to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

流体力学用語集 非線形音響学(Nonlinear acoustics)

A discrete technique of the Schwarz alternating method is presented in this last chapter, to combine the Ritz-Galerkin and finite element methods. This technique is well suited for solving singularity problems in parallel, and requires a little more computation for large overlap of subdomains. The convergence rate of the iterative procedure, which depends upon overlap of subdomains, will be studied. Also a balance strategy will be proposed to couple the iteration number with the element size used in the FEM. For the crack-infinity problem of singularity the total CPU time by the technique in this chapter is much less than that by the nonconforming combination in Chapter 12.

Schwarz Alternating Method

Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

Integral transforms and their applications

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Despres, SIAM J. Numer. Anal., 35 (1998), pp. 255-299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121-136], and plane wave approximation theory.

/pdf/plane-wave-discontinuous-galerkin-methods-for-the-2d-tf8l9vefgi.pdf

Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version

Foreword and commentary

Over the last twenty years, many ideas have been suggested to design sub-wavelength absorbers that couple a classical single-degree of freedom liner with a vibrating part that resonates at low frequencies. In this paper, the acoustic behaviour of a light and thin sound absorber composed of an elastic latex membrane placed on top of a closed 3D-printed cavity is studied. It is found experimentally and analytically that membrane modes imply a great shift of the cavity resonance towards the low frequencies and add several supplementary transmission drops. To investigate the effects of flow, numerical time-domain simulations are conducted and validated after comparisons with experimental data. The three approaches show that membrane absorbers are highly resistive, with a weak sensibility against flow and non linear effects. They are thus well-suited for absorption purposes in aeronautic applications. 

Drum-like liners to attenuate low frequencies in presence of flow: an analytical, experimental and numerical study

This paper presents two novel techniques to introduce source terms in the linearized Euler equations for the simulation of aeroacoustic propagation on a background mean flow. The first technique al...

Interface Source Terms for High-Order Aeroacoustics

Vibro-acoustic interactions with non-uniform mean flows

Passive metamaterials provide efficient solutions for sound absorption in the low‐frequency regime with deep subwavelength dimensions. They have been extensively applied in unidimensional reciprocal problems considering that an incident wave is either reflected or transmitted at the outlet boundary. However, the generalized problem with impedance boundary condition is not well understood yet. This work presents a general design methodology of metamaterial absorbers for open‐duct problems, which is a special case of impedance outlet boundary encountered in broad practical applications, for example, noise‐attenuation problems in heat ventilation and air conditioning systems. By properly using monopolar point scatterers made of arrays of Helmholtz resonators, the design process is significantly simplified; the transfer matrix modeling is sufficiently accurate to describe the acoustic response of the system. A single monopolar point scatterer is insufficient to attenuate both the reflected and radiated waves; a frequency‐dependent maximum absorption exists and is derived analytically. To go beyond this absorption bound and achieve perfect absorption, at least two point scatterers are necessary. Specific designs are provided and validated experimentally for maximum or perfect absorption, either at single frequencies or over specific frequency bands.

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/admt.202201909

Gwenael Gabard

Papers

Foreword and commentary

Drum-like liners to attenuate low frequencies in presence of flow: an analytical, experimental and numerical study

Interface Source Terms for High-Order Aeroacoustics

Vibro-acoustic interactions with non-uniform mean flows

Subwavelength Broadband Perfect Absorption for Unidimensional Open‐Duct Problems