Determining normal mode features from numerical simulations using CEOF analysis: I. Test case using transverse oscillations of a magnetic slab 

Ramon Oliver Submitted: 20190204 01:44
We present a method to determine approximations to a system's normal mode eigenfrequency and eigenfunctions from timedependent numerical simulations. The method proceeds iteratively and each step consists of (i) a timedependent numerical simulation followed by (ii) the Complex Empirical Orthogonal Function (CEOF) analysis of the simulation results. The CEOF analysis provides an approximation to the normal mode eigenfunctions that can be used to set up the initial conditions for the numerical simulation of the following iteration, in which an improved normal mode approximation is obtained. The iterative process is stopped once the global difference between successive approximate eigenfunctions is below a prescribed threshold. In this paper we test the method with a problem for which the normal modes can be computed analytically, namely the transverse oscillations of a magnetic slab, a configuration that has been extensively used in the analysis of transverse coronal loop oscillations. Our equilibrium contains material discontinuities that result in one eigenfunction with a jump across these discontinuities and two eigenfunctions whose normal derivatives are discontinuous there. After 4 iterations, the approximation to the frequency and eigenfunctions are accurate to lesssim 0.7% except for the eigenfunction with discontinuities, which displays a much larger error at these positions.
Authors: S. Rial, I. Arregui, R. Oliver, and J. Terradas
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Publication Status: Submitted
Last Modified: 20190206 11:00


