We develop and use a novel mixed-precision weighted essentially non-oscillatory(WENO)method for solving the Teukolsky equation,which arises when modeling perturbations of Kerr black holes.We show that WENO methods out...We develop and use a novel mixed-precision weighted essentially non-oscillatory(WENO)method for solving the Teukolsky equation,which arises when modeling perturbations of Kerr black holes.We show that WENO methods outperform higher-order finite-difference methods,standard in the discretization of the Teukolsky equation,due to the need to add dissipation for stability purposes in the latter.In particular,as the WENO scheme uses no additional dissipation,it is well suited for scenarios requiring long-time evolution such as the study of price tails and gravitational wave emission from extreme mass ratio bina-ries.In the mixed-precision approach,the expensive computation of the WENO weights is performed in reduced floating-point precision that results in a significant speedup factor of≈3.3.In addition,we use state-of-the-art Nvidia general-purpose graphics processing units and cluster parallelism to further accelerate the WENO computations.Our optimized WENO solver can be used to quickly generate accurate results of significance in the field of black hole and gravitational wave physics.We apply our solver to study the behavior of the Aretakis charge—a conserved quantity,that if detected by a gravitational wave observatory like LIGO/Virgo would prove the existence of extremal black holes.展开更多
基金support of NSF Grants No.PHY-2010685(G.K)and No.DMS-1912716(S.F,S.G,and G.K),AFOSR Grant No.FA9550-18-1-0383(S.G)Office of Naval Research/Defense University Research Instrumentation Program(ONR/DURIP)Grant No.N00014181255+2 种基金the National Science Foundation under Grant No.DMS-1439786 while a subset of the authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence,RI,during the Advances in Computational Relativity program.A part of this research is sponsored by the Office of Advanced Scientific Computing ResearchUS Department of Energy,and was performed at the Oak Ridge National Laboratory,which is managed by UT-Battelle,LLC under Contract no.De-AC05-00OR22725UT-Battelle,LLC,under contract DE-AC05-00OR22725 with the US Department of Energy.
文摘We develop and use a novel mixed-precision weighted essentially non-oscillatory(WENO)method for solving the Teukolsky equation,which arises when modeling perturbations of Kerr black holes.We show that WENO methods outperform higher-order finite-difference methods,standard in the discretization of the Teukolsky equation,due to the need to add dissipation for stability purposes in the latter.In particular,as the WENO scheme uses no additional dissipation,it is well suited for scenarios requiring long-time evolution such as the study of price tails and gravitational wave emission from extreme mass ratio bina-ries.In the mixed-precision approach,the expensive computation of the WENO weights is performed in reduced floating-point precision that results in a significant speedup factor of≈3.3.In addition,we use state-of-the-art Nvidia general-purpose graphics processing units and cluster parallelism to further accelerate the WENO computations.Our optimized WENO solver can be used to quickly generate accurate results of significance in the field of black hole and gravitational wave physics.We apply our solver to study the behavior of the Aretakis charge—a conserved quantity,that if detected by a gravitational wave observatory like LIGO/Virgo would prove the existence of extremal black holes.
