Networks and Computational Partial Differential Equations

Participants photo Aims and scope. The studies follow two research lines:

  • Graph drawing using subspace correction methods for eigenvalue computations;
  • Development of monotone discretizations and fast solvers for convection diffusion equations.

The two projects involve numerical models represented by weighted (un)-directed graphs. The goals are to understand and later develop and implement prototypes of multilevel algorithms for graph drawing and other network analysis and solution of discretized convection diffusion equations.

Two reports about the research are found by visiting the report on Graph drawing or the report on monotone FE discretizations for convection-diffusion equations.

The projects are organized and led by professor Ludmil Zikatanov and John Urschel from Department of Mathematics at Penn State. The undergraduate students involved in the research are Maureen Gallagher, Bradley Thompson, Dana Tobin, and Colleen Tygh.

Support.The project is supported by research funds provided by Ludmil Zikatanov, Professor of Mathematics, Jinchao Xu, Pentz Professor of Science, and by the Department of Mathematics, Penn State.

Media. An article in the USA TODAY (July 24, 2013) about John Urschel mentioned this undergraduate summer research. The link to the article is found here (once there, click on the photo to enlarge it and reveal its caption).