Efficient Stochastic Asymptotic-Preserving IMEX Methods for Transport Equations with Diffusive Scalings and Random Inputs

Shi Jin, Hanqing Lu, Lorenzo Pareschi
(14/3/2017 preprint arXiv:1703.03841)

For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that contain both uncertainties and multiple scales.

Structure preserving schemes for nonlinear Fokker-Planck equations and applications

Lorenzo Pareschi, Mattia Zanella
(1/2/2017, preprint arXiv:1702.00088)

In this paper we focus on the construction of numerical schemes for nonlinear Fokker-Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods here developed are second order accurate, they do not require any restriction on the mesh size and are capable to capture the asymptotic steady states with arbitrary accuracy.

A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation

S. Boscarino, L. Pareschi, G. Russo 
(16/1/2017 preprint arXiv:1701.04370)

In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the asymptotic behavior which can be either hyperbolic or parabolic.

On the asymptotic properties of IMEX Runge–Kutta schemes for hyperbolic balance laws

Sebastiano Boscarino, Lorenzo Pareschi
(5/9/2016 Journal of Computational and Applied Mathematics 316, 2017, 60–73)

Implicit–Explicit (IMEX) schemes are a powerful tool in the development of numerical methods for hyperbolic systems with stiff sources. Here we focus our attention on the asymptotic properties of such schemes, like the preservation of steady-states (well-balanced property) and the behavior in presence of small space–time scales (asymptotic preservation property).