Related papers: Sensitivity analysis for active control of the Hel…
In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near field regions of an active source while maintaining desired radiation patterns in prescribed far field directions. This control…
We consider the Helmholtz equation with real analytic coefficients on a bounded domain $\Omega\subset\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\omega$ in a fixed interval $[a,b]$. We consider a…
In this paper we continue to study the feasibility of active manipulation of Helmholtz fields and by using an improved and more robust numerical strategy we present a detailed sensitivity analysis for the method proposed in our previous…
In this paper, a detailed sensitivity analysis of the active manipulation scheme for scalar Helmholtz fields proposed in our previous works, in both free space and constant-depth homogeneous ocean environments, is presented. We apply the…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with a damping on the boundary. The…
We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter $\a>0$. The high-frequency (or: semi-classical) parameter is $\eps>0$. We let $\eps$ and $\a$ go to zero simultaneously. We assume…
This article aims to present a general study of the Helmholtz problem in slowly varying waveguides. This work is of particular interest at locally resonant frequencies, where a phenomenon close to the tunnel effect for Schr\"odinger…
For $h$-FEM discretisations of the Helmholtz equation with wavenumber $k$, we obtain $k$-explicit analogues of the classic local FEM error bounds of [Nitsche, Schatz 1974], [Wahlbin 1991], [Demlow, Guzm\'an, Schatz 2011], showing that these…
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. Existence and uniqueness of the problem can be proved…
We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…
In this paper we prove that for stable semi-discretizations of the wave equation for the WaveHoltz iteration is guaranteed to converge to an approximate solution of the corresponding frequency domain problem, if it exists. We show that for…
The focus of this paper is to show the absence of critical points for the solutions to the Helmholtz equation in a bounded domain $\Omega\subset\mathbb{R}^{3}$, given by \[ \left\{ \begin{array}{l} -\rm{div}(a\,\nabla u_{\omega}^{g})-\omega…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
We study the one-dimensional Helmholtz equation with (possibly perturbed) quasiperiodic coefficients. Quasiperiodic functions are the restriction of higher dimensional periodic functions along a certain (irrational) direction. In classical…
The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The discrete system matrices are huge and densely populated;…
We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R^n. We prove that the solution has a unique semi-classical measure, which is precisely described in terms of the…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…
The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…