Assistant Professor

Research Interest: Computational methods for the solution of partial differential and integral equations, with emphasis on high-order efficient simulators 
Email: akasha[AT]iitk.ac.in
Ph: +91-512-259- 7880
Website: http://home.iitk.ac.in/~akasha
My primary research interests are in the area of numerical methods for partial differential equations and integral equations. More specifically, I specialize in high order efficient numerical schemes for solutions of such equations. In particular, my research work belongs to the field of computational electromagnetics and acoustics and deals with efficient high-order integral equation methods for surface and volumetric scattering in two and three dimensions. The main goal of computational electromagnetics and acoustics is to design and implement numerical schemes that can be used to efficiently simulate electromagnetic and acoustic wave interactions with complex material structures. Encompassing numerical methods for wave propagation and scattering, inverse problems and geometrical optics, computational electromagnetics and acoustics represent a broad and important area of present day computational science. Its spectacular growth in the past decades, largely enabled by concomitant developments in the computer industry, was primarily triggered by the increasing spectrum of its applications. Indeed, today applications are found in communications (transmission through optical fiber lines or wireless communication), remote sensing and surveillance (radar and sonar systems), geophysical prospecting, materials science and biomedical imaging (optical coherence tomography), to name a few.

Assistant Professor

Research Interests: Homogenization and Variational Methods for PDE's, Elliptic PDE's, Optimal controls
Email: tmk[AT]iitk.ac.in
Ph:+91-512-259-7911
Website: http://home.iitk.ac.in/~tmk
The theory of homogenization is, in a nut-shell, the asymptotic analysis of a system. A layman motivation towards homogenization can be given from the material science point of view. It is a mathematical concept that incorporates the study of the macroscopic behaviour of a composite medium through its microscopic properties. The known and unknown quantities in the study of physical or mechanical processes in a medium with microstructure depend on a small parameter $\varepsilon = \frac{l}{L}$, where $L$ is the macroscopic scale length of the dimension of a specimen of the medium and $l$ is the characteristic length of the medium configuration. The study of the limit, as $\varepsilon\rightarrow 0$, is the aim of the mathematical theory of homogenization. The case $\varepsilon\rightarrow 0$ is important as a tool for numerical computations. Over the time, the theory of homogenization has found application in various branches. One of them being Shape optimization. Simply put, one may be interested in finding the optimal shape of a body that will have, for instance, maximal conductivity, rigidity etc. All these physical problems end up as a PDE with rapidly oscillation coefficients.