Abstract
In this article we describe applications of the numerical method of discrete differential forms in computational general relativity (GR). In particular, we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As described in an earlier paper, the discrete differential form approach provides accurate results in spherically symmetric static spacetimes [R. Richter, J. Frauendiener, and M. Vogel, Classical Quantum Gravity, 24 (2007), p. 433], and it is manifestly coordinate independent. Here, we extend the method to time dependent systems. We use the polarized Gowdy solution as a testbed for two numerical schemes. One scheme reproduces that solution very well; in particular, it is stable for a long time and converges quadratically.