This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two- level structure, consisting ...

Two-fluid ideal magnetohydrodynamics (MHD) equations are a generalized form of the ideal MHD equations in which the electrons and ions are considered as separate species. A ma jor difficulty in the design of efficient numerical algorithms for these equations is the presence of stiff source terms, particularly for realistic charge to mass ratio (i.e. low Larmor radius). Following [9, 10, 11], we design implicit-explicit (IMEX) Runge-Kutta ...

We investigate a qualitative method for imaging acoustic obstacles in two and three dimensions by boundary measurements. The imaging scheme makes use of the hypersingular point sources. Rigorous mathematical justification of the imaging method is established, and numerical experiments are presented to illustrate the effectiveness of the proposed imaging scheme.

We present a shock-capturing space-time Discontinuous Galerkin method to approximate all speed flows modeled by systems of conservation laws with multiple time scales. The method provides a very general and computationally efficient framework for approximating such systems on account of its ability to incorporate large time steps. Numerical examples ranging from computing the incompressible limit (robustness with respect to Mach number) ...