Prof. Jeff Cash, Imperial College, London

Email: j.cash @ imperial.ac.uk
Web URL: http://www.ma.ic.ac.uk/

A history of deferred correction for solving two point boundary value problems

Deferred correction is a very powerful method for solving differential equations. Some of the original ideas of Fox and Goodwin for initial value problems date back to 1949 and many of the key ideas were extended by Fox in 1957. The present talk traces the development of deferred correction from these humble beginnings to the present day. The key question is how to define the correction term and we will explain how this problem was tackled in 1957, how these ideas were extended to boundary value problems by Lentini and Pereyra who released the widely used boundary value code PASVA3 and how the concept of deferred correction was extended by Lindberg in 1971. Some of the best codes for solving BVPs currently available are based on deferred correction. The theory behind these methods will be given and some recent developments will be discussed.

Prof. John Butcher, University of Auckland

Email: butcher @ math.auckland.ac.nz
Web URL: http://www.math.auckland.ac.nz/~butcher/

110 Years of Runge-Kutta Methods

Within a few years of each other, and with an average date in 1899, three remarkable papers appeared. Runge's paper announced order 2 one-step methods, Heun's paper completed the study of order 3 methods and Kutta's paper completely classified Runge-Kutta methods of order 4. The complexity of these famous numerical methods greatly increases with order and it was not until 1925 that Hystroem was able to correctly obtain methods of order 5. In the search for increasingly high orders, and therefore greater potential for efficient and accurate computations, the next important step was made by Anton Huta of former Czechoslovakia who first derived methods of order 6. This talk is a tribute to these early pioneers and also a record of more recent and more surprising developments which link RungeKutta methods to combinatorics, graph theory, group theory, Gaussian quadrature, Lie-algebras, nuclear physics and non-commutative geometry.

Prof. Rolf Jeltsch, ETH Zurich

Email: jeltsch @ math.ethz.ch
Web URL: http://www.sam.math.ethz.ch/~jeltsch/

High-order Semi-Lagrangian Numerical Method for the Large-Eddy Simulation of Reactive Flows

Rolf Jeltsch (1), Julián T. Becerra Sagredo (2), Wesley P. Petersen (1), Jürg Gass (3)

(1) Seminar for Applied matheamtics, ETH Zurich
(2) Center for Energy Research, National University of Mexico, Temixco, Mexico
(3) Laboratory of Thermodynamics in Emerging Technologies, ETH Zurich

A high-order Semi-Lagrangian numerical method is developed for the simulation of a subsonic methane/air flame. The fluid is described by the Navier-Stokes equations for a mixture of ideal gases. Turbulence is modelled using Large- Eddy simulation (LES) together with a transport equation for the subgrid kinetic energy. For the chemical reactions we use an unsteady flamelet model based on transport equations for the mixture fraction and a reaction progress variable. This allows for extinctions and re-ignitions by not assuming fast chemistry nor steady flamelets. To solve the resulting system of coupled transport equations a Semi-Lagrangian (FSL) method, known from climate modeling, is used. For the interpolations from the Lagrangian mesh points to a fix mesh an interpolation based on piece wise polynomials of degree 2m which are m-tmes differentiable are used. This interpolation is easy to implement, computations are fast. It is conservative, conservative and creates low or zero numerical diffusion and dispersion. Finally the FSL method is used to simulate Sandia flame D. For the 3-d simulations a mesh in cylindrical coordinates is used where singular derivatives and high frequencies at the polar axis are controlled.

Prof. Khalid Al-Begain, University of Glamorgan

Email: kbegain @ glam.ac.uk
Web URL: http://people.glam.ac.uk/view/287/

Modelling and Simulation of Multimedia Streaming in Modern Wireless Data Networks

Providing high speed data has been always an important goal of the wireless community. Third Generation Partnership Project (3GPP) has been introducing new technologies to add higher data rate capabilities to existing wireless cellular networks. One important step forward in this direction is the High Speed Downlink Packet Access (HSDPA). HSDPA evolved from 3G through utilising a number of existing technologies to compensate for the changing link conditions. The main theme is based on link adaptation by modifying the transmission parameters of the system to adapt to the instantaneous transmission conditions. This allowed improved data rates enabling multimedia communications. This, however, necessitates data buffering at the air interface which poses a bottleneck to end-to-end communication and thus buffer management in the base station is an essential and critical for Quality of Service provision.

The talk will briefly present the technology and the system components in modern wireless systems and then discusses various packet scheduling algorithms that have been proposed for HSDPA. Packet scheduling algorithms that support multimedia traffic with diverse concurrent classes of flows being transmitted to the same end user will be covered. Furthermore, new approaches for such end-user multimedia sessions based on integrated packet scheduling with buffer management are also presented in the talk. In these approaches, the packet scheduling functionality selects a user for downlink transmission based on a given scheduling discipline (i.e. inter-user prioritization), while the buffer management scheme determines the class of flow to be transmitted from the users multiplexed flows (i.e. inter-class prioritization). The talk will also discuss a novel proposal for optimising the performance of multimedia session quality of service provision.

The talk will present different approaches for modelling traffic and buffer management including analytical, numerical as well as simulation.