Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical and numerical study of a three-dimensional inverse eddy
  current problem   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 non-uniqueness of the
recovery process. Then by virtue of non-radiating 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 non-convex 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.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an