Multidomain spectral method for the helically reduced wave equation

✍ Scribed by Stephen R. Lau; Richard H. Price

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 995 KB
• Volume: 227
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2007.08.032

✦ Synopsis

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.