My research interests are, broadly speaking, applied and computational science with a goal towards solving pressing problems of today. We solve and investigate applied problems and application driven basic problems using a plethora of theoretical and numerical tools. We also explore the possibility of useful changes in various applied fields by developing new as well as by making use of existing algorithms, applicable knowledge and software.
Specific research interests are in fluid mechanics of simple and complex fluids, interface problems, numerical methods, scientific computing, fast algorithms, inverse problems, and many other classical areas of applied mathematics. Such problems arise in host of important areas such as petroleum engineering, health and biological sciences, earth and environmental sciences, space exploration, neuroscience and cognitive science, and so on. With over three decades of experience in applied, engineering and computational mathematics, we are ready to help solve pressing problems of tomorrow in collaboration with colleagues, undergraduate and graduate students, and postdoctoral scholars. In application areas, we are exploring ways to develop efficient and fast methods for multiphase flows, in particular porous media flows that arise in the context of chemical enhanced oil recovery. We are also interested in high Reynolds number multi-phase flows. We are working on the development, implementation and application of analysis based fast boundary integral type methods. Another area of current interest is in control of instabilities in fluid flows such as in mixing, viscous fingering and channeling. We are also interested in the development of probabilistic methods and techniques including use of data driven and Bayesian scientific computing, reduced order modeling, uncertainty quantification, deep learning and other modern numerical methods.