Numerical Relativity

The numerical solution of Einstein's equations of general relativity promises to become one of the most potent tools for for understanding the complex behavior of strong dynamical gravitational fields. In recent years the field of numerical relativity has grown substantially, engaging the efforts of large groups of researchers across the globe. Despite some promising results, the development of accurate, efficient, and validated algorithms for Einstein's equations remains elusive. This is in part due to the size and complexity of the equations, but also due to fundamental issues which remain to be fully understood.

The problems of numerical relativity share many features with other large scale problems of computational physics, and it is highly likely that lessons learned in fields such as computational fluid dynamics, solid mechanics, and electromagnetics will help advance numerical relativity. But the fundamental differences between general relativity and classical field theories also bring major new computational issues.

This workshop will bring together numerical relativists and mathematicians working in fields such as numerical analysis, scientific computation, partial differential equations, and geometry, for an intense but informal period aimed at maximal communication and interaction between diverse researchers. The primary goals are to bring new ideas and techniques into the numerical relativity community and to propel applied mathematicians with relevant skills and interests into NR. We hope that this workshop will lead to continued interactions which could take place at many venues such as the Center for Gravitational Wave Physics at Penn State, the Institute for Theoretical Physics at UC Santa Barbara, the Caltech Visitors Program in the Numerical Simulation of Gravitational Wave Sources, and the IMA. Such interactions can lay the foundation for the formation of multidisciplinary teams better equipped to tackle the challenges of numerical relativity.

The workshop will focus on a few of the many issues in numerical relativity, selected for their importance, mathematical nature, and relative accessibility. Main among these are the initial value problem of vacuum relativity, including the encoding as partial differential equations; discretization techniques for these equations; treatment of black hole spacetimes; the imposition of boundary conditions; and the determination of physically relevant initial data.

Outline

• Monday: Introduction to GR for computational scientists, with an emphasis on the vacuum field equations and issues like geometric well-posedness; PDE formulations; initial value problems; gauge freedom, etc. This will be most directed at the participants who have not had much to do with GR in the past, but will also serve to set a common vocabulary for the remainder of the week. The day will end with a reception at which all participants are invited to display posters.
• Tuesday: The morning will focus on key ideas from better developed areas of computational science: electromagnetics and hyperbolic systems from other applications. The afternoon will focus on formulations of GR for computation.
• Wednesday: The morning will extend the tutorials of the first day to issues involving black holes and horizons. The remaining talks will focus on the main conceptual and numerical challenges in numerical relativity. During dinner there will be the possibility for any participants with relevant software and computations to demonstrate to do so.
• Thursday: The day will focus on some particular challenges and promising techniques for numerical relativity.
• Friday: The day will again focus on some particular challenges facing numerical relativity and promising techniques.
• Saturday: The workshop will conclude with discussions and summary presentations assessing what was learned and future directions.