A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions

Authors:	Shi Jin Chunxiong Zheng

Affiliation:	(1) Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA;(2) Department of Mathematical Science, Tsinghua University, Beijing, 100084, P.R. China

Abstract:	The generalized Zakharov system (ZS) couples a dispersive field E (scalar or vectorial) and $\mathcal{J}$ nondispersive fields $\{n_j\}_{j=1}^\mathcal{J}$ with a propagating speed of $1/\in_j$ . In this paper, we extend our one-dimensional time-splitting spectral method (TSSP) for the generalized ZS into higher dimension. A main new idea is to reformulate the multi-dimensional wave equations for the nondispersive fields into a first-order system using a change of variable defined in the Fourier space. The proposed scheme TSSP is unconditionally stable, second-order in time and spectrally accurate in space. Moreover, in the subsonic regime, it allows numerical capturing of the subsonic limit without resolving the small parameters $\in_j$ . Numerical examples confirm these properties of this method

Keywords:	Zakharov system time-splitting spectral method subsonic regime multi-dimensions
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