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

This Letter reports a folded metaporous surface optimized to achieve sub-wavelength and broadband perfect absorption. Its unit cell is composed of four different helicoidal cavities filled by porous media, which are structured and quasi-isotropic micro-lattices with a variable lattice constant. The effective thickness and intrinsic losses of each helicoidal cavity can be adjusted independently by varying their macro- and micro-structures, namely, the number of revolution of the folded structure and the lattice constant of the micro-lattice. An analytical model predicting the physical properties of this metaporous surface is developed. The macro- and micro-structures are then jointly optimized for sub-wavelength broadband perfect absorption. Finally, the system is 3D printed and experimentally tested. The experimental results are found to be in good agreement with the theory and show an almost perfect absorption over a frequency range out of reach for the homogeneous constitutive porous medium and the only helicoidal cavities.

Folded metaporous material for sub-wavelength and broadband perfect sound absorption

A Computational Mode Matching Approach for Propagation in Three-Dimensional Ducts with Flow

Aft fan noise is becoming a more dominant source as engine bypass ratio is increased n this paper an assessment of the effect of the mean flow gradients on fan exhaust noise propagation is carried out using both analytical models for simplified problems and numerical methods for realistic configurations. Fan exhaust noise can be significantly refracted by the mean flow gradients in the jet mixing layer, especially at high operating conditions (i.e. during take off). The refraction effect is predicted using either Lilley’s equation or the linearized Euler equations. For parallel base flows, an issue with these linear models is the presence of Kelvin-Helmholtz instabilities whose unlimited exponential growth is unphysical and problematic for computational methods. This problem is less critical for developing mixing layer for instance where the growth of the vorticity thickness reduces the growth of the instability waves [1]. Various techniques have been used for suppressing the instability; these include adding non-linear terms to saturate the growth of the instability [2], using frequency domain analysis [3], or removing the mean flow gradient terms [4]. It is the last approach, termed Gradient Term Suppression (GTS), which is investigated in the present work.

Gwenael Gabard

Papers

Folded metaporous material for sub-wavelength and broadband perfect sound absorption

A Computational Mode Matching Approach for Propagation in Three-Dimensional Ducts with Flow

Influence of mean flow gradients on fan exhaust noise predictions

Anisotropic adaptivity of the p-FEM for time-harmonic acoustic wave propagation

Boundary layer effects on liners for aircraft engines