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 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.

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 and Chemical Reaction models. They become more difficult to solve numerically when junctions are present in the curve (or surface) networks or there are nonlocal terms in the geometric motion. 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.

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. My expertise in electrochemical system modelling has found recent outlets in generalized dialysis systems and lithium ion battery packs. These latter projects are driven by collaboration with researchers in the Chemical and Biological Engineering Department.

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

- A Numerical Framework for Singular Limits of a Class of Reaction Diffusion Problems (revised version), accepted in JCP.

- Christlieb, Jones, Promislow, Wetton and Willoughby,
"High accuracy solutions to energy gradient flows from material science models",
Journal of computational physics 257, 193-215 (2014).
- 1D Cahn Hillard video
- 2D Cahn Hillard video
- 2D Functionalized Cahn Hillard video
- 2D vector Cahn Hillard video
- The MATLAB code for the 2D Cahn-Hilliard simulation in the paper, shown in the video above.

I value the achievements of graduate students, post-doctoral fellows, research associates, and undergraduate summer students I supervised. It was a pleasure working with 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.
- Michael Lindstrom, now an Assistant Adjunct Professor (Program in Computing) at UCLA.
- Ricardo Martins.
- Iain Moyles, now a research assistant at Limerick, Ireland.
- 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 UBC.
- Mark Willoughby.
- 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," Journal of the Acoustical Society of America 87, 624-632 (1990).
- Ascher, Ruuth, and Wetton, "Implicit-Explicit Methods for Time-Dependent PDE's," SIAM Journal on Numerical Analaysis 32, 797-823 (1995).
- Bronsard and Wetton, "A Numerical Method for Tracking Curve Networks Moving with Mean Curvature Motion," Journal of Computational Physics 120, 66-87 (1995).
- Wetton, "Error Analysis for Chorin's original fully discrete projection method and regularizations in space and time", SIAM Journal on Numerial Analysis 34, 1683-1697 (1997).
- Stockie and Wetton, "Analysis of stiffness of the immersed boundary method and implications for time-stepping schemes," Journal of Computational Physics 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," Journal of Computational Physics 223, 797-821 (2007).
- Bridge and Wetton, "A mixture formulation for numerical capturing of a two-phase/vapour interface in a porous medium," Journal of Computational Physics 225, 2043-2068 (2007).
- Pan and Wetton, "A numerical method for coupled surface and grain boundary motion," European Journal of Applied Mathematics 19, 311-327 (2008).
- Promislow and Wetton, "PEM Fuel Cells: A Mathematical Overview" (invited review article) SIAM Journal of Applied Mathematics 70, 369 (2009).
- Christlieb, Jones, Promislow, Wetton and Willoughby, "High accuracy solutions to energy gradient flows from material science models", Journal of computational physics 257, 193-215 (2014).
- Lindstrom, Wetton and Kiefl, "Mathematical modelling of the effect of surface roughness on magnetic field profiles in type II superconductors," Journal of Engineering Mathematics 85, 149-177 (2014).
- Moyles and Wetton, "A numerical framework for singular limits of a class of reaction diffusion problems," Journal of Computational Physics 300, 308-326 (2015).

- Modelling Lithium Ion Batteries UBC SCAIM Seminar, November, 2017. seminar May 27, 2016. Accompanying video:
- Numerical Methods for Interface Motion PIMS Numerical Methods for PDEs on Surfaces Workshop, June, 2017.
- A general framework for high accuracy solutions to energy gradient flows from material science models Southern China University of Science and Techonlogy May, 2017.
- Mathematical Models of Electrochemical Systems, given at the Mathematics Applications Consortium for Science and Industry tenth anniversary workshop, Limerick, Ireland, December, 2016. Some additional detail on the basic fuel cell model described in the main part of the talk, and its computational approximation, can be found in the hand written notes used at a workshop given at the Polytechnic University of Catalunya, October, 2011: part I, part II, part III. Matlab code: stack.m and solve_stack.m.
- Asymptotic Error Analysis, at the SIAM student day in Limerick, Ireland, December, 2016. Different versions were given at the PIMS Young Researcher Conference at UBC, June 2014, the PIMS-Shell Lunchbox series in Calgary, April 25, 2013 and University of Hawaii at Manoa Mathematics Department Seminar, February 24, 2012.
- PIMS Graduate Mathematical Modelling in Industry Workshop, Vancouver,
August 2016:
- My Presentation.
- Battery manufacturer's specification sheet .
- Independent tests on this battery type: link.
- A journal article with a basic approach to battery modelling.
- A PhD thesis that is the basis for the quasi-2D approach to battery modelling.

- Computational approaches to a model problem of two phase flow in porous media with phase change MSU applied mathematics seminar May 27, 2016. Accompanying videos:
- Modelling a Generalized Dialysis Device at the Universitat Polytechnica de Catalunya, November 2015. This was given to a audience in a capstone undergraduate applied mathematics class. The computations discussed in the talk are done with the MATLAB code nitric_iv.m with function calls to nitric_solve.m. Sorry, these are not pretty codes.
- A numerical framework for tracking interfaces in generalized Mullins-Sekerka dynamics MSU applied mathematics seminar May 29, 2015. A shorter version was given at the CAIMS annual meeting in Waterloo in June, 2015.
- Computational Models of Electrochemical Systems in the UBC SCAIM seminar January 2015.
- 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 seminar, 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 here: 2D Cahn Hilliard code (preconditioned conjugate gradient solve).