Homogénéisation en milieu périodique... ou non

Une introduction

Xavier Blanc, Claude Le Bris (Autoren)

Buch | Softcover

XVIII, 488 Seiten

2023 | 1re �d. 2022
Springer International Publishing (Verlag)
978-3-031-12800-4 (ISBN)

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The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.

Cet ouvrage est une introduction pedagogique a la theorie de l'homogeneisation, et aux approches numeriques associees, pour la comprehension et la simulation des problemes a plusieurs echelles. La presentation est axee sur les differentes hypotheses possibles pour mettre en oeuvre la theorie, selon que le milieu ambiant a une geometrie periodique ou non. Le public vise est celui des cycles M et D des universites ainsi que celui des ecoles d'ingenieurs et formations equivalentes.

Xavier Blanc is Professor at Universite Paris Cite. His research has focused on the analysis of partial differential equations, and on numerical methods. Applications include superfluids, plasma physics, radiative transfer. Claude Le Bris holds positions as Civil Engineer-General and Research Scientist at Ecole des Ponts, as well as scientific leader of the MATHERIALS research team at Inria. He serves on several advisory boards of international research institutes and has extensive editorial responsibilities for book series and journals. His research has focused on mathematical analysis and numerical methods for partial differential equations, with contributions in several areas including the mathematics of computational chemistry and physics, multiscale problems and homogenization theory.

1 La dimension "zero".- 2 Homogeneisation en dimension 1.- 3 Dimension 2 : Les cas "simples" : abstrait ou periodique.- 4 Dimension 2 : Des cas explicites au-dela du periodique.- 5 Approches numeriques.- 6 Au-dela de l'equation de diffusion et sujets varies.

Erscheinungsdatum	14.02.2023
Reihe/Serie	Mathématiques et Applications
Zusatzinfo	XVIII, 488 p. 1 ill.
Verlagsort	Cham
Sprache	französisch
Maße	155 x 235 mm
Gewicht	764 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	approches multiéchelles • homogénéisation aléatoire • homogénéisation périodique • Homogenization theory • méthodes numériques multiéchelles • multiscale methods • nonperiodic homogenization • Théorie de l'homogénéisation • Théorie de l’homogénéisation
ISBN-10	3-031-12800-1 / 3031128001
ISBN-13	978-3-031-12800-4 / 9783031128004
Zustand	Neuware