Theme of Conference:

Many computationally challenging problems that arise in science and engineering exhibit multiscale behaviour. Relevant examples of practical interest include: structural analysis of composite and foam materials, fine-scale laminates and crystalline microstructures, flow through porous media, dendritic solidification, turbulent transport in high Reynolds number flows, weather forecasting, large-scale data visualization, spray combustion and detonation, many-body galaxy formation, large-scale molecular dynamic simulations, ab-initio physics and chemistry, and a multitude of others.

In stark contrast with the multiscale behaviour exhibited by such problems, classical computational methods for the numerical simulation of multiscale physical phenomena have been designed to operate at a certain preselected scale fixed by the choice of a discretisation parameter. As a result of this, the task of numerically computing or even representing all of the physically relevant scales present in the problem by classical numerical techniques results in excessive algorithmic complexity. The consequential difficulties manifest themselves in various guises: An attempt to represent all relevant scales in the physical model may lead to an extremely large set of unknowns, requiring a tremendous amount of computer memory and CPU time; For certain multiscale problems one is not actually interested in the fine scale information; however, due to the presence of nonlinearities in the model, the effect of the fine, unresolvable scale information on coarse scales cannot be ignored and must be precisely incorporated in order to achieve physically meaningful computational results; Exacerbating the computational problem is the fundamental question of optimal data representation for multiscale problems where it is known that even modern wavelet basis representations can yield overall suboptimal algorithmic complexity when the quantity of interest contains embedded low-dimensional manifolds across which the function or its derivatives exhibit discontinuities (as is the case in nonlinear hyperbolic conservation laws, for example).

Programme content:
Multiscale problems will remain computationally expensive or completely intractable for the foreseeable future unless new algorithmic paradigms of computation are developed which fundamentally embrace the multiscale nature of these problems.

Thus far, there has been little interaction between these communities despite a considerable overlap in their scientific objectives. The aim of the meeting is to stimulate interactions and cross-fertilisation between the various subject areas involved, an assessment by leading researchers of the state-of-the-art in the field, identification of key problems and obstacles to progress, and indication of promising directions for future research.

Technical topics:
Multiscale modelling techniques in science and engineering:
Mathematical modelling of multiscale phenomena; Homogenisation theory for partial differential equations; Hierarchical modelling.

Computational multiscale modelling:
Computational/algebraic homogenisation; Multiscale finite element methods; Subgrid scale modelling and upscaling; Variational multiscale methods and residual free bubble algorithms.

Optimal-complexity and adaptive algorithms for multiscale problems:
Multiresolution algorithms; Adaptive wavelet algorithms; Adaptive h- and hp- version finite element algorithms based on a posteriori error analysis.

Structure of the meeting:
The meeting will include the following:

15 one-hour in-depth invited lectures from leading specialists (with 3 invited lectures scheduled for each of the 5 days),

17 thirty-minute contributed talks chosen from abstract submissions; abstracts will be competitively selected, with the possibility of adding an optional poster session. Short abstracts of 500 words or less are requested, for submission to the Scientific Committee on or before 15 November, 2002 with selected abstracts announced by 15 December, 2002.

5 one-hour coordinated discussion sessions with a preselected topical subject area; the subjects of these will be identified 6 months before the meeting to ensure that they are of current research interest; the topics will be chosen in consultation with the invited speakers, some of whom will be asked to act as moderators for the discussion sessions.

4 two-hour informal breakout sessions and informal time for researchers from various disciplines to explore (and exchange ideas about) future solutions to currently unsolved problems.

a thirty-minute closing session to summarise the outcome of the meeting and identify major open problems.

Schedule of the meeting:
09:00 - 10:00 Invited lecture
10:00 - 11:00 Coordinated discussion session with a preselected topical theme
11:00 - 11:30 Coffee break
11:30 - 12:30 Invited lecture
12:30 - 13:30 Lunch break [Wolfson Court]
14:00 - 15:00 Invited lecture
15:00 - 15:30 Tea break
15:30 - 16:00 Contributed lecture
16:00 - 16:30 Contributed lecture
16:30 - 17:00 Contributed lecture
17:00 - 18:45 Informal time for researchers from various disciplines to exchange ideas and explore currently unsolved problems.
18:45 - 19:30 Dinner

Note:
The first and last days of the meeting deviate slightly from this pattern.

Monday:
08.30-09.55 Registration
09.55-10.00 Opening remarks
10.00-11.00 Invited lecture
followed by the same pattern as above.

Friday: The afternoon invited lecture is followed by a closing 30 minute discussion.

See also the Computational Challenges in Partial Differential Equations Program.