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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 …

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz
obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds …

6.1▪“When All Else Fails, Integrate by Parts”: New and Old Variational Formulations for
Linear Elliptic PDEs 6.1. 1▪ Introduction Although the motto “when all else fails, integrate by …

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 propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for
time-harmonic scattering problems of Helmholtz type with high wavenumber. On a coarse …

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a
nontrapping obstacle, with boundary data coming from plane-wave incidence, by the …

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 …

This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation
posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the …

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 …