A Mathieu function boundary royalsocietypublishing.org/journal/rspa spectral method for scattering by multiple variable poro-elastic plates, with Research Cite this article: Colbrook MJ, Kisil AV. 2020 A applications to metamaterials Mathieu function boundary spectral method and acoustics for scattering by multiple variable poro-elastic plates, with applications to metamaterials and Matthew J. Colbrook1 and Anastasia V. Kisil2 acoustics. Proc.R.Soc.A476: 20200184. http://dx.doi.org/10.1098/rspa.2020.0184 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK Received: 17 March 2020 2Department of Mathematics, The University of Manchester, Accepted: 10 August 2020 Manchester, M13 9PL, UK MJC, 0000-0003-4964-9575; AVK, 0000-0001-7652-5880 Subject Areas: applied mathematics, computational Many problems in fluid mechanics and acoustics can mathematics, differential equations be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function Keywords: expansions, for Helmholtz scattering off multiple boundary spectral methods, Mathieu variable poro-elastic plates in two dimensions. Such functions, acoustic scattering, poro-elastic boundary conditions, namely the varying physical boundary conditions, metamaterials parameters and coupled thin-plate equation, present a considerable challenge to current methods. The new Author for correspondence: method is fast, accurate and flexible, with the ability to compute expansions in thousands (and even tens Matthew J. Colbrook of thousands) of Mathieu functions, thus making it e-mail:
[email protected] a favourable method for the considered geometries. Comparisons are made with elastic boundary element methods, where the new method is found to be faster and more accurate.