基于转换矩阵的人工边界法研究及其在纳米天线模拟中的应用

项目名称： 基于转换矩阵的人工边界法研究及其在纳米天线模拟中的应用

项目编号： No.61201113

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 刘阳

作者单位： 北京应用物理与计算数学研究所

项目金额： 25万元

中文摘要： 人工边界法已在许多无界区域的偏微分方程边值问题的求解中得到了广泛应用。针对含有单个或多个分布集中的目标体的问题，人工边界法的高效性得到了充分体现，然而，随着电磁场应用领域提出的问题越来越复杂，如何实现高效数值求解含有多个或多组分散且结构复杂目标体的问题已成为一个有着工程应用背景的热点前沿课题。本项目希望在保持人工边界法能够高精度地将无界区域问题转换为有界规则区域问题的特点以及与有限元法耦合在求解复杂区域问题的高效性的同时，借鉴转换矩阵方法处理多目标体之间信息交换的思想，实现高效求解含多个或多组分散且结构复杂目标体的问题。研究内容如下：1. 研究基于转换矩阵的人工边界方法用于高效求解含有多个或多组分散且结构复杂目标体的问题；2. 为改进后的人工边界法，开发用于求解含大量目标体问题的快速算法；3. 将改进后的人工边界法及其相应的快速算法应用于一类典型多目标问题（纳米天线阵）的数值模拟。

中文关键词： 有限元方法；边界积分方法；转换矩阵法；快速算法；纳米天线模拟

英文摘要： The artificial boundary method has been very popular in solving many boundary value problems of partial differential equations. For handling the problems having one object or many objects distributed concentratedly, the artificial boundary method is illuminated efficiently. However, to meet the needs of electromagnetic field, more and more complex problems should be considered. The kind of problems, which contain many (or many groups of) complex objects distributed dispersedly, has become a hot and frontier research topic due to its wide applications in electromagnetic field. This project aims to develop a new artificial boundary method based on the idea of transition matrix method for dealing with the information exchange between many objects. The developed artificial boundary method not only can keep the advantages of original artificial boundary method in transforming the problems in unbounded domain into the problems in bounded and regular domain and in coupling with the finite element method to handle the complex problems in bounded domain but also can efficiently solve the problems having many (or many groups of) objects distributed dispersedly. Our research topics are given in the following. (1) Develop the new artificial boundary method based on the transition matrix method for efficiently solving the pr

英文关键词： Finite element method；boundary integral method；transition matrix method；fast solver；simulation of nanoantennas