Research Accomplishments

My research focuses on numerical methods for partial differential equations (PDEs) and scientific computing. I have been working on several areas including new Eulerian techniques to approximate high frequency asymptotic solutions to wave phenomena and their related inverse problems, numerical methods for interracial motions, variational and statistical methods for image processing, and Eulerian method for nonlinear dynamical systems visualization. Results from these projects are useful in many applications. For example, accurate methods for interface motions are important for modeling multi-phase or spiral crystal growth; efficient algorithms in those inverse problems can benefit seismic imaging, underwater acoustics and oil exploration; efficient numerical techniques in visualizing a dynamical system will help identify special structure in the flow; new image processing techniques can advance the technologies in medical imaging. In the following sections, I will briefly describe my accomplishments in each of these projects.