Research

Brief description:

My research lies in the area of applied and computational mathematics, focusing on multiscale modeling and structure-preserving schemes. I have built interdisciplinary collaborations with mathematicians, physicists and engineers in the following areas:

(1) bottom-up atomistic-to-continuum (AtC) methods for modeling crystalline materials;

(2) top-down quasi-nonlocal methods for studying the nonlocal-to-local (NtL) problems;

(3) stable schemes for solving stochastic dynamical systems, with applications to random matrices ensembles and the kinetic theory of shock clustering with coarse graining;

(4) high order positivity-preserving local discontinuous Galerkin schemes for solving the Patlak-Keller-Segel chemotaxis systems with blow-up solutions;

(5) high order energy-conserved splitting finite-difference time-domain (FDTD) methods for the Maxwell's equations in large-scale fields and long-time duration.