Derives a provably stable 3D SBP scheme for linear waves on hyperboloidal slices using compactification, rescaling, and abstract dissipation in spherical polar coordinates.
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. II. The evolution equations
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abstract
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution equations obtained from the conformal field equations. In particular we discuss in detail the choice of gauge source functions and the treatment of the boundaries. Of particular importance is the process of ``radiation extraction'' which can be performed in a straightforward way in the present formalism.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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3d Summation-by-Parts scheme for Linear Wave Equations on Hyperboloidal Slices
Derives a provably stable 3D SBP scheme for linear waves on hyperboloidal slices using compactification, rescaling, and abstract dissipation in spherical polar coordinates.