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© 2017

Uncertainty Quantification for Hyperbolic and Kinetic Equations

  • Shi Jin
  • Lorenzo Pareschi

Benefits

  • The first-ever book on kinetic equations

  • Presents several different approaches by top authors in the field

  • Offers an up-to-date survey of current applications, including examples in the social sciences

Book

Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 14)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Rémi Abgrall, Svetlana Tokareva
    Pages 1-57
  3. Guillaume Bal, Wenjia Jing, Olivier Pinaud
    Pages 59-92
  4. Heyrim Cho, Daniele Venturi, George Em Karniadakis
    Pages 93-125
  5. Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella
    Pages 151-191
  6. Jingwei Hu, Shi Jin
    Pages 193-229

About this book

Introduction

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.


Keywords

Kinetic equations Hyperbolic equations Uncertainty quantification Galerkin methods Monte Carlo methods

Editors and affiliations

  • Shi Jin
    • 1
  • Lorenzo Pareschi
    • 2
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di FerraraFerraraItaly

About the editors

Shi Jin is a Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin-Madison. He earned his B.S. from Peking University and his Ph.D. from the University of Arizona. His research fields include computational fluid dynamics, kinetic equations, hyperbolic conservation laws, high frequency waves, quantum dynamics, and uncertainty quantification – fields in which he has published over 140 papers. He has been honored with the Feng Kang Prize in Scientific Computing and the Morningside Silver Medal of Mathematics at the Fourth International Congress of Chinese Mathematicians, and is a Fellow of both the American Mathematical Society and the Society for Industrial and Applied Mathematics (SIAM).

Lorenzo Pareschi is a Full Professor of Numerical Analysis at the Department of Mathematics and Computer Science, University of Ferrara, Italy. He received his Ph.D. in Mathematics from the University of Bologna, Italy and subsequently held visiting professor appointments at the University of Wisconsin-Madison, the University of Orleans and University of Toulouse, France, and the Imperial College, London, UK. His research interests include multiscale modeling and numerical methods for phenomena described by time dependent nonlinear partial differential equations, in particular by means of hyperbolic balance laws and kinetic equations. He is the author/editor of nine books and more than 110 papers in peer-reviewed journals.

Bibliographic information

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