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The aim of this work is to model the evolution of the modal distribution of the electromagnetic field as it propagates along a randomly deformed multimode optical waveguide. When the number of guided modes becomes large we can regard the discrete set of modes as a quasi continuum. In some cases, nearest neighbor coupling predominates over other power(More)
The classical boundary element formulation for the Helmholtz equation is rehearsed, and its limitations with respect to the number of variables needed to model a wavelength are explained. A new type of interpolation for the potential is then described in which the usual boundary element shape functions are modified by the inclusion of a set of plane waves,(More)
A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions.(More)
The Method of Fundamental Solutions (MFS) is now a well-established technique that has proved to be reliable for a specific range of wave problems such as the scattering of acoustic and elastic waves by obstacles and inclusions of regular shapes. The goal of this study is to show that the technique can be extended to solve transmission problems whereby an(More)
It is well known that the use of conventional discrete numerical methods of analysis (FEM and BEM) in the solution of Helmholtz and elastodynamic wave problems is limited by an upper bound on frequency. The current work addresses this problem by incorporating the underlying wave behaviour of the solution into the formulation of a boundary element, using(More)
A mode matching method for predicting the transmission loss of a cylindrical shaped dissipative silencer partially filled with a poroelastic foam is developed. The model takes into account the solid phase elasticity of the sound-absorbing material, the mounting conditions of the foam, and the presence of a uniform mean flow in the central airway. The(More)
SUMMARY In this paper we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as 'bubble' shape functions. A series of simple test(More)
In the present work, the propagation of sound in a lined duct containing sheared mean flow is studied. Walls of the duct are acoustically treated with absorbent poroelastic foams. The propagation of elasto-acoustic waves in the liner is described by Biot's model. In the fluid domain, the propagation of sound in a sheared mean flow is governed by the(More)
An analytical model based on a homogenization process is used to predict and understand the behavior of finite length splitter/baffle-type silencers inserted axially into a rigid rectangular duct. Such silencers consist of a succession of parallel baffles made of porous material and airways inserted axially into a rigid duct. The pore network of the porous(More)
Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a(More)