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This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

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…

Analysis of PDEs · Mathematics 2020-07-23 Frédéric Magoulès , Thi Phuong Kieu Nguyen , Pascal Omnes , Anna Rozanova-Pierrat

We present Helmholtz or Helmholtz like equations for the approximation of the time-harmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models…

Analysis of PDEs · Mathematics 2019-05-22 Kersten Schmidt , Anastasia Thöns-Zueva

Erosion of rocky coasts spontaneously creates irregular seashores. But the geometrical irregularity, in turn, damps the sea-waves, decreasing the average wave amplitude. There may then exist a mutual self-stabilisation of the waves…

Statistical Mechanics · Physics 2009-11-10 B. Sapoval , A. Baldassarri , A. Gabrielli

A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…

Numerical Analysis · Mathematics 2024-11-11 Johan Helsing , Shidong Jiang

Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…

Numerical Analysis · Mathematics 2022-06-28 Said Kerrache , Yasushi Nakauchi

In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…

Optimization and Control · Mathematics 2020-12-17 Daniel Luft , Volker H. Schulz , Kathrin Welker

Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…

Geophysics · Physics 2021-06-04 Tariq Alkhalifah , Chao Song , Umair bin Waheed , Qi Hao

Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…

Analysis of PDEs · Mathematics 2025-11-06 Thorsten Hohage , Meng Liu

In this paper we discuss the convergence of state-of-the-art optimized Schwarz transmission conditions for Helmholtz problems defined on closed domains (i.e. setups which do not exhibit an outgoing wave condition), as commonly encountered…

Numerical Analysis · Mathematics 2021-03-18 Nicolas Marsic , Herbert De Gersem

A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…

Mathematical Physics · Physics 2016-06-21 Subhasis Panda , S. Pratik Khastgir

A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…

Computational Physics · Physics 2018-08-01 Johan Helsing , Anders Karlsson

We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…

Analysis of PDEs · Mathematics 2019-04-09 Thomas Baden-Riess

Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…

Analysis of PDEs · Mathematics 2021-06-21 Stefano Almi , Ulisse Stefanelli

We propose a novel on-surface radiation condition to approximate the outgoing solution to the Helmholtz equation in the exterior of several impenetrable convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann operator…

Computational Physics · Physics 2021-02-01 Sebastian Acosta

Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…

Analysis of PDEs · Mathematics 2016-04-26 Y. A. Antipov

We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and…

Numerical Analysis · Mathematics 2020-06-30 Stefan Sauter , Céline Torres

High frequency estimates for the Dirichlet-to-Neumann and Neumann-to-Dirichlet operators are obtained for the Helmholtz equation in the exterior of bounded obstacles. These a priori estimates are used to study the scattering of plane waves…

Mathematical Physics · Physics 2013-07-18 Evgeny Lakshtanov , Boris Vainberg

We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…

This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…

Numerical Analysis · Mathematics 2024-01-08 Manaswinee Bezbaruah , Matthias Maier , Winnifried Wollner