Conference Agenda

This paper deals with numerical techniques for finite element modeling of superconductors. For that, we use different methods: full storage (FS), compressed storages (CRS and CCS) and normalized formulation (NF). After improving and testing the program, we observe the computation time. Then we compare the results obtained by using different methods for some important parameters: the critical current density, the maximum magnetic induction and the angle of the applied magnetic field.

In this paper, a new fixed-point technique for solving magnetic field problems under non-sinusoidal excitation is proposed. Since hysteresis is branching, discontinuing the derivative at the reversals could become problematic when implementing the local-coefficient method(LCM). To enhance convergence stability at the reversal points, typical approaches usually employ a large fixed-point coefficient. However, this approach considerably impedes the convergence speed, especially in the cases of multiple reversal points under non-sinusoidal excitation. Therefore, a new fixed-point technique is developed, incorporating the Anderson acceleration with LCM. This method aims to substantially accelerate the iterative convergence speed while guaranteeing the overall convergence of the iterative process. Finally, the effectiveness of the proposed technique is rigorously validated through a comparative analysis of the computational costs incurred in numerical simulation experiments.

Numerical investigations on Poisson’s equations with nonlinear parameters play a critical role in modeling various physical problems, such as electric fields in nonlinear dielectrics and magnetic fields in ferromagnetic domains. This study proposes a nonlinearity-degree-reduction method for solving highly nonlinear Poisson’s equations by the cell method, aiming to reduce the computational complexity. The proposed approach characterizes a dependent nonlinear physical parameter at the midpoint of a line in a cell complex using weighted combinations of the independent variable values at the line’s endpoints. By carefully selecting these combination conditions, the nonlinearity in the derived discrete equations can be propagated from the entire solution domain to the external boundaries. This redistribution reduces the overall computational burden by lowering the degrees of nonlinearity. To validate the method, a nonlinear electrostatic problem is solved using the proposed method and a conventional fixed-point code. Simulation results and iteration steps are compared to demonstrate the accuracy and efficiency of the proposed approach.

The arc linear flux switching permanent magnet motor (AL FSPM) is suitable for large-scale scanning equipment and robotic joints, featuring flexible installation, high positioning accuracy, and low torque ripple. Additionally, compared to traditional rotor permanent magnet(PM) arc line motors, it solves the issues of exposed PM and low utilization. Although the subdomain method offers high computational accuracy in analyzing magnetic fields, it has not yet been applied to the magnetic field analysis of AL FSPM. This paper proposes a subdomain model for the magnetic field of AL FSPM, solving for the motor vector magnetic potential distribution at different rotor positions, and subsequently calculating the magnetic field distribution of the motor's transient field. Ultimately, key electromagnetic parameters such as air gap flux density, winding flux linkage, inductance, and losses are determined. This method can effectively shorten the computation time while ensuring accuracy, laying the foundation for the optimization of AL FSPM.

Conventional numerical simulation methods may become challenged when handling complex geometries due to ineffective discretization and large number of degrees of freedom. Based on the integral representation of electric potential derived from Green's theorem, a recursive estimate of the potential can be obtained. The walk-on-spheres algorithm is introduced to solve the Poisson equation when abrupt change of material exists. The proposed method is mesh-free and progressive, which has been validated by comparing the results with conventional methods, showing great potential in handling problems with complex geometries.

When calculating the induced currents in second-generation high-temperature superconductors (HTS), the strong nonlinear resistivity of HTS poses a critical challenge. This issue is typically addressed using the Newton-Raphson method, which requires extensive computation of Jacobian matrices. However, the introduction of the J−ϕ volume integral formulation enables explicit time domain difference method, thereby avoiding the handling of nonlinear resistivity. Nevertheless, this method is conditionally stable and requires precise control of the time step to prevent divergence of results.

