Tools for Characterizing the Numerical Error of Stellar Oscillation Codes

TL;DR

This paper introduces tools called 'error measures' to quantify the numerical errors in stellar oscillation codes, focusing on the GYRE code but applicable broadly, by analyzing how calculation parameters affect accuracy.

Contribution

The paper presents a novel set of error measures for characterizing numerical errors in stellar oscillation codes, with a detailed analysis of their behavior and an idealized error model.

Findings

Error measures effectively quantify numerical errors.

Error behavior depends on calculation parameters like grid points.

The analysis is applicable beyond the GYRE code.

Abstract

Stellar oscillation codes are software instruments that evaluate the normal-mode frequencies of an input stellar model. While inter-code comparisons are often used to confirm the correctness of calculations, they are not suitable for characterizing the numerical error of an individual code. To address this issue, we introduce a set of tools -- 'error measures' -- that facilitate this characterization. We explore the behavior of these error measures as calculation parameters, such as the number of radial grid points used to discretize the oscillation equations, are varied; and we summarize this behavior via an idealized error model. While our analysis focuses on the GYRE code, it remains broadly applicable to other oscillation codes.