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Titre : Introduction to partial differential equations Type de document : Guide/Manuel Auteurs : David Borthwick, Auteur Editeur : Springer International Publishing Année de publication : 2016 Importance : 636 p. Format : 18 x 26 cm ISBN/ISSN/EAN : 978-3-319-48936-0 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes IGN] équation de Laplace
[Termes IGN] équation différentielle
[Termes IGN] équation linéaire
[Termes IGN] onde acoustique
[Termes IGN] série de Fourier
[Termes IGN] transformation de FourierRésumé : (éditeur) This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject.
No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens'. Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.Note de contenu : 1- Introduction
2- Preliminaries
3- Conservation Equations and Characteristics
4- The Wave Equation
5- Separation of Variables
6- The Heat Equation
7- Function Spaces
8- Fourier Series
9- Maximum Principles
10- Weak Solutions
11- Variational Methods
12- Distributions
13- The Fourier TransformNuméro de notice : 25868 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel DOI : 10.1007/978-3-319-48936-0 En ligne : https://doi.org/10.1007/978-3-319-48936-0 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95528 A synergy method to improve ensemble weather predictions and differential SAR interferograms / Franz-Georg Ulmer in ISPRS Journal of photogrammetry and remote sensing, vol 109 (November 2015)
[article]
Titre : A synergy method to improve ensemble weather predictions and differential SAR interferograms Type de document : Article/Communication Auteurs : Franz-Georg Ulmer, Auteur ; Nico Adam, Auteur Année de publication : 2015 Article en page(s) : pp 98 - 107 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Traitement d'image radar et applications
[Termes IGN] correction différentielle
[Termes IGN] effet atmosphérique
[Termes IGN] équation différentielle
[Termes IGN] image radar moirée
[Termes IGN] interferométrie différentielle
[Termes IGN] interféromètrie par radar à antenne synthétique
[Termes IGN] Pays-Bas
[Termes IGN] prévision météorologiqueRésumé : (auteur) A compensation of atmospheric effects is essential for mm-sensitivity in differential interferometric synthetic aperture radar (DInSAR) techniques. Numerical weather predictions are used to compensate these disturbances allowing a reduction in the number of required radar scenes. Practically, predictions are solutions of partial differential equations which never can be precise due to model or initialisation uncertainties. In order to deal with the chaotic nature of the solutions, ensembles of predictions are computed. From a stochastic point of view, the ensemble mean is the expected prediction, if all ensemble members are equally likely. This corresponds to the typical assumption that all ensemble members are physically correct solutions of the set of partial differential equations. DInSAR allows adding to this knowledge. Observations of refractivity can now be utilised to check the likelihood of a solution and to weight the respective ensemble member to estimate a better expected prediction.
The objective of the paper is to show the synergy between ensemble weather predictions and differential interferometric atmospheric correction. We demonstrate a new method first to compensate better for the atmospheric effect in DInSAR and second to estimate an improved numerical weather prediction (NWP) ensemble mean. Practically, a least squares fit of predicted atmospheric effects with respect to a differential interferogram is computed. The coefficients of this fit are interpreted as likelihoods and used as weights for the weighted ensemble mean. Finally, the derived weighted prediction has minimal expected quadratic errors which is a better solution compared to the straightforward best-fitting ensemble member. Furthermore, we propose an extension of the algorithm which avoids the systematic bias caused by deformations. It makes this technique suitable for time series analysis, e.g. persistent scatterer interferometry (PSI). We validate the algorithm using the well known Netherlands-DInSAR test case and first show that the atmospheric compensation improves by nearly 40% compared to the straightforward technique. Second, we compare our results with independent sea level pressure data. In our test case, the mean squared error is reduced by 29% compared to the averaged ensemble members with equal weights. An application demonstration using actual Sentinel-1 data and a typical test site with significant subsidence (Mexico City) completes the paper.Numéro de notice : A2015-858 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1016/j.isprsjprs.2015.09.004 Date de publication en ligne : 29/09/2015 En ligne : https://doi.org/10.1016/j.isprsjprs.2015.09.004 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=79240
