Mathematical and Numerical Study of a Three-Dimensional Inverse Eddy Current Problem
Publication in refereed journal

香港中文大學研究人員

引用次數
替代計量分析
.

其它資訊
摘要We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the nonuniqueness of the recovery process. Then by virtue of nonradiating source conceptions, we establish a regularity result for the tangential trace of the true solution on the boundary, which is necessary to justify our subsequent mathematical formulation. After that, we formulate the inverse problem as a constrained optimization problem with an appropriate regularization and prove the existence and stability of the regularized minimizers. To facilitate the numerical solution of the nonlinear nonconvex constrained optimization, we introduce a feasible Lagrangian and its discrete variant. Then the gradient of the objective functional is derived using the adjoint technique. By means of the gradient, a nonlinear conjugate gradient method is formulated for solving the optimization system, and a Sobolev gradient is incorporated to accelerate the iterative process. Numerical examples are provided to demonstrate the feasibility of the proposed algorithm.
出版社接受日期15.04.2020
著者Junqing Chen, Ying Liang, Jun Zou
期刊名稱SIAM Journal on Applied Mathematics
出版年份2020
月份6
卷號80
期次3
出版社Society for Industrial and Applied Mathematics
頁次1467 - 1492
國際標準期刊號0036-1399
電子國際標準期刊號1095-712X
語言美式英語
關鍵詞inverse eddy current, regularity, ill-posedness, stability, Lagrangian, adjoint problem

上次更新時間 2020-18-09 於 00:16