An integral method using the magnetic scalar potential to solve nonlinear magnetostatic problems is developed. This method uses the range interactions between magnetizable elements and it is particularly well suited to compute field in the air domain which do not need to be meshed. The collocation and Galerkin approaches are presented and compared to solve the nonlinear magnetostatic equation. Both methods need the construction of full interaction matrices which may be computed with analytical formulae. A Newton-Raphson method, in which the interaction matrix must be built at each solver iteration, is used to solve the nonlinear formulation. A modified fixed point scheme, in which the interaction matrix is built only once, is also proposed. 3-D numerical examples are given and results of the different methods are compared.
Volume integral equation methods are particularly well suited to solve electromagnetic problems, where the air domain is predominant. However, their use leads to the heavy resolution of a dense matrix system. The Adaptive Cross Approximation (ACA) combined with hierarchical matrices (H-matrices) decomposition is an algebraic method allowing the compression of fully populated matrices. This paper presents the ACA technique applied to a volume integral equation to solve nonlinear magnetostatic problems.
An unstructured-PEEC method for modelling electromagnetic thin regions is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. Dynamic effects across the the thickness of the sheet are modeled by equivalent complex conductivity and reluctivity. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation. The formulation enables the computation of eddy current losses and can be coupled with external circuits, PEEC cables or coil thanks to the circuit representation.
This article deals with the use of the Volume Integral Method (VIM) to compute the magnetic anomaly created by a non-conductive ferromagnetic thin shell placed in a static inductor field. An original facet integral formulation considering the magnetic induction as unknowns is presented. The use of thin shell element assumption leads to a surface mesh decreasing highly the number of elements so the computation cost. The method is very performant in terms of speed and accuracy. Index Terms-Magnetostatic, volume integral method, thin shell element, shielding modeling.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.