A Defect Corrected Finite Element Approach for the Accurate Evaluation of Magnetic Fields on Unstructured Grids
For engineers simulating magnets and machines, this provides an easy-to-implement alternative to higher-order finite elements for accurate local field evaluation.
The paper proposes a defect correction scheme using radial basis functions to improve the accuracy of magnetic field evaluation on unstructured grids, achieving significantly improved local convergence orders. The method is demonstrated on a Stern-Gerlach magnet simulation.
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.