Research Overview
My research has advanced the state of the art in scientific computing, particularly numerical methods and
computational continuum mechanics. In particular, a large part of my research involves the multi-physics
simulation of solids, fluids, and granular materials, especially through the enhancement of numerical methods
for partial differential equations (PDEs) in terms of the scope of material modeling, geometric complexity,
scale and resolution, efficiency, as well as stability, robustness, accuracy, and real-world predictivity. The majority of my research to date has focused on the Particle-In-Cell (PIC), the Material-Point-Method (MPM),
and the Finite Element Method (FEM) class of numerical methods. Not only have my research efforts yielded
innovations in relatively traditional areas such as geophysics and contact mechanics, but, more significantly,
they have also enabled modern applications, including virtual reality and high-fidelity visual effects for the
entertainment industry, surgical training technologies, computer vision and soft robotics, computational
fabrication, and exascale computational platforms.