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.

- "Mathematical Modeling of Magnetic Field Profiles in Superconductors" with Michael Lindstrom and Rob Kiefl, accepted in the Journal of Engineering Mathematics.
- "High accuracy solutions to energy gradient flows from material science models," with Andrew Christlieb, Jaylan Jones, Keith Promislow, and Mark Willoughby, accepted in the Journal of Computational Physics.
- Meander and Pearling of Single-Curvature Bilayer Interfaces, Doelman, Hayrapetyan, Promislow and Wetton, submitted to SIAM Journal of Applied Mathematics.
- A Comparison of Fick and Maxwell-Stefan Diffusion Formulations in PEMFC Cathode Gas Diffusion Layers with Michael Lindstrom, submitted to the Journal of Power Sources.
- Optimal Covering Points and Related Problems," with Justin Tzou, submitted to the Canadian Applied Mathematics Quarterly.
- Investigation into Fusion Feasibility of a Magnetized Target Fusion Reactor," with Michael Lindstrom and Sandra Barsky submitted to the Journal of Fusion Energy.
- Fingering phenomena in immiscible displacement in porous media flow with Iain Moyles, submitted to the Journal of Engineering Mathematics.

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!

- Sandra Barsky, currently a research scientist at General Fusion.
- Lloyd Bridge, now a Lecturer at the University of Swansea.
- Atife Caglar, now a faculty member at the University of Wisconsin - Green Bay.
- Paul Chang, now working at Microsoft.
- Roger Donaldson, now an Industrial Mathematics Consultant in Vancouver.
- Brieuc Gilles.
- Ana Granados.
- Natalia Kouzniak, now a senior lecturer at SFU Surrey.
- Margaret Liang.
- Ricardo Martins.
- Arian Novruzi, now a faculty member at the University of Ottawa.
- Zhenguo Pan.
- Steve Ruuth, now a faculty member at SFU.
- John Stockie, now a faculty member at SFU.
- Cyrus Towfighi, now an engineer at Enbridge.
- Justin Tzou, currently a PDF at Dalhousie.
- Cheng Zhang.

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

- Wetton and Brooke, "One-way wave equations for seismo acoustic propagation in elastic wave guides," J. Acoust. Soc. Amer. 87, 624-632 (1990).
- Ascher, Ruuth, and Wetton, "Implicit-Explicit Methods for Time-Dependent PDE's," SINUM 32, 797-823 (1995).
- Bronsard and Wetton, "A Numerical Method for Tracking Curve Networks Moving with Mean Curvature Motion," JCP 120, 66-87 (1995).
- Wetton, "Error Analysis for Chorin's original fully discrete projection method and regularizations in space and time", SINUM 34, 1683-1697 (1997).
- Stockie and Wetton, "Analysis of stiffness of the immersed boundary method and implications for time-stepping schemes," JCP 154, 41-64 (1999).
- Berg, Promislow, St-Pierre, Stumper, Wetton, "Water Management in PEM fuel cells," Journal of the Electrochemical Society 151, A341-A353 (2004).
- Donaldson and Wetton, "Solving Steady Interface Problems Using Residual Velocities," IMA Journal of Applied Mathematics 71, 877-897 (2006).
- Chang, Kim, Promislow and Wetton, "Reduced Dimensional Computational Models of Polymer Electrolyte Membrane Fuel Cell Stacks," JCP 223, 797-821 (2007).
- Bridge and Wetton, "A mixture formulation for numerical capturing of a two-phase/vapour interface in a porous medium," JCP 225, 2043-2068 (2007).
- Promislow and Wetton, "PEM Fuel Cells: A Mathematical Overview" (invited review article) SIAM Journal of Applied Mathematics 70, 369 (2009).

- Modelling fuel cells in start-up and reactant starvation conditions at the IPAM workshop on Batteries and Fuel Cells, November 7, 2013 and previously in the Industrial Mathematics Session, CAIMS annual meeting, June 20, 2013.
- Successes and Challenges of Industrial Mathematics, in the IAM semninar, September 16, 2013 and also a Public Lecture at the CAIMS annual meeting, June 16, 2013.
- Lecture notes, for the summer school on Microstructure Evolution and Dynamics at the Technion in Israel, August 25-29, 2013. The MATLAB codes referred to in the notes can be found at the following links: 1D Cahn Hilliard code (direct solve for implicit time steps) and 2D Cahn Hilliard code (preconditioned conjugate gradient solve).
- A general framework for high accuracy solutions to energy gradient flows from material science models in the UBC SCAIM seminar, January, 2013; a (shorter) version given subsequently at the CAIMS annual meeting in the Canadian Symposium on numerical Analysis and Scientific Computing June, 2013. Previously given at the SIAM annual meeting in Minneapolis July, 2012; at the FACM meeting in Newark, May, 2012; the SFU CRC Seminar, September, 2011; and at the BCAM (Spain) seminar, November 14, 2011.
- Asymptotic Error Analysis in the PIMS-Shell Lunchbox series in Calgary, April 25, 2013. A different version was given in the University of Hawaii at Manoa Mathematics Department Seminar, February 24, 2012.
- IAM directorship interview open forum presentation, March 13, 2013.
- Jobs in "Industry" PIMS PDF Job Forum, October, 2012.
- Workshop on fuel cell modelling, given at the Polytechnic University of
Catalunya, October, 2011. Hand written notes for the lectures:
part I,
part II,
part III.
Matlab code:
- For exercise #1: fni.m, fni_test.m
- Exercise #4: unit.m
- Exercise #12: stack.m

- Two Phase Transport in Porous Media at the CRM (Spain) CAMP seminar, October 19, 2011; also at the BCAM (Spain) seminar, November 14, 2011.
- Asymptotic Error Analysis, a series of four lectures given at the Centre of Mathematical Modelling and Scientific Computing at the National Chiao Tung University in Taiwan, December, 2010, part I and part II. Some additional handwritten notes can be found here.
- Approximating the arctan function (notes for a blackboard talk) in the UBC Undergraduate Mathematics Colloquium, September 2010. Also given at the National Chiao Tung University in Taiwan, December, 2010.
- Asymptotic error analysis of projection methods in the UBC SCAIM seminar, September, 2010 and also in the Scientific Computing session of the CAIMS annual meeting, St. John's, July, 2010.
- Mathematical Modelling of Hydrogen Fuel Cells at the CAIMS annual meeting, St. John's, July, 2010. I also gave this talk at the SIAM Materials Meeting, Philadelphia, May, 2010. A slightly different version was given at the PIMS Summer School on Computer Models and Geophysical Risk Analysis in August, 2010.
- Asymptotic error analysis on piecewise uniform grids in the Fluids Session of the CAIMS annual meeting, St. John's, July, 2010.