Search results for " Helmholtz equation"

showing 3 items of 3 documents

Multi-parameter analysis of the obstacle scattering problem

2022

Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.

integral equationsshape sensitivity analysisassociated exterior Dirichlet problemDirichlet-to-Neumann operatorApplied MathematicsHelmholtz equation; acoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; shape sensitivity analysis; perturbed domain; integral equationsacoustic scatteringComputer Science ApplicationsTheoretical Computer Scienceperturbed domainMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaSignal ProcessingFOS: Mathematicsacoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; Helmholtz equation; integral equations; perturbed domain; shape sensitivity analysisHelmholtz equation35J25 35J05 35P25 31B10 45A05Mathematical PhysicsAnalysis of PDEs (math.AP)
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High performance algorithms based on a new wawelet expansion for time dependent acoustics obstale scattering

2007

This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems. The method proposed is a generalization of the ``operator expansion method" developed by Recchioni and Zirilli [SIAM J.~Sci.~Comput., 25 (2003), 1158-1186]. The numerical method proposed reduces, via a perturbative approach, the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations. The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved. A computational method has been developed to solve these challenging p…

Time dependent acoustic scattering Helmholtz equation integral equation methodswavelet bases sparse linear systems
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A RADIATION CONDITION FOR UNIQUENESS IN A WAVE PROPAGATION PROBLEM FOR 2-D OPEN WAVEGUIDES

2009

We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Final…

Electromagnetic fieldAsymptotic analysisHelmholtz equationWave propagationGeneral Mathematicsmedia_common.quotation_subject78A40 35J05 78A50 35A05Mathematical analysisGeneral Engineeringelectromagnetic fields • wave propagation • Helmholtz equation • optical waveguides • uniqueness of solutions • radiation conditionInfinitylaw.inventionAmplitudeMathematics - Analysis of PDEslawFOS: Mathematicswave propagation; Helmholtz equation; optical waveguides; radiation condition; uniqueness theoremsUniquenessWaveguidemedia_commonMathematicsAnalysis of PDEs (math.AP)
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