A defect corrected finite element approach for the accurate evaluation of magnetic fields on unstructured grids

作者：Roemer Ulrich; Schoeps Sebastian; De Gersem Herbert

来源：Journal of Computational Physics, 2017, 335: 688-699.

DOI：10.1016/j.jcp.2017.01.041

• Finite element method
• Defect correction
• Adjoint equation
• Radial basis functions
• Error estimation

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 (RBFs) 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.

• 出版日期2017-4-15