I. Gerace, P. Pucci, N. Ceccarelli, M. Discepoli, R. Mariani
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引用次数: 4
Abstract
In this paper we propose a method for the discretization of the parabolic p-Laplacian equation. In particular we use alternately either the backward Euler scheme or the Crank-Nicolson scheme for the time-discretization and the first order Finite Element Method for space-discretization as in [7]. To obtain the numerical solution we have to invert a block Toeplitz matrix with Toeplitz blocks. To this aim we use a Conjugate Gradient (CG) algorithm preconditioned by a block circulant matrix with circulant blocks. A Two-Dimensional Discrete Fast Sine-Cosine Transform (2D-DFSCT) is applied to invert the block circulant matrix with circulant blocks. The experimental results show how the application of the preconditioner reduces the iterations of the CG algorithm of about the 56% –75%. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
p- laplace抛物方程的预条件有限元法
本文提出了抛物型p-拉普拉斯方程离散化的一种方法。特别地，我们交替使用后向欧拉格式或Crank-Nicolson格式进行时间离散，一阶有限元方法进行空间离散，如[7]所示。为了得到数值解，我们必须用Toeplitz块对一个块Toeplitz矩阵进行反演。为此，我们使用了一种共轭梯度(CG)算法，该算法以具有循环块的块循环矩阵为前提条件。采用二维离散快速正弦余弦变换(2D-DFSCT)对具有循环块的块循环矩阵进行逆变换。实验结果表明，前置条件的应用使CG算法的迭代次数减少了56% ~ 75%。(©2004 WILEY-VCH Verlag GmbH &KGaA公司，Weinheim)
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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