TITLE

Fast numerical treatment of nonlinear wave equations by spectral methods

AUTHOR(S)
Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.
PUB. DATE
February 2011
SOURCE
Physics of Plasmas;Feb2011, Vol. 18 Issue 2, p022103
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schrödinger equation applies.
ACCESSION #
58700675

 

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