Computational Physics, Mathematical and Computational Biology, Numerical Solution of Differential Equations, Scientific Computing
Ph.D., Brown University, 2003
M.S., Nankai University, China, 1999
Dr. Zhang works on developing efficient and high order accuracy numerical methods on structured and unstructured meshes for solving partial differential equations, and their applications in computational analysis of physical and biological problems. The numerical methods he is currently researching include weighted essentially non-oscillatory (WENO) finite difference / finite volume methods, fast sweeping methods, high order time-stepping exponential integrators such as implicit integration factor methods and their high dimensional implementation, discontinuous Galerkin (DG) finite element methods, sparse grid methods, etc., to solve mathematical models including hyperbolic conservation laws and convection dominated equations, stiff advection-reaction-diffusion equations, and Hamilton-Jacobi equations, etc. He is applying these numerical methods for studying problems in computational biology (e.g., morphogenesis and tissue patterning) and computational physics (e..g. interaction of shock waves with complex flows), high spatial dimension systems, etc.