Numerical recovery of magnetic diffusivity in a three dimensional spherical dynamo equation

IF 1.5 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI:10.3934/ipi.2020037

Djemaa Messaoudi, Osama Said Ahmed, Komivi Souley Agbodjan, Ting Cheng, Daijun Jiang

引用次数: 0

Abstract

This paper is concerned with the analysis on a numerical recovery of the magnetic diffusivity in a three dimensional (3D) spherical dynamo equation. We shall transform the ill-posed problem into an output least squares nonlinear minimization by an appropriately selected Tikhonov regularization, whose regularizing effects and mathematical properties are justified. The nonlinear optimization problem is approximated by a fully discrete finite element method and its convergence shall be rigorously established.

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三维球面发电机方程磁扩散系数的数值恢复

本文研究了三维球形发电机方程中磁扩散率的数值恢复分析。我们将通过适当选择的Tikhonov正则化将不适定问题转化为输出最小二乘非线性最小化，其正则化效果和数学性质是合理的。非线性优化问题用完全离散有限元法逼近，其收敛性必须严格证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.