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.

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

/pdf/numerical-investigation-on-the-spectral-broadening-of-4n195x68ra.pdf

Numerical Investigation on the Spectral Broadening of Acoustic Waves by a Turbulent Layer

La propagation et la production de bruit dans les ecoulements de fluides representent un probleme crucial pour de nombreuses applications industrielles en particulier les transports. Cette these a pour originalite d’utiliser un modele peu employe, l’equation de Galbrun, pour modeliser la propagation acoustique dans les ecoulements. Concernant les methodes numeriques, on presente une analyse de dispersion de plusieurs methodes d’elements finis pour la propagation aeroacoustique. D’autre part, plusieurs conditions de non-reflexion pour l’equation de Galbrun dans le domaine frequentiel sont obtenues. On propose deux modeles de sources aeroacoustiques formules a l’aide de l’equation de Galbrun. Le premier modele est issu du modele de source propose pour les equations d’Euler linearisees par Bailly et le second modele est obtenu par la methode des developpements autour d’un ecoulement incompressible initialement developpee par Hardin et Pope.

Méthodes numériques et modèles de sources aéroacoustiques fondés sur l’équation de Galbrun

A dispersion analysis of the fully-discrete, nodal discontinuous Galerkin method (DGM) for the solution of the time-domain linearized Euler equations (LEE) is performed. Two dispersion analysis methods are developed, considering both uniform and non-uniform mean-flow effects. Convergence studies are performed for the dispersion, dissipation, and nodal solution errors of the acoustic, entropy, and vorticity modes. The accuracy and stability of the DGM are analyzed in the context of aeroacoustic applications, and guidelines are proposed for the choice of optimal discretizations. Computational costs are estimated for a model problem and related to the choice of the element size, polynomial order, and time step. Results indicate that temporal error can become a dominant source of error for high accuracy requirements and long distance wave propagation. The stability of the scheme is analyzed for a shear layer mean flow profile. Aliasing-type errors are found to contribute to the formation of numerical instabilities which are further strengthened by increases in the polynomial order.

/pdf/performance-of-the-dgm-for-the-linearized-euler-equations-134jsvulm4.pdf

Performance of the DGM for the linearized Euler equations with non-uniform mean-flow

A boundary element method in a transformed Taylor-Lorentz space-time is presented to solve sound propagation and scattering in weakly non-uniform subsonic potential flows. Boundary element solutions are conventionally provided for sound propagation and scattering in quiescent media. On the other hand, an effective approach to solve wave propagation in a non-uniform mean flow using boundary element methods has yet to be demonstrated. Although either the Taylor or Lorentz transform being applied separately has been commonly used to provide boundary integral solutions including mean flow effects on wave propagation, in this work a combination of these transformations is proposed. The Taylor-Lorentz transform allows an approximate formulation of the full potential linearized wave equation to be reduced to the standard wave equation in a deformed space-time, where a conventional boundary element method can then be devised. The boundary conditions for the formulation in the transformed space are also presented. Numerical experiments are performed to validate the present method.

Gwenael Gabard

Papers

Numerical Investigation on the Spectral Broadening of Acoustic Waves by a Turbulent Layer

Méthodes numériques et modèles de sources aéroacoustiques fondés sur l’équation de Galbrun

Performance of the DGM for the linearized Euler equations with non-uniform mean-flow

A variable transformation approach for boundary element solutions of wave propagation in non-uniform potential flows

Hybrid numerical model for acoustic propagation through sheared flows