11-15 July 2011

SciCADE 2011

hosted by the Fields Institute,
held at the University of Toronto

New Talent Award

Contact Us gensci(PUT_AT_SIGN_HERE)fields.utoronto.ca

Jan Verwer Memorial Minisymposium, II

Organized by Christopher Budd

Kevin Burrage, University of Queensland From cells to tissue: coping with heterogeneity through fractional models
Weizhang Huang, University of Kansas Stability of moving mesh methods for linear parabolic partial differential equations
Moving meshes have been becoming a necessary tool for use in the numerical solution of problems with time varying geometry and problems with moving features such as shock waves and interfaces. In the former case, a boundary fitted moving mesh is often used to accurately track and represent the moving boundary while in the latter case an adaptive, moving mesh is typically used to follow and adapt to the moving features. While improving accuracy and efficiency of the numerical simulation, moving meshes introduce extra convection terms and other complexities that make the theoretical analysis of moving mesh methods or methods using moving meshes challenging. In this talk, we will discuss the stability of several moving mesh methods for solving linear parabolic partial differential equations.

Co-author:Forrest Schaeffer
Jens Lang,
Darmstadt University of Technology

Linearly Implicit Methods for Optimal Control Problems

In this talk, we will consider time discretizations of linearly implicit type for ODE-constrained nonlinear optimal control problems. The ODE is first discretized and the arising discrete optimal control problem is then solved by approximating the first order optimality conditions. For Runge-Kutta methods, additional order conditions have to be satisfied to achieve order three for optimal control problems (Hager, 2000). For large scale problems, the complexity of implicit Runge-Kutta schemes can be significantly reduced by applying linearly implicit Runge-Kutta-Rosenbrock methods with inexact Jacobians. We will present order conditions for these methods up to order three. The performance of newly designed methods is discussed for academic as well as real-life problems.