Research

My original background is in Numerical Analysis of methods used to compute approximate solutions of partial differential equations. I have since become more motivated by industrial applications and have developed a skill in mathematical modelling.

I have an ongoing interest in the development of numerical methods for geometric motion (curvature motion and surface diffusion for example) of curves in 2D and surfaces in 3D. These geometric problems are idealizations of some Material Science models. They become more difficult to solve numerically when junctions are present in the curve (or surface) networks. Much of my work in this area has been in an idealized setting, although some recent models developed by Keith Promislow show that geometric motion can also arise in models of the pore structure in fuel cell membranes (or more generally, in functionalized polymer materials). I have recently become interested in adaptive time and space methods for phase field versions of these geometric models working with Keith Promislow and others at Michigan State University.

Another problem that is of interest to me is the computational capturing of two phase zones in porous media. There are underyling questions of how to handle the degenerate parabolic features of such models numerically and analytically. Interest in this problem has also led to the development of some novel methods to compute a general class of steady free boundary value problems.

I am still interested in some theoretical questions in Numerical Analysis and have some recent results in the analysis of errors from piecewise uniform grids used to approximate smooth solutions. I have also found a particularly simple setting to describe known results on the errors from a large class of projection methods for incompressible flow. I am considering writing a longer review on the subject of Asymptotic Error Analysis, the technique used to obtain these results and many other results from early in my career.

In the period 1998-2008, my main research activity was fuel cell modelling. In general terms, the work focussed on the development of computational design tools for the fuel cell industry. We developed models describing various aspects of unit cell operation (transport and chemical processes) and investigated coupling effects of the unit cells in stack operation. Corresponding computational models were developed. This was a larger project done in collaboration with the company, Ballard Power Systems, and the MITACS NCE. I am still interested in fuel cell modelling although I am also interested in pursuing other industrial projects with local industries.

Slides from some of my latest talks are listed at the bottom of the page.

Some recent preprints

Former Students

I celebrate the achievements of graduate students, post-doctoral fellows, research associates, and undergraduate summer students I supervised. It was a pleasure working with you, best of luck to you all!

Selected Publications

Some selected publications I'm proud of for various reasons:

Some recent talks