clusters occurred infrequently and were challenging to investigate as cases were few, and temporally and/or geographically dispersed. A single linkage cluster threshold of 5-SNPs has utility for the detection of outbreaks linked to both persistent and point sources. Deeper phylogenetic analysis revealed that the distinction between domestic UK and imported isolates could be inferred at the sub-lineage level. Cases associated with domestically acquired infection that fall within clusters that are predominantly travel associated are likely to be caused by contaminated imported food.

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

Communications in Computational Physics ◽

10.4208/cicp.231109.090710s ◽

2012 ◽

Vol 11 (2) ◽

pp. 303-318 ◽

Cited By ~ 2

Author(s):

J. Coatléven ◽

P. Joly

Keyword(s):

Multiple Scattering ◽

Random Number ◽

Good Method ◽

Computational Domain ◽

Periodic Media ◽

Scattering Problems ◽

Compact Perturbations ◽

Time Harmonic ◽

Operator Factorization ◽

Interior Problem

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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