A New Adaptive Mesh Refinement Method in FEA Based on Magnetic Field Conservation at Elements Interfaces and Non-Conforming Mesh Refinement Technique

Abstract

Mesh quality strongly affects the solution accuracy in electromagnetic finite-element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, and generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewicz-Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1% compared with that of the ZZ method, which yields error of 8.6%, for the same model

An Adaptive FEM Based on Magnetic Field Conservation Applying to Ferromagnetic Problems

“…As an error indicator, a weighted tangential component of magnetic field d was proposed in the previous paper [1] as follows:…”

“…A NOVEL adaptive finite-element method (FEM) has previously been proposed utilizing a magnetic field conservation evaluation as an error indicator and a non-conforming mesh-refinement technique as a mesh-refinement scheme [1]. Our goal is to improve the simulation accuracy with less number of elements.…”

“…Some error indicators were proposed [2]- [5], and an error indicator based on the conservation of magnetic field H on the interface between two elements [1], [5] are very promising from the mathematical viewpoint. Meanwhile, a few kinds of non-conforming techniques were also proposed such as the discontinuous Galerkin method [6], the mortar FEM [7], and the mesh interpolating method [8].…”

“…Meanwhile, a few kinds of non-conforming techniques were also proposed such as the discontinuous Galerkin method [6], the mortar FEM [7], and the mesh interpolating method [8]. The interpolating method is well suited for the proposed adaptive FEM [1].…”

“…1 shows the flow of a common adaptive FEM. The magnetic field conservation indicator [5] and the non-conforming mesh-refinement technique are used in the proposed method [1]. In this paper, an edge-based tetrahedral finite element is employed.…”