Cauchy boundaries in linearized gravitational theory
arXiv:gr-qc/9912030 · doi:10.1103/PhysRevD.62.104006
Abstract
We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-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 3+1 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.
23 pages including 3 figures and 2 tables, revtex
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