Bulletin of the American Physical Society
APS April Meeting 2018
Volume 63, Number 4
Saturday–Tuesday, April 14–17, 2018; Columbus, Ohio
Session X15: Numerical Relativity: Algorithms and Code Development |
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Sponsoring Units: DGRAV Chair: Mark Scheel, Caltech Room: B230-231 |
Tuesday, April 17, 2018 10:45AM - 10:57AM |
X15.00001: Generating Gravitational Waveforms Beyond BBHs Using Waveform Splicing Kevin Barkett, Vijay Varma, Mark Scheel, Yanbei Chen It is important for gravitational wave detectors to distinguish between binary black hole mergers and systems that incorporate additional physics, such as the presence of neutron star matter or beyond-GR effects. Properly capturing this additional information requires waveform models that encompass the space of theoretically possible waveforms to match against detector data. However, running full numerical simulations over the entire parameter space, including matter or additional physics, is prohibitively expensive, while analytic perturbative results lack the requisite accuracy for comparison. 'Waveform Splicing' utilizes those perturbative expressions to enhance the numerical solutions of binary black hole coalescence, sidestepping the drawbacks of both methods. We demonstrate how Waveform Splicing can be used to incorporate tidal information for binary neutron stars, as well as the merger of black hole objects in theories beyond GR. [Preview Abstract] |
Tuesday, April 17, 2018 10:57AM - 11:09AM |
X15.00002: Tuning spin and eccentricity for generic binary black hole simulations Harald Pfeiffer, Katerina Chatziioannou Numerical simulations of binary black holes play an important role in constructing waveform models for gravitational wave detectors, and in interpreting the recent gravitational wave observations by LIGO and Virgo. Such simulations require specification of initial data parameters, which indirectly control masses, spins and the geometry of the orbit, including the orbital eccentricity. Initial data parameters must be tuned to achieve a binary with certain physical properties. For zero eccentricity and non-precessing spins, this problem was solved by iterative eccentricity removal, where one analyzes preliminary evolutions, and then corrects the initial data parameters. This talk presents generalizations of this procedure that allow us to control the spin-directions even in the presence of precession as well as the orbital eccentricity. [Preview Abstract] |
Tuesday, April 17, 2018 11:09AM - 11:21AM |
X15.00003: SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics Lawrence Kidder We provide an update on the development of SpECTRE (https://github.com/sxs-collaboration/spectre), a new open-source relativistic astrophysics code that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers, while making efficient use of the largest supercomputers. [Preview Abstract] |
Tuesday, April 17, 2018 11:21AM - 11:33AM |
X15.00004: Solving Einstein's Equations Using Discontinuous Galerkin Methods Eamonn O'Shea The success of LIGO in discovering gravitational waves from binary black hole (BBH) mergers has been aided by several large catalogs of waveforms produced from simulations of BBH mergers through inspiral, merger and ringdown. One such catalog was produced using the SpEC code, which solves the Generalized Harmonic form of Einstein's equations using spectral collocation methods. With the advent of multi-messenger astrophysics, we require codes that can accurately calculate the gravitational wave signals from merger events involving neutron stars, which are beyond the capabilities of spectral methods. Discontinuous Galerkin (DG) methods have emerged as a robust method which demonstrate spectral convergence for smooth solutions, and can also capture shocks present in hydrodynamical systems. SpECTRE is a code which implements DG methods using task based parallelism, shown by Kidder et al.\footnote{Kidder et al., arXiv:1609.00098} to effectively scale to massive supercomputers when solving various hydrodynamics problems.We show how the Generalized Harmonic form of Einstein's equations can be implemented within SpECTRE. With the specific example of a 3D Kerr-Schild black hole, we show that we achieve exponential convergence and also a stable evolution over long times. [Preview Abstract] |
Tuesday, April 17, 2018 11:33AM - 11:45AM |
X15.00005: General-relativistic neutron star evolutions with the discontinuous Galerkin method Francois Hebert, Lawrence Kidder, Saul Teukolsky Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin (DG) method combines these features --- a high order of convergence in regions where the solution is smooth, and shock-capturing properties for regions where it is not --- with geometric flexibility, and is therefore well-suited to solve the PDEs describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the DG method. We simultaneously evolve the spacetime geometry and the neutron star matter on the same computational grid, which we conform to the spherical geometry of the problem. The evolutions show long-term stability, good accuracy, and improved rate of convergence versus a comparable-resolution finite volume method. [Preview Abstract] |
