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arXiv · gr-qc/0308007

Summation by parts and dissipation for domains with excised regions

Gioel Calabrese·Luis Lehner·Oscar Reula·Olivier Sarbach·Manuel Tiglio
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Abstract

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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Gioel Calabrese, Luis Lehner, Oscar Reula, Olivier Sarbach, Manuel Tiglio. 2004-10-18. Summation by parts and dissipation for domains with excised regions. https://doi.org/10.1088/0264-9381%2F21%2F24%2F004

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