文档介绍：上海交通大学
硕士学位论文
光波导器件中有限元算法分析及仿真软件设计
姓名:桂云松
申请学位级别:硕士
专业:电磁场与微波技术
指导教师:陈建平
20060101
上海交通大学硕士学位论文
光波导器件中有限元算法分析及仿真软件设计
摘要
本文从理论建模、有限元前期网格剖分、边界条件的应用等角度出
发,详细研究了有限元算法在光波导模场计算中的应用,对相应的不
足进行了改进。
文章着重论述了有限元算法前期网格划分过程中,原始算法所存在
的初始特定点的设定方式较难适用于复杂的曲线边界的问题。本文针
对性地提出了一种改进的节点插入算法,其基本思想是首先定义边界
“类”数据结构存储边界曲线段信息,其中包括该曲线段的空间函数,
通过对此类中数据应用数值计算处理,可以使该改进算法能有效地应
用于复杂曲线边界情况下。
当有限元方式应用到光波导计算时,经常遇到需要求解开域问题的
情况。而有限元的特点是对封闭区域进行处理。因此,人们提出了很
多方式把无限大的开域空间限制到有限范围的封闭区域中。其中,吸
收边界条件和完美匹配层就是其中两种比较有效的方法,在文章的第
四章中,我们提出根据面向对象的思想,阐述了吸收边界条件和完美
匹配层的实现方式。
最后介绍了软件整体的构架并通过一个算例验证程序的有效性。
关键字: 有限元光波导网格划分吸收边界条件完美匹配层
III
上海交通大学硕士学位论文
STUDY ON THE WAVEGUIDE ANALYSIS ALGORITHM
BASED ON THE FEM AND ITS IMPLEMENTATION
ABSTRACT
This article studies the application of FEM in the filed calculation of the optical
waveguide, covering topics including theoretical modeling, grid generation and
boundary condition determination. Improvement are proposed according to the
shortage of the algorithm.
The current grid generation algorithm is difficult to deal with the curve
boundary point initialization. In order to e this ing, a new
algorithm is proposed, which can solve the above problem. The basic idea of this
algorithm is to create the Edge Class to treat the curve boundary firstly. Then we
can find the correct point more quickly and accurately by making some numerical
process to the Edge.
When applying the FEM to puting, we often confront with open
domain problem which is difficult for the FEM. So researchers have carried out
many ways to truncate the open domain to closed domain. Among these ways,
two outstanding ones are absorbing boundary condition and perfectly matched
layers. In chapter four, we show the implementation of these two ways by using
the oriental object programming.
At last, we present the infrastructure of the software and demonstrate the
effectiveness of the program by some examples.
KEY WORDS: FEM, optical waveguide, grid generation, ab