Bulletin of the American Physical Society
2006 APS April Meeting
Saturday–Tuesday, April 22–25, 2006; Dallas, TX
Session J11: Advances in Numerical Relativity I |
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Sponsoring Units: GGR Chair: Bernard Kelly, The University of Texas at Brownsville Room: Hyatt Regency Dallas Cumberland E |
Sunday, April 23, 2006 1:15PM - 1:27PM |
J11.00001: Elliptic gauge conditions for binary black hole evolutions Harald Pfeiffer Elliptic gauge conditions have many attractive features for black hole evolutions and have been used very successfully in simulations in one and two spatial dimensions. In three dimensions, however, elliptic gauge conditions have hardly been explored because of the traditionally high computational cost. With recent efficient elliptic solvers, computational cost is greatly reduced, and 3-D black hole evolutions employing elliptic gauge conditions become possible. This talk presents preliminary results, addressing questions like: Do elliptic gauge conditions control effectively the coordinates and the location of the black holes? How often does one have to solve elliptic equations? What is the computational cost? [Preview Abstract] |
Sunday, April 23, 2006 1:27PM - 1:39PM |
J11.00002: Constraint damping in the KST evolution system Robert Owen Much effort in recent years has been directed toward expressing the evolution equations of general relativity in forms where constraint violations are dynamically damped away during the simulation. We will discuss a trick which naturally appears in the context of explicit first-order reductions of second-order evolution systems. This trick presents a simple means to modify the evolution of certain constraints, without altering hyperbolicity. As an example, we will discuss a generalization of the KST evolution systems, that damps away most constraints exponentially on a tunable timescale, and present results of its use in numerical simulations. [Preview Abstract] |
Sunday, April 23, 2006 1:39PM - 1:51PM |
J11.00003: Expanding Cosmological Spacetimes Containing Gravitational Waves Beverly K. Berger Most analysis of expanding cosmologies focus on matter (exotic or otherwise) in a spatially homogeneous background although spatial inhomogeneities clearly exist. To examine the possible effects of these inhomogeneities on expanding cosmologies, models with 3-torus topology and spatial dependence only in one direction are considered. The behaviors of vacuum and fluid-filled cases are contrasted with the vacuum and fluid-filled anisotropic but spatially homogeneous Kasner models where it is known that the latter case approaches isotropy. The results of numerical simulations will be used to illustrate unusual behavior for vacuum spatially inhomogeneous models as well as their approach to the standard cosmology when matter dominates the dynamics. [Preview Abstract] |
Sunday, April 23, 2006 1:51PM - 2:03PM |
J11.00004: Finite Elements in Numerical Relativity Matthew Anderson, Luis Lehner, Jorge Pullin We employ finite elements in solving the Einstein equations for hyperspherical black hole and black string spacetimes. We present examples solving the elliptic initial data equations to study the possible black string-hole transition in higher dimensional gravity. [Preview Abstract] |
Sunday, April 23, 2006 2:03PM - 2:15PM |
J11.00005: Gravitational Collapse With Distributed Adaptive Mesh Refinement Steven Liebling, Luis Lehner, Patrick Motl, David Neilsen, Tanvir Rahman, Oscar Reula Gravitational collapse is studied using distributed adaptive mesh refinement (AMR). The AMR infrastructure includes a novel treatment of adaptive boundaries which allows for high orders of accuracy. Results of the collapse of Brill waves to black holes are presented. Combining both vertex centered and cell centered fields in the same evolution is discussed. [Preview Abstract] |
Sunday, April 23, 2006 2:15PM - 2:27PM |
