Une nouvelle formulation variationnelle des équations d'onde en fréquence PDF Download
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Author: Olivier Cessenat
Publisher:
ISBN:
Category :
Languages : fr
Pages : 108
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Book Description
Author: Olivier Cessenat
Publisher:
ISBN:
Category :
Languages : fr
Pages : 108
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Book Description
Author: OLIVIER.. CESSENAT
Publisher:
ISBN:
Category :
Languages : fr
Pages : 250
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Book Description
UNE NOUVELLE TECHNIQUE DE RESOLUTION DES EQUATIONS AUX DERIVEES PARTIELLES ELLIPTIQUES LINEAIRES A ETE INTRODUITE DANS DES94. NOUS APPELLERONS CETTE TECHNIQUE FORMULATION VARIATIONNELLE ULTRA FAIBLE (UWVF). L'OBJET DE CE TRAVAIL EST L'ETUDE DES POTENTIALITES DE CETTE METHODE POUR LES PROBLEMES D'ONDE, EN PARTICULIERS LES PROBLEMES DE HELMHOLTZ ET DE MAXWELL. CES DEUX PROBLEMES ONT DE LARGES APPLICATIONS INDUSTRIELLES. CITONS POUR HELMHOLTZ LES PROBLEMES DE PROSPECTION MINIERE, DE NAVIGATION SOUS-MARINE, DE CONTROLE DES STRUCTURES DANS LES CENTRALES NUCLEAIRES OU POUR LE BATIMENT, DE RECHERCHE ARCHEOLOGIQUE, DE FACON GENERALE POUR TOUS LES PROBLEMES DE DETECTION DE FISSURES OU DE CAVITE. DE PLUS, LE CAS SIMPLIFIE DE HELMHOLTZ SCALAIRE DANS UN MILIEU BORNE BI-DIMENSIONNEL A CARACTERISTIQUES CONSTANTES NON DISSIPATIVES EST INTERESSANT POUR SES VERTUS PEDAGOGIQUES. CETTE ETUDE FAIT L'OBJET D'UNE PREMIERE PARTIE DONT LA PRESENTATION SUIT CELLE DE LA METHODE DES ELEMENTS FINIS (FEM). EN EFFET, SI LES DEUX METHODES SONT CONCEPTUELLEMENT DIFFERENTES, ELLES SONT PROCHES DANS LA MISE EN OEUVRE PRATIQUE. LE PREMIER CHAPITRE EST DEDIE A L'ETUDE DU PROBLEME CONTINU ET DE LA FORMULATION VARIATIONNELLE. LE DEUXIEME CHAPITRE CONCERNE LA TECHNIQUE DE DISCRETISATION DE TYPE GALERKIN. LE TROISIEME CHAPITRE ETUDIE L'EFFICACITE DE LA METHODE DU POINT DE VUE DE L'ORDRE DE CONVERGENCE. CECI EST REALISE PAR DES DEMONSTRATIONS MATHEMATIQUES AINSI QU'UNE LARGE SERIE D'EXPERIENCES NUMERIQUES. EN PARTICULIER, IL EST MONTRE ET PROUVE QUE L'ORDRE DE CONVERGENCE EST MINORE PAR UNE LOI LINEAIRE EN FONCTION DU NOMBRE DE DEGRES DE LIBERTE. DES APPLICATIONS A DES PROBLEMES DE DIFFRACTION SONT PRESENTEES DANS UN QUATRIEME CHAPITRE. ENFIN, UN DERNIER CHAPITRE GENERALISE LA FORMULATION VARIATIONNELLE AU CAS DE COEFFICIENTS VARIABLES. POUR D'AUTRES APPLICATIONS INDUSTRIELLES, LA DEUXIEME PARTIE DE CET OUVRAGE ETUDIE LES PROBLEMES HARMONIQUES D'ELECTROMAGNETISME EN DOMAINE BORNE DANS DES MILIEUX AUX CARACTERISTIQUES SCALAIRES COMPLEXES. ENTRE AUTRES APPLICATIONS, CITONS LES PROBLEMES DE COMMUNICATIONS, LIBRES DANS L'ESPACE OU CANALISEES PAR UN GUIDE D'ONDE, ET LES PROBLEMES DE DETECTION AUX NOMBREUSES APPLICATIONS MILITAIRES. CETTE PARTIE, LEGEREMENT MOINS COMPLETE QUE LA PREMIERE EN CE QUI CONCERNE LES ANALYSES THEORIQUES DE LA METHODE, PRESENTE UN GRAND NOMBRE DE SIMULATIONS NUMERIQUES ET DE COMPARAISONS AUX METHODES CLASSIQUES. NEANMOINS L'ANALYSE DU PROBLEME SUIT LA MEME DEMARCHE LOGIQUE EN PRESENTANT LES DIFFICULTES SUPPLEMENTAIRES INDUITES PAR LE CARACTERE TRI-DIMENSIONNEL DES INCONNUES ET DU DOMAINE AINSI QUE PAR LES CONDITIONS SUPPLEMENTAIRES QUE SONT LES RELATIONS DE GAUSS OU RELATIONS DE DIVERGENCE. UN RESULTAT IMPORTANT NON TRIVAL CONCERNE L'ORDRE DE CONVERGENCE DE LA METHODE DANS LE VIDE POUR UN PROBLEME SANS SOURCE VOLUMIQUE. L'ORDRE DE LA METHODE EVOLUE EN RACINE CARREE DU NOMBRE DE DEGRES DE LIBERTE, CE QUI, POUR UN PROBLEME TRI-DIMENSIONNEL, CONSTITUE UN BON RESULTAT.
