Volker Mehrmann
Numerical methods for model reduction and the control of partial differential equations

We discuss model reduction techniques for control problems arising in the control of semi-discretized partial differential equations. In particular we study the method of balanced truncation which leads to a system of large scale Lyapunov equations. These equations are solved via a low rank ADI method. We show explict decay rates for the singular values of the Lyapunov solutions and demonstrate the results for the control of the heat equation and the Stokes equation.

Graph theory and graph algorithms appear in an amazing variety of numerical computations: modeling path structure in sparse matrices, modeling locality in parallel computing, providing data structures and algorithms to represent, organize, and manipulate discretized versions of continuous phenomena.

I will describe some of the ways graph algorithms and numerical linear algebra have enriched each other in the past, and will pose some challenges to be met by finding new ways for them to interact in the future.

Chen Greif
On the solution of indefinite linear systems

An important class of linear systems are ones whose associated matrix is indefinite and can be presented in a 2x2 block form with a zero block. Many applications lead to such a structure; among them we mention constrained optimization, inverse problems, and the linearized Navier-Stokes equations. In this talk we will discuss some characteristics of such systems, and present recent results related to solution techniques in cases where the (1,1) block is singular or ill-conditioned. Joint work with Gene Golub.

Mike Foreman
Modelling tidal resonance and tidal power around Vancouver Island

As the tidal currents in some of the narrow passages around Vancouver Island are among the largest in the world, their potential as a source of renewable energy has received considerable interest. Though there have been numerous models for Juan de Fuca Strait, the Strait of Georgia, and the west coast of Vancouver Island, only recently has a model been developed that provides adequate resolution for the complicated network of channels north of Campbell River where many of the strong flows are found. In this talk we will briefly describe the finite element and control theory techniques that are presently being used to simulate tidal flows and elevations in this region. Resonance, tidal dissipation, and preliminary results on the potential for power generation will all be discussed.

John Fyfe
Numerical methods in climate research

Through numerical simulation we aim to better understand past, present and future climate and climate variability. In this talk I will briefly describe the climate system and global climate models (GCMs), and then will highlight some numerical issues that arise. Namely: 1) Gibbs oscillations in truncated spectral expansions; 2) "dynamical" convergence of GCM solutions and 3) artificial boundary-induced wave breaking.