J11.00006: The Lazarus Project II: Space-like extraction with the Quasi-Kinnersley tetrad Manuela Campanelli, Bernard Kelly, Carlos Lousto The Lazarus project was designed to make the most of limited 3D binary black-hole simulations, through the identification of perturbations at late times, and subsequent evolution of the Weyl scalar $\Psi_4$ via the Teukolsky formulation. Here we report on new developments, employing the concept of the ``quasi-Kinnersley'' (transverse) frame, valid in the full nonlinear regime, to analyze late-time numerical space-times that should differ only slightly from Kerr. This allows us to extract the essential information about the background Kerr solution, and through this, to identify the radiation present. We explicitly test this procedure with full numerical evolutions of Bowen-York data for single spinning black holes, head-on and orbiting black holes near the ISCO regime. These techniques validate previous Lazarus results, provide a measure of the errors intrinsic to the method, and give as a by-product a more robust wave extraction method for numerical relativity. [Preview Abstract] |
Sunday, April 23, 2006 2:27PM - 2:39PM |
J11.00007: Wave extraction using the Newman-Penrose formalism: theory and applications Andrea Nerozzi, Marco Bruni, Virginia Re, Lior M. Burko Newman-Penrose quantities such as Weyl scalars are potentially a powerful wave extraction tool especially in those cases where a solid wave extraction technique has not been developed yet, like, for example, in simulations relying on the ADM formulation of Einstein's equations. Here we present the progress done in building up a novel technique which optimizes the process of calculating Weyl scalars for wave extraction purposes and we apply these results to a specific numerical example. [Preview Abstract] |
Sunday, April 23, 2006 2:39PM - 2:51PM |
J11.00008: Estimating the gravitational-wave content of initial-data sets for numerical relativity using the Beetle--Burko scalar Lior M. Burko The Beetle--Burko radiation scalar is a gauge independent, tetrad independent, and background independent quantity that depends only on the radiative degrees of freedom where the notion of radiation is incontrovertible, and can be computed from spatial data as is typical in numerical relativity simulations even for strongly dynamical spacetimes. We show that the Beetle--Burko radiation scalar can be used for estimating the graviational-wave content of initial-data sets in numerical relativity, and can thus be useful for the construction of physically meaningful ones, and the identification of ``junk'' data on the intial value surface. We apply this method for the case of a momentarily stationary black hole binary, and demonstrate how the Beetle-- Burko scalar distinguishes between Misner and Brill--Lindquist initial data. The method, however, is robust, and is applicable to generic initial data sets. In addition to initial data sets, the Beetle--Burko radiation scalar is equally applicable also for evolution data. [Preview Abstract] |
Sunday, April 23, 2006 2:51PM - 3:03PM |
J11.00009: Simulation of a Boosted Black Hole with Overlapping Coordinate Systems Paul Walter, Andrea Nerozzi, Richard Matzner, Matt Anderson We discuss the simulation of a boosted Kerr-Schild black hole using overlapping spheriodal grids around the excision region. We make use of constrained evolution, periodically solving the constraints to better than truncation error. Fisheye is used to increase the size of the domain while Robin boundary conditions are used at the outer boundary. We discuss the current state of the code and the impediments to long-time integration. [Preview Abstract] |
Sunday, April 23, 2006 3:03PM - 3:15PM |
J11.00010: Evaluating Spectral Techniques in Numerical Relativity Michael Boyle, Lee Lindblom, Harald Pfeiffer, Mark Scheel, Lawrence Kidder We analyze the behavior of a pseudo-spectral code evolving the KST formulation of Einstein's equations. In an effort to better compare different analytical formulations of Einstein's equations and numerical techniques for implementing them, a set of standardized tests for numerical relativity codes has been suggested by the ``Apples with Apples'' collaboration. The tests involve simple, three-dimensional spacetimes with known analytic solutions evolved in a space without boundaries (a 3-Torus) with prescribed evolution parameters such as resolution and time step. We have implemented these tests with our code. We find that the exponential convergence of spectral spatial differentiation and the stability of the KST formulation allow us to evolve these spacetimes on low-resolution grids, limited most strongly by machine precision. We derive expressions to estimate the growth of errors due to machine precision in arbitrary spacetimes, and show that these limits are easily achieved by our code, with good stability of the analytical formulation and numerical implementation. [Preview Abstract] |
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