Multidomain spectral method for the helically reduced wave equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:227

Article

Lau, Stephen R.^1,2  Price, Richard H.³ 

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87111 USA

[3] Univ Texas Brownsville, Dept Phys & Astron, Ctr Gravitat Wave Astron, Brownsville, TX 78520 USA

关键词: helical symmetry;    spectral methods;    gravitational waves;    mixed PDE;   

DOI  :  10.1016/j.jcp.2007.08.032

来源: Elsevier

【 摘 要 】

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the eigenspectral method. Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free