Title: A remark on the multi-domain hybrid method for calculating the power-law decay of the gravitational radiation waveforms with analytic radiation boundary conditions
Authors: Joshua Buli; Jae-Hun Jung; Debananda Chakraborty
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA; Department of Mathematics, University of California, Riverside, Riverside, CA 92521, USA
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
Department of Mathematics, Virginia Intermont College, Bristol, Virginia 24201, USA
Abstract: A hybrid method based on the multi-domain spectral and finite difference methods is considered for computing the power-law decay of gravitational radiation waveforms. For the radiation boundary condition, we adopt the analytic radiation boundary condition based on the Laplace transformation of kernel functions developed by Lau (2005). In this note, we present several numerical results for the orbital index l = 2 with the hybrid and Lau's method. The Lau's method enables the hybrid method to obtain the power-law decay even when the computational domain is small, but the numerical results show that the proper power-law decay rate, p = 7 is not obtained. Instead, we obtained p ∼ 4, which corresponds to the power-law decay rate extracted when the outer domain goes to ∞. We remark that the system of equations or high order method with high precision is necessary for obtaining the proper decay rate.
Keywords: radiation boundary conditions; gravitational radiation waveforms; spectral methods; finite difference method; FDM; power law decay; Laplace transformation; kernel functions; decay rate.
Int. J. of Applied Nonlinear Science, 2014 Vol.1, No.2, pp.104 - 121
Submission date: 25 Jan 2013
Date of acceptance: 09 Sep 2013
Available online: 24 May 2014