Summation by parts and dissipation for domains with excised regions

GIOEL CALABRESE, LUIS LEHNER, OSCAR REULA, OLIVIER SARBACH, MANUEL TIGLIO

CLASSICAL AND QUANTUM GRAVITY

Año: 2004 vol. 21 p. 5735 - 5758

0264-9381

We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct dissipative and difference operators that satisfy the {\it summation by parts} property in domains with excised multiple cubic regions. This property can be used to derive semi-discrete energy estimates for the associated initial-boundary value problem which in turn can be used to prove numerical stability.