Accurate magnetostatic simulation of step-lap joints in transformer cores using anisotropic higher order FEM

Abstract

Purpose

The purpose of this paper is to propose a solution strategy for both accurate and efficient simulation of nonlinear magnetostatic problems in thin structures using higher order finite element methods. Special interest is put in the investigation of the step-lap joints of transformer cores, with a focus on the spatial resolution of the field quantities.

Design/methodology/approach

The usage of hierarchical finite elements of higher order makes it possible to adapt the local accuracy in different spatial directions in thin steel sheets. Due to explicit representation of gradients in the basis functions, a simple Schwarz-type block preconditioner with a conjugate gradient solver can efficiently solve the arising algebraic system. By adapting the block size automatically according to the aspect ratio, deterioration of convergence in case of thin elements can be prevented. The resulting Newton scheme is accelerated utilizing the hierarchical splitting in a two-level scheme, where an initial guess is computed on a coarse sub-space.

Findings

Compared to an isotropic choice of polynomial order for the basis functions, significant runtime and memory can be saved in the simulation of thin structures without losing accuracy. The iterative solution scheme proves to be robust with respect to the polynomial order, even for aspect ratios of 1:1000 and anisotropies in two directions. An additional saving in runtime and Newton iterations can be achieved by solving the nonlinear problem initially on the lowest order basis functions only and projecting the solution to the complete space as starting value, analogous to a full multigrid scheme.

Originality/value

Within the presented solution strategy, especially the anisotropic block preconditioner and the accelerated Newton scheme based on the two-level splitting constitute a novel contribution. They provide building blocks, which can be utilized for other types of magnetic field problems like transient nonlinear problems or hysteresis modeling as well.

Citation

Hauck, A., Ertl, M., Schöberl, J. and Kaltenbacher, M. (2013), "Accurate magnetostatic simulation of step-lap joints in transformer cores using anisotropic higher order FEM", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 5, pp. 1581-1595. https://doi.org/10.1108/COMPEL-04-2013-0134