title: An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions.
abstract: This paper presents a high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of "thin" structures as they arise in certain applications (e.g., material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and "partitions of unity" (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented, together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results.
authors.affiliation: Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA. anand@acm.caltech.edu
authors.forename: Akash
authors.initials: A
authors.lastname: Anand
authors.forename: Fernando
authors.initials: F
authors.lastname: Reitich
mesh_terms: D000162:Acoustics; D000465:Algorithms; D015233:Models, Statistical; D009038:Motion; D013016:Sound