Experimentally constructing finite difference algorithms in numerical relativity

Matthew Anderson, University of Texas

Computational studies of gravitational radiation require numerical algorithms with long-term stability (necessary for convergence). However, constructing stable finite difference algorithms (FDA) for the Arnowitt-Desser-Misner (ADM) formulation of the Einstein equations, especially in multiple dimensions, has proven difficult. Most FDA’s are constructed using rules of thumb gained from experience with simple model equations. To search for FDA’s with improved stability, we adopt a brute-force approach, where we systematically test thousands of numerical schemes. We sort the spatial derivatives of the Einstein equations into groups, and parameterize each group by finite difference type (centered or upwind) and order.

We present results from numerical simulations of single and multiple black hole spacetimes using various finite difference algorithms.

Abstract Author(s): Matthew Anderson<br />David Neilsen<br />Richard Matzner