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We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A.S. Fokas and co-authors, analysing particular instances of this method, proposed by J.A. DeSanto and co-authors, for problems of acoustic scattering by diffraction gratings.
We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable to any lo
Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretization matrix are given by lower-dimensional integrals. For that same reason, the matrix assembly also requi
In this paper we discuss a hybridised method for FEM-BEM coupling. The coupling from both sides use a Nitsche type approach to couple to the trace variable. This leads to a formulation that is robust and flexible with respect to approximation spaces
We study time-harmonic scattering in $mathbb{R}^n$ ($n=2,3$) by a planar screen (a crack in the context of linear elasticity), assumed to be a non-empty bounded relatively open subset $Gamma$ of the hyperplane $mathbb{R}^{n-1}times {0}$, on which imp
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are present. The