Aliasing instabilities in the numerical evolution of the Einstein field equations

The Einstein field equations of gravitation are characterized by cross-scale, high-order nonlinear terms, representing a challenge for numerical modeling. In an exact spectral decomposition, high-order nonlinearities correspond to a convolution that numerically might lead to aliasing instabilities....

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Bibliographic Details
Published in:General relativity and gravitation Vol. 53; no. 10
Main Authors: Meringolo, C., Servidio, S.
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2021
Springer Nature B.V
Subjects:
Algorithms
Aliasing
Astronomy
Astrophysics and Cosmology
Boundary conditions
Cartesian coordinates
Classical and Quantum Gravitation
Decomposition
Differential Geometry
Einstein equations
Gravitation
Gravity
Mathematical and Computational Physics
Nonlinearity
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Research Article
Spectra
Theoretical
Wavelengths
Numerical relativity
Black hole dynamics
BSSN decomposition
Gravitational testbeds
ISSN:0001-7701, 1572-9532
Online Access:Get full text
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Summary:The Einstein field equations of gravitation are characterized by cross-scale, high-order nonlinear terms, representing a challenge for numerical modeling. In an exact spectral decomposition, high-order nonlinearities correspond to a convolution that numerically might lead to aliasing instabilities. We present a study of this problem, in vacuum conditions, based on the 3 + 1 Baumgarte–Shibata–Shapiro–Nakamura (BSSN) formalism. We inspect the emergence of numerical artifacts, in a variety of conditions, by using the Spectral-FIltered Numerical Gravity codE (SFINGE)—a pseudo-spectral algorithm, based on a classical (Cartesian) Fourier decomposition. By monitoring the highest k - modes of the dynamical fields, we identify the culprits of the aliasing and propose procedures that cure such instabilities, based on the suppression of the aliased wavelengths. This simple algorithm, together with appropriate treatment of the boundary conditions, can be applied to a variety of gravitational problems, including those related to massive objects dynamics.
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ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-021-02865-5