Professor Timothy Warburton has a B.A. and M.A. in Mathematics from Oxford University, and an Sc.M and Ph.D. in Applied Mathematics from Brown University. He is currently Associate Professor in the Department of Computational and Applied Mathematics at Rice University.
His research interests include high-performance computing, discontinuous Galerkin (DG) methods, complete radiation boundary conditions for wave problems, among others. In DG methods, he has worked with various collaborators to develop practical numerical methods for time-dependent electromagnetics, acoustics, and fluid dynamics. He is particularly interested in improving the efficiency and robustness of these methods through the use of local time-stepping methods, artificial viscosity for shock capturing, pre-codnitioners, and convergent adaptive schemes.
These methods are described in his recent book:
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis and Applications. J. S. Hesthaven and T. Warburton. Vol. 54, Springer Texts in Applied Mathematics, Springer-Verlag: New York, 2008.
- A. Kloeckner, T. Warburton, J.S. Hesthaven, Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method, Mathematical Modelling of Natural Phenomena, 6 (3): 57-83 (2011) doi:10.1051/mmnp/20116303
- A. Kloeckner, T. Warburton, J. Bridge, and J.S.Hesthaven, High-Order Discontinuous Galerkin Methods on Graphics Processors, Journal of Computational Physics, 228 (21): 7863-7882 (2009) doi:10.1016/j.jcp.2009.06.041
- Allan P. Engsig-Karup, Jan S. Hesthaven, Harry B. Bingham, and T. Warburton, DG-FEM Solution for Nonlinear Wave-structure Interaction Using Boussinesq-type Equations, Coastal Engineering, 55 (3): 197-208 (2008) doi:10.1016/j.coastaleng.2007.09.005