Andreas Pels

Optimization of a Stern–Gerlach Magnet by Magnetic Field–Circuit Coupling and Isogeometric Analysis

Stern-Gerlach magnets are used to magnetically separate a beam of atoms or atom clusters. The design is difficult, since both the magnetic field gradient and its homogeneity should be maximized. This paper proposes the numerical optimization of the devices pole-shoe shapes, starting from a reference geometry given in the literature. The main contributions of this paper are the generalization of a magnetic field-magnetic circuit coupling and the application of isogeometric analysis (IGA), which are shown to reduce the computational complexity and increase the accuracy. The field-circuit coupling significantly reduces the size of the field model part, in which the IGAs spline-based framework enables a highly accurate evaluation of local field quantities, even across elements.

Solving Nonlinear Circuits With Pulsed Excitation by Multirate Partial Differential Equations

In this paper, the concept of multirate partial differential equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains.

Solving multirate partial differential equations using hat finite element basis functions

In this digest a universal approach for solving multirate partial differential equations (MPDEs) is presented. Taking advantage of already known concepts in literature, standard finite element hat functions are used to achieve an efficient solution of a multirate problem in time-domain. The MPDE is solved by a Galerkin-ansatz with hat functions in the fast time-scale and using conventional time discretization for the slow time-scale.