Imaginative use of computational mathematics can provide insight into some of the most difficult questions about nonlinear partial differential equations. Among these are problems of transonic aerodynamics and plasma physics that appear superficially not to be well posed, but become so when weak solutions are introduced correctly. Numerical analysis of the weak solutions is a major challenge to mathematics. The investigator conducts research in this area of applied mathematics in collaboration with both graduate students and postdoctoral assistants. This project is concerned with the numerical solution of nonlinear partial differential equations, and the principal results are codes that work effectively on the latest generation of computers and have significant technological applications. Emphasis is placed on research in high performance computing that brings to bear on previous algorithms the advantages of parallel architecture. The investigator collaborates with mathematicians, physicists and engineers, aiming at successful transfer of technology to industry. A principal area of study is the problem of transport in magnetic fusion energy research. This phenomenon can be modeled by a Monte Carlo method that provides good estimates of the transport.
