Solving Unbounded Planar Electrostatic Problem by FEM Combined with Asymptotic Condition Technique

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Solving Unbounded Planar Electrostatic Problem by FEM Combined with Asymptotic Condition Technique

更新时间：2025-04-26

- Solving Unbounded Planar Electrostatic Problem by FEM Combined with Asymptotic Condition Technique
- High VoltageApparatus Issue 2, Pages: 20-24(1997)
- 作者机构：
  
  1. 西安交通大学
  2. 西安交通大学 710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TM151
- Published：1997
- 稿件说明：
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[1]郭飞,马西奎,邱关源.有限元法结合渐近边界条件技术求解无界平面静电场问题[J].高压电器,1997(02):20-24.

Solving Unbounded Planar Electrostatic Problem by FEM Combined with Asymptotic Condition Technique[J]. High voltageapparatus, 1997, (2): 20-24.
[1]郭飞,马西奎,邱关源.有限元法结合渐近边界条件技术求解无界平面静电场问题[J].高压电器,1997(02):20-24. DOI：

Solving Unbounded Planar Electrostatic Problem by FEM Combined with Asymptotic Condition Technique[J]. High voltageapparatus, 1997, (2): 20-24. DOI：

摘要

根据二维拉普拉斯方程的通解级数

推导出圆形人工边界上的零阶、一阶和二阶渐近边界条件

并将它们与有限元法结合

使得在求解区域不大情况下的二维静电场计算结果仍保持足够高的精度。同时

这种技术仍然保持了有限元刚度矩阵对称、正定和稀疏的性质。将这种方法应用于一个具有解析解的例子

说明了这种方法的正确性和有效性

也说明了在同一人工边界上

高阶的渐近边界条件较之于低阶的渐近边界条件具有更高的精度。最后

采用二阶渐近边界条件计算了一个实例。

Abstract

There are so many unbounded two - dimensional electrostatic problem in high voltage engineering field. In this paper

three types of asymptotic boundary conditions （ABC）are derived according to the general solution expansion of 2-D Laplace equation

and then these boundary conditions on the artificial circular boundary are respectively introduced into corresponding finite element varitional problems. Since the artificial circular boundary is applied forcibly

the unbounded field is truncated to an area of finite size. Thus

the method still preserves high accuracy while the computional region is reduced; it also preserves the symmetry、positive and sparsity of the finite ele- ment matrix. Numerical test shows that the high order ABC is more accurate than the lower one on the same boundary.

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