An application of the multi-grid method to the construction of initial data for Brill waves (Q911736)

The purpose of this paper is to demonstrate the efficiency and accuracy of a multi-grid algorithm for solving the time-symmetric constraint equation for axisymmetric, non rotating, vacuum spacetimes, i.e. an equation arising from the \(3+1\) description of general relativity. For the multi-grid algorithm the authors provide a local mode analysis of the difference equation and derive a value for the amplification factor used to obtain a theoretical optimal convergence rate. It is shown that the presented multi-grid algorithm can reach the convergence criterion nearly 10 times faster than a standard successive-overrelaxation scheme. Moreover, the authors compare computer resource requirements (memory and CPU time) along with efficiencies.