摘要
本文对于无界区域各向异性常系数椭圆型偏微分方程研究了一种基于自然边界归化的Schwarz交替法.利用极值原理证明了在连续情形最大模意义下的几何迭代收敛性,通过选取适当的共焦椭圆边界利用Fourier分析获得了不依赖各向异性程度的最优的迭代收缩因子.还在离散情形最大模意义下证明了几何收敛性,而且进一步得到了误差估计.最后,数值结果证实了迭代收缩因子和误差估计的正确性,表明了该方法在无界区域上求解各向异性椭圆型偏微分方程的优越性.
We investigate a Schwarz alternating method based on the natural boundary reduction on the elliptic boundary for the anisotropic elliptic PDEs with constant coefficients in unbounded domains. We prove its geometric iterative convergence with maximum norm in the continuous case by using the maximum principle, and obtain an optimal iteration contract factor, which is independent of the anisotropic degree, by using Fourier analysis with confocal elliptic boundaries. We also prove its geometric convergence in the discrete case with maximum norm and obtain an error estimate of the iterative convergent solution. Finally, our numerical results confirm the correctness of the iterative contract factor and the error estimate, and show the advantage of this method for solving the anisotropic elliptic PDEs in unbounded domains.
出处
《计算数学》
CSCD
北大核心
2009年第1期65-76,共12页
Mathematica Numerica Sinica
基金
北京市自然科学基金(1072009)资助项目.
关键词
SCHWARZ交替法
无界区域
各向异性问题
自然边界归化
误差估计
Schwarz alternating method
unbounded domain
anisotropic elliptic boundary value problem
natural boundary reduction
error estimate
