Summation by parts and dissipation for domains with excised regions

الأصل · EN

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 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.