Ph.D PROGRAMME » OVERVIEW

Sivaram Ambikasaran and Dipanjan Gope

Department of Computational & Data Sciences, IISc and Department of Electrical Communication Engineering, IISc

(a) Scattering from a penetrable medium

(b) Matrix structure for low-frequency scattering

The project will focus on fast direct solution of high-frequency electromagnetic scattering problems with applications to medium reconstruction. The most popular computational technique for solving the time-harmonic exterior scattering problem is the boundary element method, or the "method of moments". Despite the mathematically attractive feature of integral formulations, one of the challenges from a computational standpoint is that the resulting linear system (arising out of discretizing the boundary integral equation) is a dense and therefore computationally expensive (scaling asO(N3), where N is the number of unknowns) to solve. Constructing fast direct solvers for high frequency scattering problems is an open problem and has a wide range of practical applications. The overaching goal of this project will be on developing novel fast direct solvers, which scale as O(N log^a (N)), to solve high frequency scattering problems.

Preferred background:Linear Algebra, Electromagnetics, Computational science, Applied Mathematics.

Basic Qualifications:B.E./B.Tech. preferably in EE/ECE/CS/IT (or) B.Sc./M.Sc. (Mathematics/Physics)