麦克斯韦方程组数据补全问题的拟可逆性数值解法

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2020-09-02 DOI:10.3934/IPI.2020056

M. Darbas, J. Heleine, S. Lohrengel

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引用次数: 3

摘要

本文研究电场中时谐麦克斯韦方程组的数据补全问题的数值解。其目的是从有界域边界上可访问部分的测量数据中恢复出边界上不可访问部分的缺失数据。研究了非迭代拟可逆性方法，提出了不同的混合变分公式。证明了结果的适定性、收敛性和正则性。采用边缘有限元进行离散化。各种二维和三维数值模拟证明了该方法的有效性，特别是对有噪声的数据。

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Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations

This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain from measured data on the accessible part. The non-iterative quasi-reversibility method is studied and different mixed variational formulations are proposed. Well-posedness, convergence and regularity results are proved. Discretization is performed by means of edge finite elements. Various two- and three-dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.