Residual Cutting Method for Elliptic Boundary Value Problems
Residual Cutting Method for Elliptic Boundary Value Problems
复制标题
椭圆边值问题的残差切割法
DOI：
10.1006/jcph.1997.5807
复制
发表时间：
1997
影响因子：
4.1
通讯作者：
Tadayasu Takahashi
中科院分区：
文献类型：
--
作者：
A. Tamura;K. Kikuchi;Tadayasu Takahashi
针对椭圆偏微分方程的边值问题，提出了一种借助残差方程和最小二乘法实现残差约简的高效、高精度数值方法。已经解决了弯曲管流和叶栅流中压力的诺依曼、狄利克雷和三维泊松方程的混合边值问题。数值结果证明了该方法的有效性，具有较高的收敛速度和高度的鲁棒性。该方法有望成为一种适用于各种边界条件的广泛偏微分方程的有效数值求解方法。
A new, efficient, and highly accurate numerical method which achieves the residual reduction with the aid of residual equations and the method of least squares is proposed for boundary value problems of elliptic partial differential equations. Neumann, Dirichlet, and mixed boundary value problems of three-dimensional Poisson's equation for pressure in a curved duct flow and a cascade flow have been solved. Numerical results exhibit the effectiveness of the method by a high convergence rate and a high degree of robustness. The method is expected to be an effective numerical solution method applicable to a wide range of partial differential equations with various boundary conditions.