Theme of Conference:
Numerical relativity is still on the road towards reliable simulations of astrophysical scenarios such as binary black hole mergers, binary neutron star mergers, and supernova core collapse, and the mathematically intriguing problem of critical collapse of rotating systems. Key problems are achieving long-term stability of evolutions. In the last few years significant progress has been made in clarifying the underlying mathematical (continuum) problem, and various efforts are under way to transfer these insights to the numerical (discretised) problem.
The meeting will focus on two areas: mathematical aspect of the continuum and discrete problems (well-posedness, gauge, boundary conditions, discretisation methods), and simulations at the edge of what is currently possible.
Invited speakers and preliminary titles:
- Gioel Calabrese (Southampton): Finite difference approximations of first order in time, second order in space hyperbolic systems;
- Matthew Choptuik (Vancouver): Recent developments in black hole critical phenomena ;
- Joerg Frauendiener (Tuebingen): Evolutions with the conformal field equations;
- John Friedmann (Milwaukee): Self force on particles in a Kerr background;
- David Garfinkle (Oakland): Numerical simulations of gravitational singularities;
- Ian Hawke (Southampton): Gravitational waves from stellar collapse simulations;
- Heinz-Otto Kreiss (Stockholm): Boundary conditions for difference approximations of second order hyperbolic differential equations in general domains;
- Luis Lehner (Baton Rouge): Next steps in the simulation of Einstein equations;
- Frans Pretorius (Caltech: Simulations of binary black hole spacetimes;
- Oscar Reula (Cordoba): On touching grids and higher order methods on space-times with non-trivial topology;
- Olivier Sarbach (Caltech): Well-posed initial-boundary value problems in general relativity;
- John Stewart (Cambridge): to be announced
We discuss stability for finite difference approximations of Cauchy and quarter space problems for hyperbolic systems that are first order in time and second order in space, similar to those that appear in Numerical Relativity.
There are many methods to solve second order differential equations numerically. Methods based on variational principles have the advantage that the energy is conserved but they might not be as efficient as difference methods. Standard imbedded difference methods are very efficient but, for general domains, there is always the risk of instabilities. We will characterize these instabilities and discuss methods to avoid them.
Location and Cost:
The Conference will take place on the main campus of the University of Southampton and participants will be housed in Glen Eyre Hall, 10 minutes walk from the conference venue. The conference package, costing £180, comprises 3 nights accommodation in en-suite rooms, breakfast, buffet lunch, cafeteria style dinner and refreshments, from a buffet dinner on Wednesday 17 August 2005 to breakfast on Saturday 20 August 2005.
The conference is supported by the European Community and funding is available, please indicate on the application form which EC category is applicable. Self-supporting participants are very welcome to apply. Participants who wish to attend but do not require the Conference Package will be charged a registration fee of £57.
Are available here. Invited participants to the semester long programme whose dates coincide with those of the workshop need not apply or pay any registration fee.
The closing date for the receipt of applications has been extended to 15 July 2005 but earlier applications will be considered as will the request for financial support in the order of received applications.