µ-diff: A matlab toolbox for multiple scattering problems by disks

Abstract

The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in µ-diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on these expressions, an efficient spectrally accurate finite-dimensional solution of multiple scattering problems can be simply obtained for complex media even when many scatterers are considered as well as large frequencies. The solution of the global linear system to solve can use either direct solvers or preconditioned iterative Krylov subspace solvers for block Toeplitz matrices. Based on this approach, this paper explains how the code is built and organized. Some complete numerical examples of applications (direct and inverse scattering) are provided to show that µ-diff is a flexible, efficient and robust toolbox for solving some complex multiple scattering problems.

Whispering Gallery Modes Formed by Scattering of an Electromagnetic Plane Wave by Two Cylinders

“…The propagation and scattering of the electromagnetic plane wave was studied using MATLAB toolbox that was developed in Ref. [9]. A transverse-electric (TE) polarized plane wave (λ = 532 nm) To determine how the positions of cylinder B affect the maximal absolute field value inside the cylinder A, we varied its positions by moving the centers within the ring defined in polar coordinates as interval of radii [R A + R B , R A + 1.6*R B ].…”

Numerical robustness of single-layer method with Fourier basis for multiple obstacle acoustic scattering in homogeneous media

“…We denote by r the obstacle radius, d the distance between the centers of two adjacent obstacles, and by λ the wavelength of the plane wave. For the first two experiments, while the 200 size of the visualization domains is within the acceptable range for Montjoie 19 , being 11λ × 16λ and 31λ × 23λ respectively, the obstacles are much smaller than the wavelength, being 1 16 λ and 1 21 λ respectively. The third experiment is designed to estimate the time cost of a 'forward problem', if FSSL or Montjoie is employed in a full-waveform inversion algorithm 20 .…”

“…18 However neither the code nor the method exploits these specificities (equal-sized obstacles and periodic spacing), and the same results should be observed for configurations with different sized obstacles as long as they are within the current smallness assumption (3). 19 See Footnote 5 in Introduction. 20 The goal of inverse problem is to reconstruct the true parameters which give rise to the observed data.…”

“…Despite the existence of pieces of software for this type of simulation, e.g. the Matlab toolbox µ-diff 55 [19], see also [9] for a review of available packages, we would like to develop a high-performance computing software that can work on clusters 9 . Our codes offer choices of the direct solvers (Mumps, Lapack and Scalapack), and GM-RES (with restart) solvers [20] with various preconditioners.…”

Effect of the Multiple Cylinders Scattering of an Electromagnetic Plane Wave on the Formation of Whispering Gallery Modes

“…The propagation and scattering of the electromagnetic plane wave was studied using MATLAB toolbox developed in Ref. [16]. TE-polarized plane wave (λ = 532 nm) was used as the incident wave.…”