基于迭代的Sylvester系统泊松求解器

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-06-05 DOI:10.4236/AM.2018.96052

Michael Franklin, A. Nadim

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引用次数: 0

摘要

给出了二维泊松方程的迭代解。利用有限差分，我们将方程离散成一个Sylvester系统，AU +UB = F，涉及三对角线矩阵a和b。在引入一个使最优化收敛的通缩型参数后，迭代直接发生在Sylvester系统上。在迭代矩阵的谱半径上得到了解析界。我们的方法可与连续过度松弛(SOR)相比较，并且适用于通过向量/数组操作进行紧凑规划。它也可以在多网格框架中实现，并在性能上有相当大的改进，如下所示。

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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A Poisson Solver Based on Iterations on a Sylvester System

We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occur on this Sylvester system directly after introducing a deflation-type parameter that enables optimized convergence. Analytical bounds are obtained on the spectral radii of the iteration matrices. Our method is comparable to Successive Over-Relaxation (SOR) and amenable to compact programming via vector/array operations. It can also be implemented within a multigrid framework with considerable improvement in performance as shown herein.

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来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.