Efficient approximation of the exponential operator for discrete 2D advection–diffusion problems
Efficient approximation of the exponential operator for discrete 2D advection–diffusion problems
复制标题
离散二维平流扩散问题指数算子的高效逼近
DOI：
10.1002/nla.288
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发表时间：
2003
影响因子：
4.3
通讯作者：
M. Vianello
中科院分区：
文献类型：
--
作者：
L. Bergamaschi;M. Caliari;M. Vianello
本文比较了Krylov子空间方法和Faber级数展开式在大的、稀疏的、非对称矩阵上逼近矩阵指数算子的方法。我们特别考虑了切比雪夫级数的情况，它对应于一个合适的椭圆对矩阵谱的初始估计。对二维平流扩散问题的空间离散化产生的大尺寸矩阵的实验结果表明，切比雪夫方法可以有效地替代克里洛夫方法。版权所有©2002约翰威利父子有限公司
In this paper we compare Krylov subspace methods with Faber series expansion for approximating the matrix exponential operator on large, sparse, non‐symmetric matrices. We consider in particular the case of Chebyshev series, corresponding to an initial estimate of the spectrum of the matrix by a suitable ellipse. Experimental results upon matrices with large size, arising from space discretization of 2D advection–diffusion problems, demonstrate that the Chebyshev method can be an effective alternative to Krylov techniques. Copyright © 2002 John Wiley & Sons, Ltd.