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 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. I have also explored recently
equivalent formulations for the Oxygen Depletion problem (the simplest
implicit free boundary value problem) and their corresponding numerical
approximation.
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.
Some recent preprints
Former Students
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.
-
Lloyd Bridge, now a Lecturer at UWE Bristol.
- Atife Caglar,
now a faculty member at the University of Wisconsin - Green Bay.
- Paul Chang, now working at Microsoft.
- Xinyu Cheng,
now in a tenure track position at the Research Institute of Intelligent Complex Systems (IICS), Fudan University.
- Roger Donaldson, now working at Avigilon in Vancouver.
- Zhaohui Fu, now a PDF at Singapore National University.
- Brieuc Gilles.
- Ana Granados, now a Faculty member at the St. Louis
University in Madrid.
- David Kong, now a software engineer in Vancouver.
-
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 faculty member at York University.
-
Arian Novruzi,
now a faculty member at the University of Ottawa.
- Wesley Ridgway, now a PhD student at Oxford.
- Zhenguo Pan.
- Steve Ruuth, now
a faculty member at SFU.
- John Stockie, now a
faculty member at SFU.
- Cyrus Towfighi.
-
Justin Tzou, now a faculty member at Macquarie Univeristy in Australia.
- Mark Willoughby.
- Cheng Zhang.
Selected Publications
Some selected publications I am 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).
- Church, Guo, Jimack, Madzvamuse, Promislow, Wetton, Wise, Yang,
"High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics,"
Communications in Computational Physics 26, 947-972 (2019).
- Cheng, Li, Promislow, Wetton, "Asymptotic Behaviour of Time Stepping
Methods for Phase Field Models," Journal of Scientific Computing 86,
Article #32 (2021).