in ISPRS Journal of photogrammetry and remote sensing > vol 109 (November 2015) . - pp 98 - 107[article]Boundary element and finite element coupling for aeroacoustics simulations / Nolwenn Balin in Journal of Computational Physics, vol 294 ([01/08/2015])
[article]
Titre : Boundary element and finite element coupling for aeroacoustics simulations Type de document : Article/Communication Auteurs : Nolwenn Balin, Auteur ; Fabien Casenave , Auteur ; François Dubois, Auteur ; Eric Duceau, Auteur ; Stefan Duprey, Auteur ; Isabelle Terrasse, Auteur Année de publication : 2015 Article en page(s) : pp 274 - 296 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique
[Termes IGN] méthode des éléments finisRésumé : (auteur) We consider the scattering of acoustic perturbations in the presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl–Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary. Validations against analytic, another numerical method and measurements on different test cases are presented. Numéro de notice : A2015-003 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1016/j.jcp.2015.03.044 Date de publication en ligne : 31/03/2015 En ligne : https://doi.org/10.1016/j.jcp.2015.03.044 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93241
in Journal of Computational Physics > vol 294 [01/08/2015] . - pp 274 - 296[article]
Titre : Les lignes géodésiques d'un tore Type de document : Guide/Manuel Auteurs : Abdelmajid Ben Hadj Salem, Auteur Editeur : Tunis [Tunisie] : République tunisienne. Ministère de l’Equipement et de l’Environnement Année de publication : 2015 Autre Editeur : Tunis : Office de la Topographie et de la Cartographie OTC Importance : 6 p. Note générale : bibliographie Langues : Français (fre) Descripteur : [Vedettes matières IGN] Géodésie
[Termes IGN] équation différentielle
[Termes IGN] ligne géodésique
[Termes IGN] résolution de problème
[Termes IGN] toreRésumé : (auteur)[Introduction] Dans cet article, nous proposons d’écrire les équations des géodésiques d'un tore, et de les résoudre. Note de contenu : 1. Introduction
2. Les équations différentielles des lignes géodésiques
3. Résolution du problème dans le cas généralNuméro de notice : 19753 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=84552 Documents numériques
en open access
Les lignes géodésiques d'un toreAdobe Acrobat PDF
Titre : Methods of Mathematical Modelling : Continuous Systems and Differential Equations Type de document : Guide/Manuel Auteurs : Thomas Witelski, Auteur ; Mark Bowen, Auteur Editeur : Springer International Publishing Année de publication : 2015 Importance : 324 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-3-319-23042-9 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes IGN] analyse mathématique
[Termes IGN] calcul différentiel
[Termes IGN] calcul variationnel
[Termes IGN] équation différentielle
[Termes IGN] équation linéaire
[Termes IGN] modèle mathématique
[Termes IGN] série de Fourier
[Termes IGN] variableRésumé : (éditeur) This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences. Note de contenu : Part I- Formulation of Models
1- Rate equations
2- Transport equations
3- Variational principles
4- Dimensional scaling analysis
Part II- Solution Techniques
5- Self-similar scaling solutions of differential equations
6- Perturbation methods
7- Boundary layer theory
8- Long-wave asymptotics for PDE problems
9- Weakly-nonlinear oscillators
10- Fast/slow dynamical systems
11- Reduced models for PDE problems
Part III- Case Studies
12- Modelling in applied fluid dynamics
EpilogueNuméro de notice : 25830 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel En ligne : https://doi.org/10.1007/978-3-319-23042-9 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95152 PermalinkMathématiques programme 2012 Term. [terminale] STI2D, Term. STL / Jean-Denis Astier (2012)PermalinkAnalysis of long-term GPS observations in Greece (1993-2009) and geodynamic implications for the Eastern Mediterranean / Michael D. Müller (2011)PermalinkFinite element method for solving geodetic boundary value problems / Z. Faskova in Journal of geodesy, vol 84 n° 2 (February 2010)PermalinkTransformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion / Bernd Richter in Journal of geodesy, vol 84 n° 1 (January 2010)PermalinkSingularity free formulations of the geodetic boundary value problem in gravity-space / G. Austen in Journal of geodesy, vol 83 n° 7 (July 2009)PermalinkPermalinkPermalinkAirborne LaCoste & Romberg gravimetry: a space domain approach / M. Abbasi in Journal of geodesy, vol 81 n° 4 (April 2007)PermalinkEtude des ondelettes multipôles de Poisson / Lâmân Lelégard (2007)Permalink