Faculty & Staff Resources

My primary research interests are: 1) Inverse problems- My research on inverse problems is primarily in context of medical imaging and fluid flows. In the field of medical imaging, I develop frameworks for efficient reconstruction of physical properties arising in various imaging modalities such as X-ray, Computed Tomography, Ultrasound imaging, Hybrid imaging. This research will help in more accurate detection of cancers and tumors. For fluid flows, I use optical flow tracer techniques to determine the fluid velocities. Such a method has applications in ball-tracking, cloud motion. 2) Optimal control of stochastic processes: I develop PDE frameworks for optimal control of stochastic processes leading to Liouville and Fokker Planck equations. Such frameworks are theoretically and computationally very extensive and robust and the methods involved are challenging yet exciting and are particularly important in devising new and effective treatments for cancer. 3) Discontinuous Galerkin schemes for fluid flows- I develop higher order TVD DG schemes, mainly in the finite element framework, for Euler and Navier-Stokes equations and apply it to various problems arising in medical sciences. 4) Shape optimization- I am interested in shape optimization problems related to placement of obstacles to optimize the Dirichlet eigenvalues. Such methods have applications in design of musical instruments and optimal accelerator cavities, building non-resonant structures.