Solution of three-dimensional multiple scattering problems by the method of difference potentials

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

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Fast Solution of Multiple Scattering Problems

Fast Multipole Methods for the Helmholtz Equation in Three Dimensions ◽

10.1016/b978-008044371-3/50014-4 ◽

2004 ◽

pp. 465-498

Author(s):

NAIL A. GUMEROV ◽

RAMANI DURAISWAMI

Keyword(s):

Multiple Scattering ◽

Scattering Problems ◽

Fast Solution

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Distributed equivalent dipole solutions of three-dimensional scattering problems

10.1109/aps.1988.94368 ◽

2003 ◽

Author(s):

H. Shigesawa ◽

M. Tsuji ◽

M. Mishimura

Keyword(s):

Three Dimensional ◽

Scattering Problems ◽

Equivalent Dipole

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Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2021064 ◽

2021 ◽

Author(s):

Changkun Wei ◽

Jiaqing Yang ◽

Bo Zhang

Keyword(s):

Time Domain ◽

Electromagnetic Scattering ◽

Scattering Problem ◽

Three Dimensional ◽

Scattering Problems ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Time Domain Electromagnetic ◽

Numer Anal ◽

The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

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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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