Physical Sciences and Mathematics Commons^™

Sparse Spectral-Tau Method For The Three-Dimensional Helically Reduced Wave Equation On Two-Center Domains, Stephen R. Lau, Richard H. Price

Physics and Astronomy Faculty Publications and Presentations

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 …