Summation by parts and dissipation for domains with excised regions

Details Summation by parts and dissipation for domains with excised regions Summation by parts and dissipation for domains with excised regions

2003-08-03

arxiv.org/abs/gr-qc/0308007v2

Class.Quant.Grav. 21 (2004) 5735-5758

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Some minor changes in presentation, to appear in CQG. 20 pages

Scientific paper

10.1088/0264-9381/21/24/004

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.

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