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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

Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…

Numerical Analysis · Mathematics 2018-01-16 Daan Huybrechs , Peter Opsomer

Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs)…

Numerical Analysis · Mathematics 2020-06-17 Vianey Villamizar , Dane Grundvig , Otilio Rojas , Sebastian Acosta

This paper establishes a complete time-harmonic scattering theory for hyperbolic space, formulating it within the classical Sommerfeld-Rellich paradigm centered on far-field patterns--a foundational framework that has been absent despite…

Analysis of PDEs · Mathematics 2026-03-11 Lu Chen , Hongyu Liu

We present a solution for the scattered field caused by an incident wave interacting with an infinite cascade of blades with complex boundary conditions. This extends previous studies by allowing the blades to be compliant, porous or…

Fluid Dynamics · Physics 2020-08-26 Peter J. Baddoo , Lorna J. Ayton

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…

Numerical Analysis · Mathematics 2015-06-22 Jun Lai , Motoki Kobayashi , Leslie Greengard

Scalar wave scattering by many small particles with impedance boundary condition and creating material with a desired refraction coefficient are studied. The acoustic wave scattering problem is solved asymptotically and numerically under…

Numerical Analysis · Mathematics 2017-10-17 Nhan Tran

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…

Computational Physics · Physics 2019-10-02 Q. Sun , E. Klaseboer , B. C. Khoo , D. Y. C. Chan

For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…

Numerical Analysis · Mathematics 2018-05-24 Andrew Gibbs , Stephen Langdon , Andrea Moiola

Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…

Numerical Analysis · Mathematics 2016-02-16 Alexander Ramm , Nhan Tran

A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…

Numerical Analysis · Computer Science 2018-05-18 J. Poblet-Puig , A. V. Shanin

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…

Numerical Analysis · Mathematics 2014-01-14 David P. Hewett , Simon N. Chandler-Wilde , Stephen Langdon , Ashley Twigger

We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…

Numerical Analysis · Mathematics 2018-11-20 Shelvean Kapita , Ming Jun Lai

We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions,…

Classical Physics · Physics 2016-04-27 Ory Schnitzer , Richard V. Craster

It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resolved by any grid-based method. In this paper, we intend to…

Numerical Analysis · Mathematics 2024-01-30 Jiangxing Wang , Lilian Wang , Bo Wang

In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…

Classical Physics · Physics 2017-11-21 Wen Geyi

We present a numerical approach to the solution of elastic phonon scattering problems based on a frequency domain decomposition of the atomistic equations of motion and the use of perfectly matched layer or PML boundaries. Unlike MD…

Mesoscale and Nanoscale Physics · Physics 2017-01-27 Rohit R. Kakodkar , Joseph P. Feser

We established the propagation equation of acoustical wave in media with the solid/porous media cylindrical boundary and obtained the analytic solution. We suggested the boundary condition on solid-porous media cylindrical boundary. Based…

Materials Science · Physics 2015-11-11 Un-Son Ri , Un-Gyong An , Song-Jin Im

In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om scheme…

Computational Physics · Physics 2015-06-12 Johan Helsing , Anders Karlsson