Research

My research interests lie in the area of numerical analysis and computational and applied mathematics, primarily in time integration of partial differential equations (PDEs). 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. I am also interested in geometric numerical integration, splitting methods, and scattered data approximation/interpolation problems using mesh-free methods.  I have also developed and am further 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.

Current Research:   My research is currently supported by NSF grant awards DMS–2012022 and DMS–2309821.

              

My significant contributions have been in the following themes:

 Below are some simulation videos and pictures resulted from our work for applications in Visual Computing (computer animation):

Simulation of hair during a woman’s head shake carried out with our method (highlighted by Technical Papers Preview Trailer, SIGGRAPH 2017)

 

Simulation of a frontal crash of a car into a wall

Simulation of an oscillating coil spring

Past Research: