Fast Solution of Multiple Scattering Problems

Newton-Like Method for Solving Inverse Obstacle Acoustic Scattering Problems

10.1115/imece2000-1594 ◽

2000 ◽

Author(s):

Rabia Djellouli ◽

Charbel Farhat ◽

Radek Tezaur

Keyword(s):

Acoustic Scattering ◽

Numerical Procedure ◽

Decomposition Methods ◽

Computationally Efficient ◽

Scattering Problems ◽

Absorbing Boundary ◽

Element Discretization ◽

Jacobian Matrices ◽

Fast Solution ◽

Acoustic Scattering Problems

Abstract A Newton-like method is designed for determining the shape or sought-after shape modifications of a scatterer from the knowledge of acoustic far-field patterns at a given number of observation points. This method distinguishes itself from existing numerical procedures by the following features: (a) exact Jacobian matrices for the linearized problems rather than approximate ones, (b) a fast numerical procedure for computing these Jacobian matrices, (c) a computationally efficient absorbing boundary condition for the finite element discretization, and (d) a numerically scalable domain decomposition methods for the fast solution of high-frequency direct acoustic scattering problems.

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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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