We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, ie the
equation∇⋅(A∇ u)+ k 2 nu=− f where both A and n are functions of position. We prove new …

It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

We study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well
known that for such manifolds the outgoing resolvent satisfies∥ χ R (k) χ∥ L 2→ L 2≤ C k …

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the Helmholtz
equation with high contrast. The method is constructed for a setting as in Bouchitte and …

We present a wavenumber-explicit convergence analysis of the hp finite element method
applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients …

In this paper, we present a multiscale framework for solving the Helmholtz equation in
heterogeneous media without scale separation and in the high frequency regime where the …

We consider one-level additive Schwarz domain decomposition preconditioners for the
Helmholtz equation with variable coefficients (modelling wave propagation in …

Over the last 10 years, results from [JM Melenk and S. Sauter, Math. Comp., 79 (2010), pp.
1871–1914],[JM Melenk and S. Sauter, SIAM J. Numer. Anal., 49 (2011), pp. 1210–1243],[S …

This article considers the computational (acoustic) wave propagation in strongly
heterogeneous structures beyond the assumption of periodicity. A high contrast between the …

The goal of this paper is to investigate the stability of the Helmholtz equation in the high-
frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains …