PhD Defense: "Higher Order Numerical Discretization Methods on Scattered Grids"

Karthik Jayaraman Raghuram

July 22nd (Friday), 3:30pm
Harold Frank Hall (HFH), Rm 4164

Beginning with the suppression of Runge Phenomenon which arises in equispaced polynomial interpolation, we present the Minimum Sobolev Norm interpolation technique which we generalize to produce Finite Difference (MSNFD) type weights for differential operators. It is shown that these weights yield higher order approximations to these operators with increasing stencil sizes, and that the idea generalizes to non-uniform grids easily. Thus perhaps for the first time, a systematic means of producing higher order FD weights on irregular grids is discussed. After the basic theoretical discussions on the interpolation process and local convergence of weights, the idea of solving elliptic PDEs using these MSNFD weights is discussed. A set of extensive numerical experiments on standard second order problems as well as the Exterior Laplace problem and the biharmonic equations are discussed. Finally the short-comings associated with solving ill-conditioned problems such as the biharmonic equation and the scattering problem are presented. The idea of lifting using Div-Curl systems is presented as a possible future work and extension.

About Karthik Jayaraman Raghuram:

Karthik Jayaraman Raghuram obtained his Masters degree in Electrical and Computer Engineering majoring in Communications, Controls and Signal Processing in 2008 from UCSB. Prior to pursuing graduate studies, he was with Texas Instruments India, Bangalore working on embedded multimedia systems. He obtained his Bachelors degree in Electronics and Communications from PSG College of Technology, Coimbatore, India. His areas of interest include Signal Processing, Numerical Analysis, Applied Linear Algebra, Scattering and Numerical Methods for PDEs.

Hosted by: Professor Shivkumar Chandrasekaran