Uncertainty Quantification for Hyperbolic and Kinetic Equations [Hardcover]

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.

1 The Stochastic Finite Volume Method.- 2 Uncertainty Modeling and Propagation in Linear Kinetic Equations.- 3 Numerical Methods for High-Dimensional Kinetic Equations.- 4 From Uncertainty Propagation in Transport Equations to Kinetic Polynomials.- 5 Uncertainty Quantification for Kinetic Models in Socio-Economic and Life Sciences.- 6 Uncertainty Quantification for Kinetic Equations.- 7 Monte-Carlo Finite-Volume Methods in Uncertainty Quantification for Hyperbolic Conservation Laws.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).