Research interests: Time integration of PDEs, Numerical analysis and scientific computing, Computational and applied mathematics, Meteorological/Numerical weather prediction models, Visual computing (elastodynamic models), Multirate methods for multi-physic PDEs, Geometric numerical integration, Mesh-free methods using RBFs
My research interests lie in the area of applied mathematics, primarily in time integration of partial differential equations (PDEs), numerical analysis and scientific computing. A large portion of my research has been devoted to the construction, analysis, and implementation of fast, robust and accurate numerical methods for the time integration of multi-physics, multi-rate PDEs arising in engineering and natural sciences. Currently, I am also developing new numerical techniques for meteorology, numerical weather prediction, computational fluid dynamics, biological systems, combustion, and real-time simulations of complex systems used in visual computing. I am also interested in geometric numerical integration, splitting methods, and scattered data approximation/interpolation problems using mesh-free methods.