Faculty & Staff Resources

My primary research interests are:

1) PDE optimal control in health sciences: (a) In the field of medical imaging, I have developed optimal control frameworks for efficient reconstruction of physical properties arising in various imaging modalities such as electrical impedance tomography, current density impedance imaging, photoacoustic tomography and other hybrid imaging modalities that are modeled by partial differential equations (PDE).
(b) In fluid flows, I have used optical flow tracer techniques to determine the fluid velocities. Such a method has applications in motion tracking and cloud motion.
(c) I have developed PDE frameworks for optimal control of stochastic processes leading to Liouville and Fokker Planck equations, that model collective motion and traffic flows. Such frameworks are theoretically and computationally very extensive and robust.
(d) I am currently working on using PDE optimal control methods to devise efficient treatments of cancer. Such a process involves modeling the cancer dynamics using PDEs known as quantitative systems pharmacology (QSP) and estimating parameters using optimal control techniques.
2) Discontinuous Galerkin schemes for fluid flows- I have developed higher order TVD DG schemes, mainly in the finite element framework, for conservation laws.
3) Shape optimization- I have worked on 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.