Director of Graduate Studies
Ph.D., State University of New York at Stony Brook, 2002
M.S., Beijing University of Aerospace and Astronautics, China, 1997
Numerical Differential Equations
Mathematical and Computational Biology
Prof. Xu's recent research interests have been on the numerical methods for solving partial differential equations, specially for equations related to convection dominated flow phenomena (such as Euler equations and Navier-Stokes equations), scientific computing, and computational math-biology. He is currently working on:
- Blood flow model.
- Conservative front tracking.
- Modeling blood thrombus formation in the blood vessel with a multiscale model which couples stochastic discrete Cellular Potts Model with continuum PDE model such as Navier-Stokes equations for the blood flow and convection-diffusion-reaction equations for coagulation reactions.
- Modeling P. aeruginosa (a bacterium) swarm pattern formation. The model couples thin liquid film model with stochastic discrete off-lattice model for individual cells.
- Discontinuous Galerkin methods for solving conservation laws.