In this paper, we propose an alternating explicit-implicit time domain difference method based on the J − ϕ volume integral formulation. By inserting implicit calculations into the original explicit process, this method prevents the rapid accumulation of perturbation errors during the time-stepping process. It overcomes the limitations of explicit time domain difference method, offering unconditional stability. Compared to the implicit time domain difference method, it significantly reduces the number of Jacobian matrix computations. Additionally, we present an adaptive secondorder explicit-implicit time domain difference method, which determines whether to insert implicit calculations by estimating errors and their growth rates. This approach not only improves computational accuracy but also demonstrates high stability.

The Proper Generalized Decomposition (PGD) algorithm combined with Jacobi preconditioned biconjugate gradient stabilized method (BiCGSTAB) is presented to analyze the transient electromagnetic field of a three-phase induction motor. In Poisson equation of transient eddy current magnetic field, the motion of motor rotor is considered using Eulerian description. The PGD algorithm that separate space domain and time domain to solve the transient eddy current magnetic field is derived, and the dimension reduction calculation of space-time separation is realized. In order to ensure the convergence of spatial domain solution, the Jacobi preconditioned BiCGSTAB is introduced to solve the asymmetric positive definite equations obtained by spatial discretization. Apply the algorithm to analyze the magnetic field of three-phase induction motor in TEAM30 problem, the effectiveness and accuracy are validated. Compared with the traditional time incremental finite element method, the computational speed and efficiency are obviously improved under the same accuracy. It is suitable for large-scale transient electromagnetic field numerical computations.

This paper proposes a rapid calculation model for the loss of rectangular Litz wire high-frequency transformers based on the Proper Generalized Decomposition (PGD) spatial separation algorithm and equivalent complex permeability. A double 2D model is adopted to consider the difference of magnetic field distribution at the end windings of the inner and outer windows.in which the magnetic field is calculated by separating and reducing the two-dimensional finite element calculation into two one-dimensional finite element analysis using the PGD algorithm. Two different types of transformers are made and tested experimentally, and the calculation efficiency and accuracy of FEM, image method and PGD algorithm are compared. The results show that, compared with the FEM and the image method, the calculation speed of the model established in this paper is faster, and it can accurately and effectively calculate the loss of rectangular Litz wire high-frequency transformers

With the expanding application of wireless power transfer (WPT) technology, capacitive, hybrid, and self-resonant wireless charging methods have gained increasing attention. It is noteworthy that these WPT magnetic coupling structures often face numerical challenges due to the arbitrary connection between solid conductors (such as plates where induced eddy-currents can’t be ignored) and stranded conductors (such as litz wires where the induced eddy-currents are negligible). To address this problem where both solid and stranded conductors are connected together and the possible capacitive effect between solid conductors, this paper proposes a benchmark test case and carried out the fabrication and measurement for the magnetic field values at given points first. Finite element field-circuit coupled formulation has been designed for this new need and to be implemeted for validating the reliability of the finite element simulation results. Measurements are conducted for rigorously assess the accuracy of the oncoming numerical results.

The implementation of fast multipole method (FMM) requires querying neighbor and interaction cells in a hierarchical tree, which can be complicated when the tree is unbalanced. We present a fast and easy-to-implement method to query neighbor and interaction cells in unbalanced trees. By uniformly splitting and indexing the coordinate axes of each layer, the coordinates of the tree nodes are converted into Morton codes, and the querying neighbor querying can be readily realized by bit-shifting the Morton code, which allows fast neighbor and interaction cells querying.

A frequency-domain finite element method incorporating GSTCs is proposed, which is rather simple and perticular well-suited for the multiscale simulation of magnetically coupling resonant wireless power transfer (MCR-WPT) system. The discontinuities in electromagnetic fields across a metasurface as represented by the GSTC are modeled by assigning nodes to one side of the metasurface. The FEM-GSTC formulation is derived and implemented. Here, for simplicity, the proposed formulation is presented for analysis of 2-D problems consisting of monoisotropic metasurfaces. The extension of this method 3-D problems or bianisotropicmetasurfaces is straightforward.