Tuesday, April 17, 2018 11:45AM - 11:57AM |
X15.00006: High-order local time stepping for GR-hydrodynamics simulations William Throwe Simulations involving a large range of length or time scales are inefficient due to the number of evaluations of evolution equations being set by the most stringent scales. Using a local time stepping scheme, where different degrees of freedom are evaluated at different times, can resolve this issue, but such schemes are generally low-order or fail to preserve conservation laws. We present a conservative, high-order local time stepping scheme applied to a discontinuous Galerkin method suitable for General Relativity and hydrodynamics simulations. [Preview Abstract] |
Tuesday, April 17, 2018 11:57AM - 12:09PM |
X15.00007: Helmholtz's third theorem in numerical general relativity Charalampos Markakis The motion of strongly gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations, combining fluid dynamics with general relativity. Centuries after their advent, the solution to these equations remains mathematically and computationally difficult, and the break-down of well-posedness on the boundary interface between fluid and vacuum remains a challenging open problem. The problem manifests itself in numerical simulations of binary neutron-star inspiral. This work focuses on formulating and implementing well-posed, acoustical and canonical hydrodynamic schemes, suitable for inspiral simulations and gravitational-wave source modelling, with promising mathematical and computational applications. The scheme uses a variational principle by Carter-Lichnerowicz stating that barotropic fluid motions are conformally geodesic, Helmholtz's third theorem stating that initially irrotational flows remain irrotational, and Christodoulou's acoustic metric approach adopted to numerical relativity, in order to evolve the canonical momentum of a fluid element via Hamilton's equations. The recent observation of the inspiral of binary neutron stars by the LIGO-Virgo collaboration makes this work timely. [Preview Abstract] |
Tuesday, April 17, 2018 12:09PM - 12:21PM |
X15.00008: Scheduled Relaxation Jacobi Method for Initial Data Problems Vedant Puri, Roland Haas, Eloisa Bentivegna Modeling scenarios in astrophysics with numerical relativity simulations requires the production of suitable initial data sets--a computationally expensive task that involves solving Poisson-like elliptic partial differential equations. To facilitate and accelerate the generation of initial data, we present a novel Scheduled Relaxation Jacobi (SRJ) method, a variant of successive over-relaxation schemes, coupled with a Newton-Raphson method. SRJ computes approximate relaxation factors with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The well known Newton-Raphson methodology expands the SRJ method to nonlinear problems. We quantify the performance of our new method by computing initial data for the metric of a binary black hole system, and compare it to the solution obtained with TwoPunctures, a spectral solver in the Einstein Toolkit. [Preview Abstract] |
Tuesday, April 17, 2018 12:21PM - 12:33PM |
X15.00009: Hyperbolic Initial Data for Nontrivial Spacetimes Maria Babiuc Hamilton The first requirement for the success of numerical relativity simulations is a reliable and accurate method of constructing initial data. The standard techniques use elliptic equations that require boundary conditions, and are plagued by junk radiation. We present a novel numerical technique to generate initial data for the simulation of black holes, using a recent analytical approach in which the spacetime is described by a metric of Kerr-Schild form, with the constraints written as three strongly hyperbolic and one algebraic equation. We have completed the code that implements the algebraic algorithm for constructing hyperbolically-constrained initial data for single black holes. Tests prove the code converges, even inside the event horizon, and it has long-term, robust stability. We present our work in progress to develop key tests, such as a near-light-speed boosted black hole and a spinning Kerr hole, which are essential to prove that the code is correctly able to evolve nontrivial spacetimes. Next, the code will be tested with the geometry of a binary black hole system, a superposition of Kerr-Schild solutions. To assess its usefulness in reducing spurious radiation, this code will be tested against codes using elliptical methods, for the same binary black hole ansatz. [Preview Abstract] |
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