3D Summation-By-Parts Schemes on Hyperboloidal Slices

by István Rácz (HUN-REN Wigner RCP)

Friday 13 Feb 2026, 14:00 → 15:00 Europe/Budapest

Tanácsterem (III. ép.)

This talk addresses the numerical part of attaining a stable evolution of the hyperboloidal initial value problems for long times. I  will describe a fully 3-dimensional Summation-By-Parts (SBP) scheme for a class of linear wave equations on hyperboloidal slices, on a Minkowski background, all derived in spherical polar coordinates. The major strength of this scheme is that it is provably stable, and allows having grid points at the origin and on the z-axis, despite coordinate singularities, and at infinity, despite a formal singularity arising due to compactification. Reducing it to a Cauchy problem on the standard Cauchy slices, or on finite spacelike slices with an outer boundary, is a straightforward exercise. Its generalizations to general, including dynamical, backgrounds is also proposed, which could also be used to evolve a general matter distribution, like fluids, etc.  Promising results are obtained, giving hope for application to the nonlinear systems, like the Einstein Field Equations.