有限元—解析结合解法在无界轴对称静电场问题数值解中的应用

Applications of Hybrid FEM-Analytic Approach in Unboundary Axisymmetrical Electrostatic Field Computation

无界电磁场问题的有限元数值分析研究有着重要的理论意义和实用价值。本文采用有限元—解析结合解法实现了有限元法在无界轴对称静电场问题数值分析中的应用 ,并兼顾了计算精度和效率 ,形成了一种新型解法。以典型的静电场问题为例 ,说明了有限元—解析结合解法精度高、简单易行和方便直观 ,具有实用价值。同时 。

The researches on finite element unboundary technique are of important theoretical and practical value for the numerical computation of electromagnetic field problems. In this paper, a new technique known as the Hybrid FEM-Analytic Approach is proposed for solving unboundary axisymmetrical electrostatic field computation, so as to extend finite element method to unboundary field problems. The method has been applied to a variety of unboundary electromagnetic field problems, and shown to be accurate and powerful. The numerical examples of some canonical open region problems are included to demonstrate the accuracy, efficiency and capability of this method. The new hybrid scheme combining an analytical solution with the finite element method offers the several principal advantages: namely simpler and obvious in mathematics, more flexible for application, smaller computation contents and higher accuracy. The new method preserves the sparsity and symmetry of the finite element matrix.