基于遗传算法重建多个散射体的组合Newton法  

HYBRID NEWTON METHOD FOR RECOVERING MULTIPLE OBSTACLES BASED ON GENETIC ALGORITHM

作　　者：王泽文[1] 张文[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《计算数学》2011年第1期87-102,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10861001);江西省自然科学基金(2009GZS0001)

摘　　要：本文研究由单个入射声波或电磁波及其远场数据反演多个柔性散射体边界的逆散射问题.通过建立边界到边界总场的非线性算子及其Frechet导数,本文首先给出了基于单层位势的组合Newton法.将组合Newton法转化为泛函优化问题,从而获得了该方法重建单个散射体的收敛性分析.然后,基于遗传算法和正则化参数选取的模型函数方法,给出了组合Newton法重建多个散射体的数值实现方法.最后,给出三个数值例子来说明算法的可行性,它们分别是重建单个散射体、两个散射体和三个散射体.This paper mainly studies the inverse problem of acoustic scattering to reconstruct the shapes of multiple sound-soft obstacles from a given incident field and its corresponding far field pattern of the scattered field. After constructing a nonlinear operator that maps the unknown boundary into the total field and its Fr@chet differential, w2 investigate the hybrid Newton method via the single-layer potential. The convergence of the hybrid New- ton method is established by transforming it into an optimal problem of a cost function. Furthermore, based on Genetic algorithm and the model function method for choosing reg- ularization parameters, we present the numerical realization of the hybrid Newton method to recover multiple obstacles. Three numerical examples, which are to recover one obstacle, two obstacles and three obstacles, are given at last to show the feasibility of the method proposed in this paper.

关 键 词：逆散射 多个散射体 组合Newton法 分解算法 遗传算法 

分 类 号：O242.23[理学—计算数学]