Formula omitted]-diff: An open-source Matlab toolbox for computing 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. Program summaryProgram title:μ-diffCatalogue identifier: AEWH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 13,718No. of bytes in distributed program, including test data, etc.: 1,466,301Distribution format: tar.gzProgramming language: Matlab.Computer: PC, Mac.Operating system: Windows, Mac OS, Linux.Has the code been vectorized or parallelized?: YesRAM: 2000 MegabytesClassification: 4.6, 10, 18.Nature of problem: Modeling and simulation of two-dimensional multiple wave scattering by large clusters of circular cylinders for any frequency. The program is well-designed to manage highly accurate solutions for deterministic or random media, with various boundary conditions and physics properties of the scatterers. Pre- and post-processing facilities are designed specifically for these problems.Solution method: We use spectral Fourier approximation schemes and direct or iterative Krylov subspace methods.Running time: From a few seconds for simple problems to a few minutes for more complex situations on a medium computer.