Postdoc. University North Carolina at Chapel Hill (Applied Mathematics).
PhD. University of Alberta (Applied Mathematics, 2010).
MSc. University of Calgary (Applied Mathematics, 2005).
BSc. Simon Fraser University (Mathematical Physics, 2001).

Contact

Office:  Chapman Hall, 448
Phone:   919-843-7901
Email:   memmett@unc.edu
Mail:    Department of Mathematics
         CB #3250, Phillips Hall
         Chapel Hill, NC, 27599
CV:      PDF

Current research

I am a postdoc at UNC-CH under the supervision of Michael Minion. My research includes parallel in time integration schemes for PDEs and high-order spatial discretizations.

Time-parallel schemes

I am working with Michael Minion on a time/space parallelization technique for PDEs called the parallel full approximation scheme in space and time (PFASST).

PFASST is a novel approach to time parallelism that iteratively improves the solution on each time slice by applying deferred correction sweeps to a hierarchy of discretizations at different spatial and temporal resolutions. The coarse resolution problems are formulated using a time-space analog of the full approximation scheme used in multi-grid methods.

More details about the PFASST algorithm can be found on the PFASST website.

PFASST has been tested on a suite PDEs in simple geometries. Please see the PFASST gallery for examples. Preliminary tests have yielded parallel efficiencies typically between 40-60% on various numbers of processors from 4 to 512.

We are currently collaborating with:

• Dr. J. Bell and the CCSE group at LBL. We hope to apply PFASST techniques to VARDEN, a low-mach number fluid flow simulator developed by the CCSE.
• Dr. D. Ruprecht at the USI in Lugano, CH. We have already successfully applied PFASST to several geophysical flow examples, and ultimately hope to apply PFASST techniques to climate and weather codes.

High-order spatial reconstructions

I am also working with David Ketcheson et al. to incorporate high-order Weighted Essentially Non-oscillatory (WENO) schemes into PyClaw.

We used PyWENO (of which I am the primary author) to generate high performance Fortran 90 routines to perform WENO reconstructions within PyClaw. The routines can perform WENO reconstructions from 5th to 17th order.

The PyWENO project provides a set of open source tools for constructing high-order Weighted Essentially Non-oscillatory (WENO) methods and performing high-order WENO reconstructions.

Publications

Please see my Mendeley page for a list of my publications.

Software projects

I maintain the following software projects:

• PFASST- the PFASST (parallel-in-time) project.
• PyWENO- a Python implementation of WENO approximations.
• PyAsy- a Python module for creating plots with Asymptote.

I have also contributed to:

• PyClaw - A Python based solver for hyperbolic PDEs that includes the algorithms of ClawPack and SharpClaw.

Other research interests

My other research interests include:

• Numerical Analysis - Efficient implementation of Finite Volume schemes. Weighted Essentially Non-Oscillatory schemes for hyperbolic systems.
• Partial Differential Equations - Systems of hyperbolic conservation and balance laws, perturbation theory, Sobolev spaces, and weak solutions.
• Fluid Mechanics - Fluid dynamics, geophysical and environmental flows, gravity currents and sediment transport, free boundary flows and surface tension, turbulence, and applications in biology.
• Non-linear Dynamics and Chaos - Fixed point stability, bifurcations, and simple examples of the onset of chaos.
• Differentiable Manifolds - Hamiltonian mechanics, Lie groups, holonomic and non-holonomic reduction of constraints.
• Traffic Modeling - Incorporating stochastic phenomena into hyperbolic models of traffic flow.
• Dendrochronology - Analysing tree-ring width data to determine the time of death of dead trees.