求解波场变换反演问题的连续正则化方法  

Method of Continuous Normalization for Solving the Problem of Wave-field Inverse Tranaformation

作　　者：王贺元[1] 李伟[1] 

机构地区：[1]辽宁工业大学理学院,辽宁锦州121001

出　　处：《应用数学》2015年第3期686-691,共6页Mathematica Applicata

基　　金：国家重点基础研究发展计划(973计划)(2012CB416605);国家自然科学基金(41174090);辽宁省教育厅科研基金(L2013248);锦州市科技专项基金(13A1D32)资助

摘　　要：本文研究波场变换反演问题.利用连续正则化方法求解波场变换反演问题,构造展平泛函,基于已经正则化的变分问题用差分法作有限维逼近.利用偏差原理和Newton三阶迭代收敛格式选出最优的正则化参数,实施数值求解.通过对数值计算结果与已知波场函数对比,证明该方法的有效性和可行性.与离散正则化算法相比,本文的连续正则化算法具有保结构和收敛速度快等优点.The problem of wave-field inverse transformation was solved by using the method of continuous normalization. By constructing the flattening functional we discuss finite dimensional approximation for regularized variational problem through different methods. To obtain the regularization parameter, deviation principle and iteration formula with three order convergence are used. By comparing the results of numerical calculation and the known function of wave field, the feasibility and the effectiveness of the proposed method are proved. Comparing with discrete regularization, in this paper, the continuous regularization has the advantages such as structure preserving and faster convergence speed.

关 键 词：瞬变电磁场 波场变换 连续正则化 

分 类 号：O411.1[理学—理论物理]