Organizers:

Douglas N. Arnold	Institute for Mathematics and its Applications	arnold@ima.umn.edu
Abhay Ashtekar	Center for Gravitational Wave Physics, Penn State	ashtekar@gravity.phys.psu.edu
Pablo Laguna	Center for Gravitational Wave Physics, Penn State	pablo@astro.psu.edu

 

Description:

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.

WORKSHOP SCHEDULE

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

MONDAY, JUNE 24 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
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.
8:30 am	Coffee and Registration	Reception Room EE/CS 3-176
9:00 am	Douglas Arnold, Fadil Santosa, and Lee Samuel Finn	Welcome and Introduction
9:10-10:00 am	Douglas N. Arnold	A quick introduction to the Einstein equations notes (pdf    ps) Slides.pdf
10:00-10:30 am	Discussion
10:30-11:00 am	Break	Reception Room EE/CS 3-176
11:00-11:50 am	Alan D. Rendall Albert-Einstein-Institut	Introduction to GR for computational scientists, II notes (pdf    ps)
11:50 am-12:30 pm	Discussion
12:30-2:30 pm	Break
2:30-3:20 pm	Robert Bartnik University of Canberra	Introduction to the 3+1 Einstein equations notes (pdf    ps)
3:20-4:00 pm	Discussion
4:00-6:00 pm	Reception and Posters	IMA East, 400 Lind Hall
TUESDAY, JUNE 25 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
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.
8:30 am	Coffee	Reception Room EE/CS 3-176
9:00-9:50 am	Ralf Hiptmair IAM, Universitaet Bonn	Discretization of Maxwell's Equations (pdf    ps) slides.pdf    slides.ps
9:50-10:30 am	Discussion
10:30-11:00 am	Break	Reception Room EE/CS 3-176
11:00-11:50 am	Eitan Tadmor University of California Los Angeles	Computational Methods for Hyperbolic Systems. Preservation of Global and Local Invariants  (pdf)
11:50 am-12:30 pm	Discussion
12:30-2:30 pm	Break
2:30-3:00 pm	Oscar Reula FaMAF, Universidad Nacional de Cordoba	Formulations of GR for computation, I slides.pdf
3:00- 3:30 pm	Discussion
3:30-3:45 pm	Break	Reception Room EE/CS 3-176
3:45-4:15 pm	Manuel Tiglio Louisiana State University	Numerical relativity as an initial-boundary value problem slides.pdf
4:15-4:45 pm	Discussion
WEDNESDAY, JUNE 26 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
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.
8:30 am	Coffee	Reception Room EE/CS 3-176
9:00-9:50 am	Jeff Winicour University of Pittsburgh	Black hole spacetimes   slides.html notes (ps)
9:50-10:30 am	Discussion
10:30-11:00 am	Break	Reception Room EE/CS 3-176
11:00-11:50 am	Matthew W. Choptuik University of British Columbia	Fundamental issues of numerical relativity slides.html    slides.pdf    slides.ppt
11:50 am-12:30 pm	Discussion
12:30-2:30 pm	Break
2:30-3:20 pm	Pablo Laguna Penn State University	State of the art of numerical relativity slides.pdf
3:20-4:00 pm	Discussion
5:30-8:00 pm	Pizza Dinner/Computational Demonstrations, Lind Hall 409 The following brief presentations will be given: Jeff Winicour Well-posed initial-boundary evolutions Jinchao Xu Problem-independent adaptivity and multigrid Michael J. Holst MC, Manifold Code Robert Bartnik Null quasispherical numerical evolution Denis Pollney Gauges in the BSSN formulation of GR
THURSDAY, JUNE 27 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The day will focus on some particular challenges and promising techniques for numerical relativity.
8:30 am	Coffee	Reception Room EE/CS 3-176
9:00-9:30 am	Gregory B. Cook Wake Forest University	Computation of initial data, I slides
9:30-9:50 am	Discussion
9:50-10:05 am	Break	Reception Room EE/CS 3-176
10:05-10:35 am	Michael J. Holst University of California, San Diego	Computation of initial data, II slides.pdf
10:35-10:55 am	Discussion
10:55-11:10 am	Break	Reception Room EE/CS 3-176
11:10 am-11:25 pm	Markus Keel University of Minnesota	Linear degeneracy of the Einstein Slides
11:25-11:40 am	Discussion
11:40-11:55 am	Eitan Tadmor University of California Los Angeles	Remarks on first order formulations
11:55 am -12:10 pm	Discussion
12:10-2:30 pm	Break
2:30- 3:00 pm	Deirdre Shoemaker Penn State University	Computation of horizons and excision slides.pdf
3:00-3:30 pm	Discussion
3:30-3:45 pm	Break	Reception Room EE/CS 3-176
3:45-4:15 pm	Mark A. Scheel California Institute of Technology	Spectral methods and excision slides.pdf
4:15- 4:45 pm	Discussion
FRIDAY, JUNE 28 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The day will again focus on some particular challenges facing numerical relativity and promising techniques.
8:30 am	Coffee	Reception Room EE/CS 3-176
9:00-9:50 am	Luis Lehner University of British Columbia	Outer boundary conditions
9:50-10:30 am	Discussion
9:50-10:05 am	Break	Reception Room EE/CS 3-176
10:05-10:35 am	Richard S. Falk Rutgers University	Overview of finite element methods for linear hyperbolic problems slides.pdf    slides.ps
10:35-10:55 am	Discussion
10:55-11:10 am	Break	Reception Room EE/CS 3-176
11:10-11:25 am	Lee Lindblom Caltech	Energy norms and stability of the Einstein equations
11:25 am-11:40 pm	Discussion
11:40-11:55 am	Sasha Husa Albert-Einstein-Institut	The conformal approach slides.pdf
11:55 am-12:10 pm	Discussion
12:10-2:00 pm	Lee Samuel Finn Penn State University and Lee Lindblom Caltech	Lunchtime discussion on gravitational wave phenomenology Lind Hall 409. Lunch will be provided. GWPhenomIMA-slides.pdf LIGOMath-slides.pdf
2:00- 4:00 pm	Panel discussion on numerical methods
4:00- 4:15 pm	Break	Reception Room EE/CS 3-176
4:15- 4:30 pm	Discussion
6:15 pm	Workshop Dinner Radisson shuttle to Kikugawa at 6:00 pm	Kikugawa Restaurant 43 Main Street S.E., Minneapolis
SATURDAY, JUNE 29 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The workshop will conclude with discussions and summary presentations assessing what was learned and future directions.
9:00-10:30 am	Discussion lead by Richard Price (University of Utah), Ragnar Winther (University of Oslo) and Beverly Berger (NSF) Richard Price slides.html
10:30-11:00 pm	Break
11:00 am -12:30 pm	Discussion, continued
The workshop will end at 12:30 pm on Saturday.

