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This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…

Numerical Analysis · Mathematics 2023-01-25 Heping Dong , Peijun Li

We present a numerical method to determine the complex acoustic impedance at the open surface of an arbitrarily shaped cavity, associated to an impinging planar acoustic wave with a given wavenumber vector and frequency. We have achieved…

Fluid Dynamics · Physics 2017-01-31 Danish Patel , Prateek Gupta , Carlo Scalo , Thomas Rothermel , Markus Kuhn

This study proposes a novel coupled-mode theory for two-dimensional exterior Helmholtz problems. The proposed approach is based on the separation of the entire space R2 into a fictitious disk and its exterior. The disk is allocated in such…

Numerical Analysis · Mathematics 2022-01-25 Kei Matsushima , Yuki Noguchi , Takayuki Yamada

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…

Analysis of PDEs · Mathematics 2020-11-04 Nassif Ghoussoub , Young-Heon Kim , Hugo Lavenant , Aaron Zeff Palmer

Manipulating underwater pressure waves is crucial for marine exploration, as electromagnetic signals are strongly absorbed in water. However, the multi-path phenomenon complicates the accurate capture of acoustic waves by receivers.…

Optimization and Control · Mathematics 2025-01-03 Sebastiano Cominelli , Francesco Braghin

In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…

Analysis of PDEs · Mathematics 2013-12-05 Nicolas Chaulet

We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity…

Fluid Dynamics · Physics 2020-01-28 Rodolfo Brandão , Ory Schnitzer

This paper is a short guideline to the decomposition of a compressible velocity into vortical and compressible structures using standard flow solvers. In particular, this is a fast solution to get an idea of the compressible fields inside…

Fluid Dynamics · Physics 2023-08-10 Stefan Schoder

Physical design problems, such as photonic inverse design, are typically solved using local optimization methods. These methods often produce what appear to be good or very good designs when compared to classical design methods, but it is…

Optics · Physics 2020-05-20 Guillermo Angeris , Jelena Vuckovic , Stephen Boyd

We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…

Analysis of PDEs · Mathematics 2015-01-09 Giulio Ciraolo

This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct…

Analysis of PDEs · Mathematics 2024-11-04 Lorenzo Cavallina

Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…

Numerical Analysis · Mathematics 2017-04-17 Neeraj Sarna

We study the well-posedness of the Cauchy problem with Dirichlet or Neumann boundary conditions associated to an H 1 -critical semilinear wave equation on a smooth bounded 2D domain {\Omega}. First, we prove an appropriate Strichartz type…

Analysis of PDEs · Mathematics 2010-08-17 S. Ibrahim , R. Jrad

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…

Numerical Analysis · Mathematics 2024-02-21 Elwin van 't Wout

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…

Mathematical Physics · Physics 2016-07-20 Paolo Amore , Francisco M. Fernandez , Christoph P. Hofmann

Decorated membrane, comprising a thin layer of elastic film with small rigid platelets fixed on top, has been found to be an efficient absorber of low frequency sound. In this work we consider the problem of sound absorption from a…

Materials Science · Physics 2015-09-15 Min Yang , Yong Li , Chong Meng , Caixing Fu , Jun Mei , Zhiyu Yang , Ping Sheng

We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…

Optimization and Control · Mathematics 2015-06-11 Klaus Deckelnick , Michael Hinze , Tobias Jordan

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence…

Numerical Analysis · Mathematics 2017-01-30 Alex Bespalov , Alexander Haberl , Dirk Praetorius

The solution of the Helmholtz equation in optical semiclassic approximation is associated with the calculation of ray paths and matrices of variations. The transformation rules for elements of matrices on the boundaries of the waveguide are…

Mathematical Physics · Physics 2012-12-27 I. P. Smirnov

The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The…

Numerical Analysis · Mathematics 2022-11-01 Elwin van 't Wout , Seyyed R. Haqshenas , Pierre Gélat , Timo Betcke , Nader Saffari