Bulletin of the American Physical Society
APS April Meeting 2015
Volume 60, Number 4
Saturday–Tuesday, April 11–14, 2015; Baltimore, Maryland
Session K13: Numerical Relativity: Algorithms and Code Development |
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Sponsoring Units: GGR Chair: James Healy, Georgia Institute of Technology Room: Key 9 |
Sunday, April 12, 2015 1:30PM - 1:42PM |
K13.00001: Spectral Cauchy Characteristic Extraction: Gravitational Waves and Gauge Free News Casey Handmer, Bela Szilagyi, Jeff Winicour We present a fast, accurate spectral algorithm for the characteristic evolution of the full non-linear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate how spectral Cauchy characteristic extraction produces gravitational News without confounding gauge effects. We explain several numerical innovations and demonstrate speed, stability, accuracy, exponential convergence, and consistency with existing methods. We highlight its capability to deliver physical insights in the study of black hole binaries. [Preview Abstract] |
Sunday, April 12, 2015 1:42PM - 1:54PM |
K13.00002: Numerical Study of the Gravitational and Electromagnetic Waves on the Null Cone Maria Babiuc The numerical calculation of the Einstein-Maxwell equations in a characteristic framework has not been done numerically before and is expected to shed new light on nonlinear phenomena like null memory. The main objective of this study is the analytical and numerical modeling of the of gravitational and electromagnetic radiation in a fully general relativistic framework, as it propagates on the null cone to null infinity, with no simplifications due to assumed symmetries. Moreover, the global interaction between the gravitational and electromagnetic radiation will be closely monitored, in order to reveal the electromagnetic radiation memory induced by the gravitational field. The numerical approach used, called the ``Cauchy-characteristic extraction'' method, is the most precise method for the computation of gravitational waveforms at infinite distance from a world-tube that encloses the source. The analytical and numerical models presented here will be implemented in the PittNull code, and the experience gained will be disseminated, in order to facilitate new standalone characteristic codes.This will lead to more insight on the interaction between gravitational and electromagnetic fields, and even point to new effects. [Preview Abstract] |
Sunday, April 12, 2015 1:54PM - 2:06PM |
K13.00003: Coulomb Scalars, Tendicities, and Vorticities of Black Hole Spacetimes in Numerical Relativity Tehani Finch, Bernard Kelly, John Baker A choice of time slicing specifies a split of the Weyl tensor into gravitoelectric and gravitomagnetic components. These components can be combined into a single complex quantity, one of whose eigenvalues gives an invariant called the Coulomb scalar; or they can be treated as separate real quantities, whose respective eigenvalues have been termed the tendicity and vorticity. This latter pair has recently gained attention as a vehicle for visualization and analysis of strongly curved spacetimes, and here we compare Coulomb-scalar and tendicity-vorticity calculations for black holes in binary systems. [Preview Abstract] |
Sunday, April 12, 2015 2:06PM - 2:18PM |
K13.00004: Accelerating black hole simulations with GPUs Adam Lewis, Abdul Mrou\'e, Harald Pfeiffer Progress in numerical relativity remains constrained by the high time cost of integrating the Einstein equations. Since this cost is set mostly by floating point performance and by limits to parallelism, computation with graphical processing units (GPUs) offers great promise. We discuss our efforts to port the Spectral Einstein Code to NVIDIA GPUs, yielding a factor-7 speedup. We further discuss the challenges we encountered during the port and the new simulations it will make possible. [Preview Abstract] |
Sunday, April 12, 2015 2:18PM - 2:30PM |
K13.00005: Curvature-Based Method for Measuring Numerical Black-Hole Spins Bernard Kelly, Tehani Finch, James van Meter, John Baker Accurate determination of spin magnitude and direction over time is crucial for the development of gravitational-wave templates that faithfully reflect the dynamics of generic comparable-mass black-hole binary mergers. We report on the development of a new method for measuring black-hole spins during numerical-relativity simulations of black-hole binary mergers. This method is based on the ``spin scalar,'' a complex scalar field derived from the Coulomb scalar of Beetle \& Burko (2002). Our new method can be used to derive both spin magnitude and direction, and can be combined with other techniques, such as isolated-horizon methods. We present convergence studies, and demonstrations of behavior during precessing mergers of spinning black holes. [Preview Abstract] |
Sunday, April 12, 2015 2:30PM - 2:42PM |
K13.00006: Smooth Is Overrated: Generalizing Discontinuous Galerkin Methods for Numerical Relativity Jonah Miller, Erik Schnetter Discontinuous Galerkin Finite Element (DGFE) methods offer a mathematically beautiful and computationally efficient way to solve hyperbolic PDEs. This approach is well parallelizable and has been very successful in computational fluid dynamics and electrodynamics. Therefore, we are generalizing and adapting it to numerical relativity. In this talk, we briefly describe a generalized formulation of DGFE methods suitable for use with the BSSN formulation of Einstein's equations. We then discuss results of recent (3+1)-dimensional simulations using our formulation. [Preview Abstract] |
Sunday, April 12, 2015 2:42PM - 2:54PM |
K13.00007: Exploring the Use of Discontinuous Galerkin Methods for Numerical Relativity Francois Hebert, Lawrence Kidder, Saul Teukolsky The limited accuracy of relativistic hydrodynamic simulations constrains our insight into several important research problems, including among others our ability to generate accurate template waveforms for black hole-neutron star mergers, or our understanding of supernova explosion mechanisms. In many codes the algorithms used to evolve the matter, based on the finite volume method, struggle to reach the desired accuracy. We aim to show improved accuracy by using a discontinuous Galerkin method. This method's attractiveness comes from its combination of spectral convergence properties for smooth solutions and robust stability properties for shocks. We present the status of our work implementing a testbed GR-hydro code using discontinuous Galerkin. [Preview Abstract] |
Sunday, April 12, 2015 2:54PM - 3:06PM |
K13.00008: Adaptive Wavelets Methods in Numerical Relativity Eric Hirschmann, Matt Anderson, David Neilsen, Jackson Debuhr, Bo Zhang Adaptive, multiresolution wavelet methods are a proimising approach to obtaining robust spatial grid adaptation. Developed over the last couple of decades in the computational fluid dynamics community, we examine the applicability and utility of such methods in relativistic settings, in particular relativistic magnetohydrodynamics. We will attempt to demonstrate their good properties relative to robustness, efficiency and parallelizability. [Preview Abstract] |
Sunday, April 12, 2015 3:06PM - 3:18PM |
K13.00009: A stable high-order multipatch method for black hole accretion simulations Wyatt Brege In black hole simulations it is difficult to maintain design order accuracy for fluid evolutions in regions near excision inner-boundaries of the horizon, where many methods remove information from the matter inflow of black hole-neutron star binary evolutions and other accretion type problems. With a multipatch Energy Stable Weighted Essentially non-Oscillatory (ESWENO) scheme, high order accuracy between patch interfaces and on domain data boundaries can be ensured for the hydrodynamic variables. We present applications of a working multipatch ESWENO, focusing on multidimensional shock capture and preliminary results for black hole accretion disk problems. [Preview Abstract] |
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