Ph.D., Brown University, 2003
M.S., Nankai University, China, 1999
Numerical Differential Equations
Mathematical and Computational Biology
Applied Partial Differential Equations
High Order Numerical Methods for Partial Differential Equations on Complex Domains;
Computational & Mathematical Modeling and Analysis of Biological and Physical Problems.
Prof. Zhang works on developing efficient and high order accuracy numerical methods on structured and unstructured meshes for partial differential equations which include stiff advection-reaction-diffusion equations, hyperbolic conservation laws and convection dominated equations, and Hamilton-Jacobi equations; mathematical and computational biology for morphogenesis; and high accuracy numerical simulations of complex flow problems. The numerical methods he is currently researching include weighted essentially non-oscillatory (WENO) finite volume / finite difference methods, discontinuous Galerkin (DG) finite element methods, fast sweeping methods, and high order time-stepping implicit integration factor methods. In mathematical biology, he is currently working on computational analysis of tissue patterning in developmental biology, such as patterning in the zebrafish and Drosophila embryos, skeletal pattern formation in the vertebrate limb development, multi-stage cell lineages in tissue stratification during development of olfactory epithelium of mouse, tissue growth, and cell chemotaxis movement problems.
A list of Prof. Zhang's publications can be found here.