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
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
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
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," 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,
- Promislow and Wetton, "PEM Fuel Cells: A Mathematical Overview"
(invited review article) SIAM Journal of Applied Mathematics 70, 369 (2009).
Some recent talks
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 and at the ICIAM meeting August, 2014. 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.
- Numerical Methods for
Interface Motion SFU 2015 Symposium on Mathematics and Computation,
August 6, 2015.
- 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.
- Asymptotic Error Analysis,
plenary talk at the PIMS Young Researcher Conference at UBC, June 2014.
Different versions were given
in the PIMS-Shell Lunchbox series in Calgary, April 25, 2013 and
University of Hawaii at Manoa Mathematics Department Seminar,
February 24, 2012.
Modelling fuel cells in start-up and reactant
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).
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:
Two Phase Transport in Porous Media
at the CRM (Spain) CAMP seminar, October 19, 2011; also at the
BCAM (Spain) seminar, November 14, 2011.