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Uncertainty Quantification for Hyperbolic and Kinetic Equations (SEMA SIMAI Springer Series Book 14) by Jingwei Hu; Shi Jin is a book available to read on EtoBox.

What is Uncertainty Quantification for Hyperbolic and Kinetic Equations (SEMA SIMAI Springer Series Book 14) about?

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients, initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic models have important engineering and industrial applications. In this article we survey recent efforts in the study of kinetic equations with random inputs, including their mathematical properties such as regularity and long-time behavior in the random space, construction of efficient stochastic Galerkin methods, and handling of multiple scales by stochastic asymptotic-preserving schemes. The examples used to illustrate the main ideas include the random linear and nonlinear Boltzmann equations, linear transport equation and the Vlasov-Poisson-Fokker-Planck equations. Introduction Kinetic equations describe the non-equilibrium dynamics of a gas or system comprised of a large number of particles using a probability density function. In multiscale modeling hierarchy, they serve as a basic building block that bridges atomistic and continuum models. On one hand, they are more efficient (requiring fewer degrees of freedom) than molecular dynamics; on the other hand, they provide reliable informatio

Author

Jingwei Hu; Shi Jin

Publisher

Springer International Publishing : Imprint : Springer

Published

2017

Language

EN

ISBN

9783319671109

Subjects

Mathematics, Engineering, Science