Bulletin of the American Physical Society
2007 APS April Meeting
Volume 52, Number 3
Saturday–Tuesday, April 14–17, 2007; Jacksonville, Florida
Session U12: Advances in Numerical Relativity |
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Sponsoring Units: GGR Chair: David Neilsen, Brigham Young University Room: Hyatt Regency Jacksonville Riverfront City Terrace 8 |
Monday, April 16, 2007 3:30PM - 3:42PM |
U12.00001: Puncture evolution without BSSN David Brown The moving puncture technique is used by a number of numerical relativity groups to model binary black hole spacetimes. Thus far this technique has been limited to the BSSN formulation of the Einstein equations with 1+log slicing and gamma-driver shift conditions. In this talk I will describe my recent efforts to extend the moving puncture paradigm to include other formulations of the Einstein equations and other gauge conditions. Numerical testing of these ideas is carried out using a simple 1D code that assumes spherical symmetry, suitable for modeling a single non-spinning black hole. [Preview Abstract] |
Monday, April 16, 2007 3:42PM - 3:54PM |
U12.00002: 1+log slicing in gravitatonal collapse David Garfinkle, Carsten Gundlach, David Hilditch Computer simulations using 1+log slicing are performed of the gravitational collapse of a spherically symmetric scalar field. We find that without excision the simulations are in general badly behaved, but that they are well behaved with excision. [Preview Abstract] |
Monday, April 16, 2007 3:54PM - 4:06PM |
U12.00003: Parca: A Paramesh-Based Driver for Cactus David Fiske, Erik Schnetter, Manuel Tiglio The talk will introduce the Parca software, which allows the Paramesh AMR libraries to be used as a Cactus driver thorn. Both Paramesh and Cactus have become fixtures in the numerical relativity community, but until the development of the Parca software Paramesh-based codes were completely incompatible with Cactus-based codes and vice-versa. Preliminary results demonstrating the interoperability of the Parca driver with existing Cactus thorns will be shown. [Preview Abstract] |
Monday, April 16, 2007 4:06PM - 4:18PM |
U12.00004: Multi-block systems in numerical relativity Erik Schnetter, Peter Diener, Nils Dorband, Enrique Pazos, Manuel Tiglio Multi-block (or multi-patch) systems are computational methods to discretise manifolds by covering them with several independent blocks. Each block is then discretised in a conventional way, e.g.using finite differences. Thus multi-block systems are a natural approach in general relativity, where they correspond to using several maps to cover a domain. Multi-block systems have several major advantages: They can be used to avoid coordinate singularities, to use coordinates that are adapted to a particular problem, and to place numerical resolution where desired. In particular, they can be used to model spherical boundaries in a smooth manner and to track gravitational radiation efficiently in the wave zone of compact sources. While adaptive mesh refinement is essential to achieve a necessary accuracy \emph{locally}, multi-block methods are superior in adapting a discretisation \emph{globally} to a given problem setup. We report on recent results of fully relativistic three-dimensional time-dependent black hole simulations using multi-block systems. We will compare accuracy and efficiency to mesh refinement methods, demonstrating certain advantages of multi-block discretisations. [Preview Abstract] |
Monday, April 16, 2007 4:18PM - 4:30PM |
U12.00005: Using adaptive finite element toolkit to generate initial data for multi-block infrastructure Oleg Korobkin Applications of finite elements toolkit (FEtk) for generating initial data compatible with multiblock infrastructure are explored. In finite element methods, in particular for high-order finite element case in 3D, interpolation of solution to cartesian grid is rather time-consuming. If finite element mesh has to be generated in such a way that its vertices correspond to cartesian grid, no interpolation will be required and solution can be transparently ported to finite differences code (like Cactus), and back. An algorithm for generating such mesh for multiblock infrastructure was developed. Sample Brill wave initial data solutions obtained with use of this algorithm on FEtk with adaptive mesh refinement are presented. [Preview Abstract] |
Monday, April 16, 2007 4:30PM - 4:42PM |
U12.00006: ABSTRACT WITHDRAWN |
Monday, April 16, 2007 4:42PM - 4:54PM |
U12.00007: The Periodic Standing Wave Approximation; second-order Post-Minkowski Formalism and Methods Richard H. Price, Christopher Beetle, Benjamin C. Bromley, Napoleon G. Hernandez It has been shown with model problems involving nonlinear scalar fields that a helically symmetric solution, with standing waves, can be a useful approximation to the slow inspiral of binary neutron stars or black holes. The formalism was recently worked out to deal efficiently with linearized gravity in the harmonic gauge. We now present the extension of the method to the second-order Post-Minkowski approximation to general relativity. In particular it is shown that the formalism is easily extended to full general relativity. [Preview Abstract] |
Monday, April 16, 2007 4:54PM - 5:06PM |
U12.00008: Adapted coordinates and the ``eigenspectral'' method for solving the periodic standing wave problem Benjamin C. Bromley, Christopher Beetle, Napoleon G. Hernandez, Richard H. Price The Periodic Standing Wave (PSW) method describes the orbits of binary black holes and neutron stars in the limit when the inspiral is slow. Here, we describe a numerical approach for solving the binary problem in the PSW approximation. Our code uses grid-based finite differences and ``adapted coordinates'' whose spatial distribution is tuned for a binary pair of compact masses. We also motivate the need to use multipole filtering with ``eigenspectral'' functions, which are grid-based analogs of spherical harmonics. The geometry of the adapted coordinate grid allows only a relatively few low-order eigenspectral modes to carry nealy all of the physically relevant information, making the code both accurate and efficient. We present the results of several tests, starting with scalar models, linearized gravity, and a post-Minkowksi treatment. Finally, we discuss progress toward solving the binary black hole problem in full General Relativity. [Preview Abstract] |
Monday, April 16, 2007 5:06PM - 5:18PM |
U12.00009: Post-Minkowski Perturbation Theory for the Periodic Standing-Wave Problem Christopher Beetle This talk will present a formulation of post-Minkowski perturbation theory suitable for direct numerical implementation. It will discuss both the motion of sources and the generation of fields. This technique is currently being used to generate helically-symmetric solutions of the periodic standing-wave problem for binary black hole systems. This example will be used throughout to help clarify the motivation and content of the results. [Preview Abstract] |
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