Plenary Speakers

Irene Gamba
University of Texas-Austin

Title: Conservative Solvers for Collisional Kinetic Boltzmann and Landau-Poisson Systems

Abstract: These computational models are at the core of collisional plasma theories. In particular we will discuss several aspects of conservative solvers for the kinetic transport equations of particle interactions, that involve either linear or non-linear Boltzmann as well as the non-linear Landau equations, by means of stagger conservative DG schemes for the transport part and DG or spectral solvers for the collisional part, linked by a projection method that is conservative.
In addition we will discuss the computational aspects of boundary layer formation due to rough boundary effects for
insulating conditions.

Weizhang Huang
University of Kansas

Title: A New Implementation of the MMPDE Moving Mesh Method and Applications

Abstract: The MMPDE moving mesh method is a dynamic mesh adaptation method for use in the numerical solution of partial differential equations. It employs a partial differential equation (MMPDE) to move the mesh nodes continuously in time and orderly in space while adapting to evolving features in the solution of the underlying problem. The MMPDE is formulated as the gradient flow equation of a meshing functional that is typically designed based on geometric, physical, and/or accuracy considerations. In this talk, I will describe a new discretization of the MMPDE which gives the mesh velocities explicitly, analytically, and in a compact matrix form. The discretization leads to a simple, efficient, and robust implementation of the MMPDE method. In particular, it works for convex or nonconvex domains and is guaranteed to produce nonsingular meshes. Some applications of the method will be discussed, including mesh smoothing (to improve mesh quality), generation of anisotropic polygonal meshes, and the numerical solution of the porous medium equation and the regularized long-wave equation.

Paul Martin
Colorado School of Mines

Title: Solving the Wave Equation: Acoustic Scattering in the Time Domain

Abstract: Transient acoustic waves are generated or scattered by an obstacle. This leads to initial-boundary value problems for the wave equation. Recent studies usually assume that solutions are smooth. However, many interesting physical problems lead to non-smooth solutions: there are moving wavefronts. These situations are usually handled by seeking weak solutions, but care is needed to ensure that constraints imposed by the underlying continuum mechanics are respected. We investigate some of the consequences, with a focus on the benchmark problem of scattering by a sphere.

Robert Pego
Carnegie Mellon University

Title:  Euler Sprays and Optimal Transportation

Abstract: 

We describe a striking connection between Arnold's least-action principle for incompressible Euler flows and geodesic paths for Wasserstein distance. A connection with a variant of Brenier's relaxed least-action principle for generalized Euler flows will be outlined also.  This is joint work with Jian-Guo Liu and Dejan Slepcev.