Summation by Parts and Truncation Error Matching on Hyperboloidal Slices

Understand

We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain.

• This inclusion serves to mitigate outer boundary effects and, in the future, will help reduce systematic errors in gravitational waveform extraction.
• We also study a setup with truncation error matching.
• Our SBP-Stable scheme guarantees energy-balance for a class of linear wave equations at the semidiscrete level.