Barycentric interpolation on Riemannian and semi-Riemannian spaces

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http://hdl.handle.net/10138/308017

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Pihajoki , P , Mannerkoski , M & Johansson , P H 2019 , ' Barycentric interpolation on Riemannian and semi-Riemannian spaces ' , Monthly Notices of the Royal Astronomical Society , vol. 489 , no. 3 , pp. 4161-4169 . https://doi.org/10.1093/mnras/stz2447

Title: Barycentric interpolation on Riemannian and semi-Riemannian spaces
Author: Pihajoki, Pauli; Mannerkoski, Matias; Johansson, Peter H.
Contributor: University of Helsinki, Particle Physics and Astrophysics
University of Helsinki, Department of Physics
University of Helsinki, Particle Physics and Astrophysics
Date: 2019-11
Language: eng
Number of pages: 9
Belongs to series: Monthly Notices of the Royal Astronomical Society
ISSN: 0035-8711
URI: http://hdl.handle.net/10138/308017
Abstract: Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is a 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 space-time. 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.
Subject: black hole physics
MHD-methods: data analysis
methods: numerical
SCATTERED DATA
FIELD
CONSTRUCTION
SURFACE
SPHERE
DISKS
115 Astronomy, Space science
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