Spectral methods for nonlinear evolutionary systems in materials science and fluid dynamics.
Spectral element methods and sparse grids with applications in finance.
The nodal discontinuous Galerkin method for convection dominated problems.
Parallelized spectral methods on graphics processing units.
Numerical optimization with the spectral discretization.
Publications
Jinhae Park, Feng Chen, and Jie Shen. Modeling and simulation of switchings in ferroelectric liquid crystals, Discrete and Continuous Dynamical Systems, Series A, 26 (2010) 1419--1440. Link.
Feng Chen, Jie Shen, and Haijun Yu. A new spectral element method for pricing European options under the Black-Scholes and Merton jump diffusion models, Journal of Scientific Computing, (2011): 10.1007/s10915-011-9556-5. Link.
Feng Chen and Jie Shen. Efficient spectral-Galerkin methods for systems of coupled second-order
equations and their applications, Journal of Computational Physics. (2012): 10.1016/j.jcp.2012.03.001. Link.
Feng Chen and Jie Shen. Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems, (accepted) Communications in Computational Physics.