|Univ. of Wisconsin-Madison/Shanghai Jiao Tong Univ.
Kinetic equations have uncertain inputs, such as the scattering kernels, initial or boundary data.
In this talk we will study the generalized polynomial chaos (gPC) approach to such kinetic equations with multiple time or space scales, and show that they can be made asymptotic-preserving, in the sense that the gPC scheme preserves various asymptotic limits in the discrete space.
This allows the implemention of the gPC methods for these problems without numerically resolving (by space, time, and gPC modes) the small scales. We also give a fast gPC algorithm for the Boltzmann equation with uncertainties in its collision kernel, initial or boundary data.