My research is focused on the use of the level set method which is a numerical technique to the track moving interfaces. This method was developed originally by Osher and Sethian [survey book here]. And has been applied to a wide variety of problems like medical imaging, computational fluid dynamics, semiconductors, etc.
I am particularly focused on the use of these numeric techniques in the context of fluids and leaves simulations. In fluids simulations, the level set method allows us to track where the free surface of the fluid is at any given moment. In the case of leaf simulation, we have used the level set method to represent the boundary of the leaf while special speed functions are used to evolve the boundary in a way that it is possible to replicate the growth process of the leaf. Lately I have been interested in the numerical solutions of the Hamilton-Jacobi equations which are a generalization of the Level Set equation.
I also have experience with the Navier-Stokes equations which are usually used in conjunction with the level set method. My focus is on improving the numerical accuracy that can be achieved with the combination of these numerical methods.
My interaction with these techniques has shaped my research interests which include scientific computing, high-performance computing, and computer graphics.