A Defect Corrected Finite Element Approach for the Accurate Evaluation of Magnetic Fields on Unstructured Grids

TL;DR

This paper introduces a defect correction finite element method utilizing radial basis functions for precise local magnetic field evaluation on unstructured grids, improving accuracy and convergence in electromagnetic simulations.

Contribution

The paper presents a novel defect correction scheme using RBFs that enhances finite element accuracy on unstructured grids, enabling higher derivatives evaluation and better local magnetic field analysis.

Findings

Achieved significantly improved local convergence orders.

Successfully applied to real Stern-Gerlach magnet simulation.

Provided an easy-to-implement alternative to higher order methods.

Abstract

In electromagnetic simulations of magnets and machines one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is proposed as an easy to realize alternative to higher order finite element or hybrid approaches. Radial basis functions (RBF)s are key for the generality of the method, which in particular can handle unstructured grids. Also, contrary to conventional finite element basis functions, higher derivatives of the solution can be evaluated, as required, e.g., for deflection magnets. Defect correction is applied to obtain a solution with improved accuracy and adjoint techniques are used to estimate the remaining error for a specific quantity of interest. Significantly improved (local) convergence orders are obtained. The scheme is also applied to the simulation of a Stern-Gerlach magnet currently in operation.