Fading regularization regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Helmholtz equation

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:125

Article

Caille, Laetitia^1,2,3  Delvare, Franck^1,2,3  Marin, Liviu^4,5  Michaux-Leblond, Nathalie^1,2,3 

[1] Normandie Univ, Caen, France

[2] UNICAEN, LMNO, F-14032 Caen, France

[3] CNRS, UMR 6139, F-14032 Caen, France

[4] Univ Bucharest, Fac Math & Comp Sci, Dept Math, Acad 14, Bucharest 010014, Romania

[5] Romanian Acad, Inst Math Stat & Appl Math, 13 Calea 13 Septembrie, Bucharest 050711, Romania

关键词: Inverse problems;    Cauchy problem;    Helmholtz equation;    Method of fundamental solutions;   

DOI  :  10.1016/j.ijsolstr.2017.07.011

来源: Elsevier

【 摘 要 】

In, this paper, we combine the fading regularization method with the method of fundamental solutions (MFS) and investigate its application to the Cauchy problem for the two-dimensional Helmholtz equation. We present a numerical reconstruction of the missing data on an inaccessible part of the boundary from the knowledge of overprescribed noisy data taken on the remaining accessible boundary part for both smooth and piecewise smooth two-dimensional geometries. The accuracy, convergence, stability and efficiency of the proposed numerical algorithm, as well as its capability to deblur the noisy data, are validated by three numerical examples. (C) 2017 Elsevier Ltd. All rights reserved.

【 授权许可】

Free