Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

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

[1] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA

[2] Univ Texas Brownsville, Dept Phys & Astron, Ctr Adv Radio Astron, Brownsville, TX 78520 USA

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

关键词: Spectral methods;    Gravitational waves;    Wave equation;    Mixed-type problems;    Preconditioning;    Helical symmetry;   

DOI  :  10.1016/j.jcp.2012.07.006

来源: Elsevier

【 摘 要 】

We describe a multidomain spectral-tau method for solving the three-dimensional helically reduced wave equation on the type of two-center domain that arises when modeling compact binary objects in astrophysical applications. A global two-center domain may arise as the union of Cartesian blocks, cylindrical shells, and inner and outer spherical shells. For each such subdomain, our key objective is to realize certain (differential and multiplication) physical-space operators as matrices acting on the corresponding set of modal coefficients. We then achieve sparse realizations through the integration preconditioning of Coutsias, Hagstrom, Hesthaven, and Torres. Since ours is the first three-dimensional multidomain implementation of the technique, we focus on the issue of convergence for the global solver, here the alternating Schwarz method accelerated by GMRES. Our methods may prove relevant for numerical solution of other mixed-type or elliptic problems, and in particular for the generation of initial data in general relativity. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free