Author: Olivier Cessenat
Publisher:
ISBN:
Category :
Languages : fr
Pages : 0
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Book Description
Author: Jacques-Louis Lions
Publisher: Elsevier Masson
ISBN:
Category : Mathematics
Languages : en
Pages : 832
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Book Description
Author: J.F. Allard
Publisher: Springer Science & Business Media
ISBN: 9401118663
Category : Technology & Engineering
Languages : en
Pages : 296
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Book Description
This book has grown out of the research activities of the author in the fields of sound propagation in porous media and modelling of acoustic materials. It is assumed that the reader has a background of advanced calculus, including an introduction to differential equations, complex variables and matrix algebra. A prior exposure to theory of elasticity would be advantageous. Chapters 1-3 deal with sound propagation of plane waves in solids and fluids, and the topics of acoustic impedance and reflection coefficient are given a large emphasis. The topic of flow resistivity is presented in Chapter 2. Chapter 4 deals with sound propagation in porous materials having cylindrical pores. The topics of effective density, and of tortuosity, are presented. The thermal exchanges between the frame and the fluid, and the behaviour of the bulk modulus of the fluid, are described in this simple context. Chapter 5 is concerned with sound propagation in other porous materials, and the recent notions of characteristic dimensions, which describe thermal exchanges and the viscous forces at high frequencies, are introduced. In Chapter 6, the case of porous media having an elastic frame is considered in the context of Biot theory, where new topics described in Chapter 5 have been included.
Author: Pierre H. Berard
Publisher: Springer
ISBN: 3540409580
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Author: Frank Ihlenburg
Publisher: Springer Science & Business Media
ISBN: 0387227008
Category : Mathematics
Languages : en
Pages : 238
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Book Description
A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.
Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3642051952
Category : Science
Languages : en
Pages : 466
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Book Description
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
Author: Julius Adams Stratton
Publisher: John Wiley & Sons
ISBN: 0470131535
Category : Technology & Engineering
Languages : en
Pages : 642
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Book Description
This book is an electromagnetics classic. Originally published in 1941, it has been used by many generations of students, teachers, and researchers ever since. Since it is classic electromagnetics, every chapter continues to be referenced to this day. This classic reissue contains the entire, original edition first published in 1941. Additionally, two new forewords by Dr. Paul E. Gray (former MIT President and colleague of Dr. Stratton) and another by Dr. Donald G. Dudley, Editor of the IEEE Press Series on E/M Waves on the significance of the book's contribution to the field of Electromagnetics.
Author: Sigeru Mizohata
Publisher: Academic Press
ISBN: 148326906X
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.
