Current Research Interests:

Efficient Meshfree Numerical Techniques: Method of Finite Spheres
In spite of the vast popularity of the traditional finite element/finite volume methods for the solution of a wide variety of boundary value problems on complex domains, there is a growing interest in the so-called “meshless” techniques over the past decade or so. This is because the generation of a good quality mesh requires considerable time and manual effort in any industrial problem. Moreover, when the structure to be modeled undergoes very large deformations or encounters changes in topology, as in dynamic crack growth, superplastic forming or machining, it has to be remeshed frequently during simulation. Numerical techniques that do not require a mesh for interpolation or integration purposes are therefore attractive.
    The method of finite spheres is a meshfree numerical technique that I have developed as part of my doctoral work. This technique shows considerable promise as being the next generation of CAD tools for the modeling and analysis of practical industrial problems in solid and fluid mechanics. However, considerable further research is required.

Multimodal Virtual Environments for Surgical Simulation:
I am interested in generating multimodal virtual environemnts for medical applications. Speciafically I am interested in laparoscopic surgical simulation. The challenge is to develop real time simulation tools for haptic as well as graphical rendering of soft tissues. I have developed a  specialized version of the method of finite spheres for this purpose.

CAD Tools for MEMS:
Micro Electromechanical Systems (MEMS) are tiny devices that can be built on a microchip. They have very complex geometries and multiple energy domains are coupled together in analysisg their response. I am interested in developing fast numerical tools for MEMS.