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arxiv: gr-qc/0308007 · v2 · submitted 2003-08-03 · 🌀 gr-qc

Summation by parts and dissipation for domains with excised regions

classification 🌀 gr-qc
keywords domainsdifferenceexcisedpartspropertyregionssummationused
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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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    Derives a provably stable 3D SBP scheme for linear waves on hyperboloidal slices using compactification, rescaling, and abstract dissipation in spherical polar coordinates.