特解边界元法数值解三维Pennes方程及其应用

计算物理 ›› 2001, Vol. 18 ›› Issue (5): 473-476.

特解边界元法数值解三维Pennes方程及其应用

刘朝霞¹, 吴声昌¹, 常谦顺¹, 黄振侃²

1. 中科院数学与系统科学研究院应用数学研究所, 北京 100080;
2. 京工业大学, 北京 100022

收稿日期:2000-12-12 修回日期:2001-04-06 出版日期:2001-09-25 发布日期:2001-09-25
作者简介:刘朝霞(1974-),女,山东,博士生,从事数值分析与计算物理研究,北京2734信箱,100080.

NUMERICAL METHODS OF THREE-DIMENSIONAL PENNESEQUATION USING PARTICULAR SOLUTION BEM AND THEIR APPLICATIONS

LIU Zhao-xia¹, WU Sheng-chang¹, CHANG Qian-shun¹, HUANG Zhen-kan²

1. Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, P R China;
2. Beijing Polytechnic University, Beijing 10002, P R China

Received:2000-12-12 Revised:2001-04-06 Online:2001-09-25 Published:2001-09-25

摘要/Abstract

摘要： 应用特解边界元法对非稳态的三维Pennes方程求解,将解分为一满足泊松方程的通解与一特解之和,通解按照边界元法求解,特解用分离变量法给出,与位置有关的部分采用截断多项式.逐时间段计算边界元的温度及热流值,然后计算域内点的值.并将该方法用于热疗温度场的数值实例计算.

关键词: 特解边界元法, Pennes方程, 常数边界元, 分离变量法

Abstract: Particular solution BEM is used to solve three-dimensional Pennes equation.The solution is devided into the common solution of Poisson equation and the particular solution.The common solution is solved by BEM while the particular solution is given by the method of separation of variables.Temperature and heatflux are computed piecewisely in each time step and then the value on the nods in the field is computed.Numerical simulation of cancer hypothermia is given based on this method.

Key words: particular solution BEM, Pennes equation, constant boundary element, the method of separation of variables

中图分类号:

O242.21

刘朝霞, 吴声昌, 常谦顺, 黄振侃. 特解边界元法数值解三维Pennes方程及其应用[J]. 计算物理, 2001, 18(5): 473-476.

LIU Zhao-xia, WU Sheng-chang, CHANG Qian-shun, HUANG Zhen-kan. NUMERICAL METHODS OF THREE-DIMENSIONAL PENNESEQUATION USING PARTICULAR SOLUTION BEM AND THEIR APPLICATIONS[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2001, 18(5): 473-476.

[1]	李细霞, 王丽, 戴海燕, 李长玉. 基于拓展分离变量法的非傅里叶传热研究[J]. 计算物理, 2018, 35(6): 685-692.
[2]	何为, 李倩, 徐征, 朱金华, 何阳光, 王磊. 头部分层球模型磁感应成像正问题的解析解[J]. 计算物理, 2010, 27(6): 912-918.
[3]	徐征, 何为, 何传红, 张占龙. 头部电阻抗成像正问题的解析解研究[J]. 计算物理, 2010, 27(1): 107-114.