Barycentric interpolation on Riemannian and semi-Riemannian spaces

Autor:	Pihajoki, Pauli, Mannerkoski, Matias, Johansson, Peter H.
Rok vydání:	2019
Předmět:	Astrophysics - Instrumentation and Methods for Astrophysics Astrophysics - High Energy Astrophysical Phenomena Mathematics - Numerical Analysis Physics - Data Analysis Statistics and Probability
Druh dokumentu:	Working Paper
DOI:	10.1093/mnras/stz2447
Popis:	Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is an ubiquitous task in all of physics. In this work we present a covariant generalization of the barycentric coordinates and the barycentric interpolation method for Riemannian and semi-Riemannian spaces of arbitrary dimension. We show that our new method preserves the linear accuracy property of barycentric interpolation in a coordinate-invariant sense. In addition, we show how the method can be used to interpolate constrained quantities so that the given constraint is automatically respected. We showcase the method with two astrophysics related examples situated in the curved Kerr spacetime. The first problem is interpolating a locally constant vector field, in which case curvature effects are expected to be maximally important. The second example is a General Relativistic Magnetohydrodynamics simulation of a turbulent accretion flow around a black hole, wherein high intrinsic variability is expected to be at least as important as curvature effects. Comment: 10 pages, 3 figures. Revised version with small additions, accepted to MNRAS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.09487 Zobrazit plný text záznamu View this record from Arxiv