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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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