The Parallel Full Approximation Scheme in Space and Time

The Faculty of Informatics is pleased to announce a seminar given by Matthew W. Emmett

DATE: Thursday, November 24th, 2011
PLACE: USI Università della Svizzera italiana, room A32, Red building (Via G. Buffi 13)
TIME: 10.30

ABSTRACT:
The Parallel Full Approximation Scheme in Space and Time (PFASST) algorithm for parallelizing PDEs in time is presented. Several applications of the algorithm will also be presented, including the Kuramoto-Silvashinsky and Navier-Stokes equations.

To efficiently parallelize PDEs in time, the PFASST algorithm decomposes the time domain into several time slices.  After a provisional solution is obtained using a relatively inexpensive time integration scheme, the solution is iteratively improved using a deferred correction scheme.  To further improve parallel efficiency,
the PFASST algorithm uses a heirarchy of discretizations at different spatial and temporal resolutions and employs an analog of the multi-grid full approximation scheme to transfer information between the  discretizations.

Applications of the PFASST algorithm will be presented for several PDEs including the Kuramoto-Silvashinsky and Navier-Stokes equations. Convergence results, parallel speedups and parallel efficiencies will be reported.

BIO:
2010 PhD at University of Alberta, Edmonton AB.
Applied Mathematics. Fluid mechanics (shallow-water sediment transport) and numerical analysis (WENO methods). Supervisor: Dr. T. B. Moodie.

Research interests
Numerical Analysis: Parallel in Time algorithms for PDEs. Efficient implementation of Finite Volume and Finite Element 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 fows, gravity currents and sediment transport, free boundary fows, 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 fow.

HOST: Prof. Rolf Krause