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T. D. Tsiboukis, T. P. Theodoulidis, N. V. Kantartzis and E. E. Kriezis, “Analytical and Numerical Solution of the Eddy-Current Problem in Spherical Coordinates Based on the Second-Order Vector Potential Formulation,” IEEE Transactions on Magnetics, Vol. 33, No. 4, 1997, pp. 2461-2472.

has been cited by the following article:

• TITLE: Generalization of the Second Order Vector Potential Formulation for Arbitrary Non-Orthogonal Curvilinear Coordinates Systems from the Covariant Form of Maxwell's Equations

  AUTHORS: Denis Prémel

  KEYWORDS: Second Order Vector Potential (SOVP); Curvilinear Coordinate System; Eddy Current Non-Destructive Testing (ECNDT)

  JOURNAL NAME: Journal of Electromagnetic Analysis and Applications, Vol.4 No.10, October 31, 2012

  ABSTRACT: A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.