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

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.

Assessing the Performance of Leja and Clenshaw-Curtis Collocation for Computational Electromagnetics With Random Input Data

“…We consider a real-world application, in particular a Rabi-type Stern-Gerlach magnet (see Figure 8(a)), similar to the one described in [27] and further studied in [36,37]. This magnet is currently in use at KU Leuven.…”

Numerical analysis of the screening current-induced magnetic field in the HTS insert dipole magnet Feather-M2.1-2

“…In numerical models, the multipole coefficients are obtained by applying the Fast Fourier Transform algorithm to the radial component of the magnetic field, calculated along the reference circumference in the magnet aperture (see section 2.2). Care has to be taken, as the finite resolution of the mesh in the spatial discretization introduces a numerical error which affects the calculation of the multipole coefficients [53]. For this reason, a mesh sensitivity analysis is carried out for a reference model where a known analytical field solution is simulated and calculated at the reference circumference.…”

Magnetodynamic Finite-Element Simulation of Accelerator Magnets

“…This is fully acceptable for visualization purposes but may be inacceptable when the field values are needed themselves. A way out is to apply local postprocessing techniques avoiding or repairing for the loss of accuracy, e.g., by defect correction [65].…”

“…The aperture field needs to be simulated with a high precision in order to predict harmonic distortion factors which are expected to be in the range of 10 −4 . Besides a-posteriori accuracy improvement techniques such as, e.g., defect correction [65], there exists the possibility to a-priori select a high-precision discretization technique for the aperture region. While for the yoke parts, the FE method is more or less inavoidable because of the material nonlinearity, the overall method becomes hybrid, which may necessitate the development of a dedicated algebraic solution technique to retain the simulation efficiency [78].…”