Finite Element Methods for the Solution of 3D Eddy Current Problems

Theory of tokamak disruptions

“…Codes that calculate the evolution of the magnetic fields in non-axisymmetric external structures exist. [59][60][61] The combination of Ohm's law and Faraday's law imply the normal field to a conductor evolves as @B Án=@t ¼r Á ðgn ÂjÞ. The development of an appropriate method of following the evolution of the external magnetic field is certainly feasible.…”

Analysis methodologies and experimental benchmarks for eddy current testing

“…The integral formulation is obtained by assuming as unknown the electric vector potential expanded in terms of edge elements based shape functions and applying the Galerkin method. Uniqueness is enforced by the tree-cotree decomposition [4]. The eddy current density is given by where and is the th shape function.…”

“…This can be properly taken into account to obtain an integral formulation yielding a reduced linear system of the order of the shape functions not vanishing in . Specifically, (see [3], [4] for details) the unknown vector can be decomposed as where the column vector accounts for the current density flowing outside accounts for the current density flowing in but outside the crack (assumed to be contained in ), and are suitably defined matrices (see [5], [6]) and is a vector arising from the superposition principle (the effect of the crack is obtained by adding a suitable imposed source current density in the crack volume). The effectiveness of the previous decomposition lies in the possibility of computing by solving a "small" linear system and obtaining from and by linear mapping: where and are suitable matrices [5], [6].…”

A reference discretization strategy for the numerical solution of physical field problems

“…We will not consider in detail this subject here, assuming this function as given. For this important topic the reader is referred to the literature, in particular to that dealing with complementary variational techniques, which appear especially suited to the determination of physically significant local error functions linked to local and global energy estimates (Albanese and Rubinacci, 1998;Golias er al., 1994;Marmin et al, 1998;Oden, 1973;Penman, 1988;Remacle et al, 1998;Rikabi et al, 1988). Substituting the reconstruction operators [Eqs.…”