Abstract
We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a three-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the formulation and measure its stability properties under Dirichlet, Neumann, and Sommerfeld boundary conditions. We demonstrate the robust stability of a specific evolution-boundary algorithm under random constraint violating initial data and random boundary data.
- Received 9 December 1999
DOI:https://doi.org/10.1103/PhysRevD.62.104006
©2000 American Physical Society