用边界粒子法求解柯西反问题的数值计算软件包  

Numerical computation software package for Cauchy inverse problems based on boundary particle method

作　　者：师晋红[1] 傅卓佳[1] 陈文[1] 

机构地区：[1]河海大学工程与科学数值模拟软件国际中心,南京210098

出　　处：《计算机辅助工程》2013年第1期64-70,共7页Computer Aided Engineering

基　　金：国家重点基础研究发展计划("九七三"计划)(2010CB832702);国家杰出青年基金(11125208)

摘　　要：为推动无网格方法在反问题中的应用及相关计算软件的发展,介绍基于MATLAB开发的用边界粒子法(Boundary Particle Method,BPM)数值模拟柯西反问题的计算软件包;描述数值算法的理论基础,并结合标准算例介绍软件包的基本功能和使用方法.该软件包可求解含不同形式源项(多项式函数、三角函数、指数函数及其耦合函数等)的椭圆型偏微分方程,并且可用于处理任意几何区域问题.本软件包具有简单易用的图形用户界面,在数值模拟柯西反问题时仅需边界测量数据,且效率高、精度高.To promote the application of meshless method in inverse problems and the development of related computation software, a MATLAB-based software package is introduced, which is developed to simulate Cauehy inverse problems numerically by Boundary Particle Method（BPM） ; the theoretical basis of the numerical algorithm is described and the basic functions and usage method of the software are introduced through the benchmark examples. The software package can solve the elliptic partial differential equation problems with a variety of source terms, such as polynomial, trigonometric, exponential, or their coupling functions, and can be used to deal with arbitrary geometry region problems. With easy-to-use graphic user interface, the software package only needs boundary measurement data for numerical simulation of Cauehy inverse problem and shows high efficiency and accuracy.

关 键 词：柯西反问题 无网格方法 正则化方法 椭圆型偏微分方程 MATLAB 

分 类 号：O245[理学—计算数学] TB115[理学—数学]