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

LIST OF CONFIRMED PARTICIPANTS
(in addition to postdocs and long-term participants)

As of 6/28/2002

Name	Department	Affiliation
Douglas N. Arnold		Institute for Mathematics and its Applications
Robert Bartnik	Mathematics and Statistics	University of Canberra
Beverly Berger	Division of Physics	National Science Foundation
David Brown	Physics	North Carolina State University
Matt Choptuik	Physics	University of British Columbia
Gregory B. Cook	Physics	Wake Forest University
Rick Falk	Mathematics	Rutgers University
Lee Samuel Finn	Director, Center for Gravitational Wave Physics	Penn State University
Jörg Frauendiener	Theoretische Astrophysik	Universität Tübingen
Ralf Hiptmair	Mathematics	University of Tübingen
Michael Holst	Mathematics	UC San Diego
Sascha Husa	Max-Planck-Institut für Gravitationsphysik	Albert-Einstein-Institut
Marcus Keel	Mathematics	University of Minnesota
Pablo Laguna	Center for Gravitational Wave Physics	Penn State University
Luis Lehner	Physics & Astronomy	University of British Columbia
Lee Lindblom	Physics, Math & Astronomy	Caltech
Peter Monk	Mathematical Sciences	University of Delaware
Arup Mukherjee	Mathematics Sciences	Montclair State University
Denis Pollney	Max-Planck-Institut für Gravitationsphysik	Albert-Einstein-Institut
Richard Price	Physics	University of Utah
Alan Rendall	Max-Planck-Institut für Gravitationsphysik	Albert-Einstein-Institut
Oscar Reula	Investigador Independiente, CONICET	FaMAF, Universidad Nacional de Cordoba
Mark A. Scheel	Physics, Mathematics, and Astronomy	California Institute of Technology
Deirdre Shoemaker	Astronomy	Penn State University
Eitan Tadmor	Mathematics	University of California Los Angeles
Blake Temple	Mathematics	University of California
Manuel Tiglio	Physics	Louisiana State University
Jeff Winicour	Physics	University of Pittsburgh
Ragnar Winther	Informatics	University of Oslo
Jinchao Xu	Mathematics	Pennsylvania State University

 

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