Modelling eddy currents in thin shields

Abstract

Purpose-The purpose of this paper is to present a simplified rigorous mathematical formulation of the problem of electric currents induced in thin shields with holes yielding more efficient numerical computations with respect to available methods. Design/methodology/approach-A surface integral equation satisfied by the current density was constructed, which is, subsequently, represented at any point by linear combinations of novel vector basis functions only associated with the interior nodes of the discretization mesh, such that the current continuity is everywhere insured. The existence of the holes in the shield is taken into account by associating only one surface vector function with each hole. A method of moments is then applied to compute the scalar coefficients of the vector functions employed. Findings-It was found that the induced current distribution for shields with holes having the complexity of real world structures can be determined with a satisfactory accuracy utilizing a moderate size processor notebook in a time of the order of minutes. Originality/value-The originality of the proposed method consists in using specialized surface vector functions only associated with individual interior nodes of the shield, its multiply connected structure being efficiently accounted for by introducing one unknown for each hole, instead of unknowns for every node along the hole contours. The method presented is straightforward and highly efficient for mathematical analysis of thin shields with holes, and of other physical fields in the presence of multiply connected surface structures.

Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents

“…Obviously, SLAE obtained in [17] by the Galerkin method is also degenerate, but the authors do not write about this. -The approach proposed in this article can be generalized to other types of boundary secondary sources, for example, on sources such as a simple layer of magnetization currents [20][21][22]. However, when deriving a SLAE for this type of sources, the law of total current should be applied.…”

A Boundary Integral Method for Computing Eddy Currents in Thin Conductors of Arbitrary Topology

“…In [4], this problem is circumvented by introducing an alternative formulation whose number of unknowns is roughly the same but it requires an additional factorization of a full matrix. A heuristic approach to solve the problem arising when multiply connected conductors are present-based on adding one specialized basis function for each hole-has been proposed in [6]. Unfortunately, this technique does not work with conductors of arbitrary topology, since-as it becomes clear at the end of this paper-it fails for surfaces with non-vanishing genus.…”

“…Generators due to holes may be easily found using the non-local basis functions used in[6] since H = GN holds, where the column of matrix N store the coefficients of the non-local basis functions of[6].…”

Solving 3-D Eddy Currents in Thin Shells of Any Shape and Topology

“…These formulations are not suitable for models with complex topology, e.g., shells with holes or bulk domains with cavities. Surface integral equation methods for thin shell problems with non-simply connected domains have been presented [7]- [9]. In particular, the integral method proposed in [7] is advantageous since unknowns are related to nodes and holes.…”