The ultimate goal of my research is to accurately and efficiently compute solutions to nonlinear partial differential equations arising in scientific and industrial settings.
Recently, I have investigated time evolution methods for PDEs with discontinuous or nonsmooth solutions. I have also developed efficient, robust methods for evolving arbitrary networks of interfaces according to interface geometry and on external physics. These methods have a wide range of application areas including the design of more robust software for computer vision, the removal of bottlenecks in rendering images and the study of materials and multi-phase fluid flows. My other main research interests include the development and analysis of implicit-explicit methods for time-dependent partial differential equations and the molecular dynamics simulation of sonoluminescence.