Yanpu Zhao

A Parameterized Mesh Generation and Refinement Method for Finite Element Parameter Sweeping Analysis of Electromagnetic Devices

A parameterized mesh generation and refinement method is presented for parameter sweeping analysis of electromagnetic designs. The advantages of the method are distinct in that the method is remeshing-free, thus it can significantly reduce the numerical simulation time during the finite element analysis (FEA) process. The refinement procedure is accomplished in an adaptive manner to concentrate the mesh vertices to regions with large solution variations. A high quality mesh can be obtained and kept by using this method with triangular finite elements. An example of parameter sweeping for optimal electric motor design is given to showcase the effectiveness of the proposed method.

A Novel Adaptive Mesh Finite Element Method for Nonlinear Magnetic Field Analysis

A novel adaptive finite element method for the numerical simulation of magnetic fields with nonlinear materials is presented. The proposed method incorporates functions of both mesh refinement and mesh coarsening. Instead of explicitly eliminating unnecessary nodes in the mesh, the proposed mesh coarsening algorithm only needs a single mesh. The procedure is to apply constraints to those degrees of freedom with small estimated error. This process avoids solution interpolation errors due to changes from a fine mesh to a coarse mesh and can be implemented readily. The slave-master technique is adopted to eliminate the constrained degrees of freedom in the linear system, which has the same effect as mesh coarsening. Implementation details of the algorithm are presented and numerical examples are tested to showcase the effectiveness of the proposed method.

A Parameterized Mesh Technique for Finite Element Magnetic Field Computation and Its Application to Optimal Designs of Electromagnetic Devices

A parameterized mesh generation is presented for design optimization of electromagnetic devices. The proposed method requires no mesh regeneration, and hence the numerical simulation time can be reduced significantly. When the coordinates of nodes in the refined mesh are changed, the mesh topology will be kept, that is, the node connection relationship will remain the same as before. Thus the nodal solutions can be carried over from previous FEM results to subsequent FEM computation without the need of mapping the nodes between two meshes. Additionally, the mesh quality can remain high using a swapping diagonal technique. Based on the sample points obtained from FEM with parameterized mesh, the optimal model is reconstructed using the response surface methodology (RSM). The particle swarm optimization (PSO) method is then used to arrive at the optimal solution swiftly and efficiently. An optimal design of electromagnetic device is reported to verify the efficiency and effectiveness of the proposed method.

An Electromagnetic Field and Electric Circuit Coupled Method for Solid Conductors in 3-D Finite-Element Method

The traditional low-frequency electromagnetic field computations do not include stray capacitive effect, while high-frequency solvers do not consider the nonlinear property of materials, and the internal regions of solid conductors as well as external circuit excitations. In this paper, the application of 3-D edge-element finite-element method (FEM) to problems with both inductive and capacitive effects for solid conductors, under external circuit excitations using the formulation with a magnetic vector potential and an electric scalar potential, is presented. The novel field-circuit coupled method that is presented does not need to look for the integration path of electromotive force computation. It has the merit of being convenient in algorithm implementation. Several numerical examples are given to showcase the proposed formulation and the developed computer program using an edge-element FEM.

Application of Edge Elements to 3-D Electromagnetic Field Analysis Accounting for Both Inductive and Capacitive Effects

The traditional low-frequency eddy-current solvers do not include displacement current effect, while high-frequency solvers do not consider the nonlinearity of material properties. A novel solver for electromagnetic field analysis that addresses both the inductive and capacitive effects is, thus, highly valuable. A stable time-domain magnetic vector potential (MVP) formulation, which includes both the inductive and capacitive effects, is proposed and numerical examples are solved using the proposed formulation. The proposed MVP formulation is very promising in further engineering applications.

Analysis of Wireless Power Transfer System Based on 3-D Finite-Element Method Including Displacement Current

With the advent of electronic technology, researchers are devoting increasing interests to wireless power transfer methods. Generally finite-element method (FEM) is a powerful tool for numerical simulation of such systems. Due to the relatively high operating frequency, the presence of inductance and distributed capacitance in the system as well as eddy current and displacement current become two essential issues in the study of electromagnetic field distribution in wireless power transfer systems. One of the major problems to be addressed is the gap between low and high frequencies as conventional low frequency methods cannot include displacement current, while common high frequency methods focus mainly on the ultrahigh frequencies, such as in antenna studies. In this paper, a 3-D FEM including displacement current is developed to model wireless power transfer system to include displacement current and eddy current and close the gap of high and low frequency modeling methods. No frequency sweeping, which is required in conventional studies, is necessary in the proposed algorithm. Hence the computing time of the proposed algorithm requires only 1.5% of the normal time domain FEM method and this is a significant accomplishment for the electromagnetic community.

An Efficient Parameterized Mesh Method for Large Shape Variation in Optimal Designs of Electromagnetic Devices

An algorithm with parameterized mesh generation, refinement and morphing is presented for the optimal design of electromagnetic (EM) devices. The method can do without mesh regeneration when changing design parameters, hence a lot of computation time can be saved in finite element (FE) parameter sweeping analysis. When the design parameters change, a new mesh can be obtained immediately with this proposed technique by simply resetting the coordinates of the nodes in the parameterized mesh. For nonlinear problems, a good initial value can be obtained from the solution on the former mesh to facilitate fast convergence of the nonlinear iterations for subsequent computation. An efficient memory procedure dealing with the design parameters and a practical technique allowing for large shape variation are also presented in the proposed method. Based on the objective function values by post-processing the FE results when sweeping certain sampling points in the design space, an optimization problem can be reconstructed using the response surface methodology. The differential evolution method is used as an optimization solver to search for the optimal solution efficiently. The TEAM Workshop Problem 25 is used as an example to showcase the efficiency and effectiveness of the proposed method.

A Local Discontinuous Galerkin Method for Eddy Current Field Analysis in High-Speed Moving Conductors

A numerical method for analyzing eddy current magnetic field in high-speed moving conductors using local discontinuous Galerkin (LDG) method is presented. A typical numerical example is chosen to illustrate the accuracy and nonoscillatory nature of the method for a convection dominated case. The simulation results using the proposed algorithm are validated using standard finite element method (FEM). As an application of LDG method in engineering problems, the TEAM workshop problem 9 is studied and solved by the proposed method with second order rectangular discontinuous elements. Numerical results show that the method can solve eddy current problems with high speed moving conductors accurately.

An Operator Splitting Finite Element Method for Eddy-Current Field Analysis in High-Speed Rotating Solid Conductors

Standard Galerkin finite element method (SGFEM) cannot solve eddy-current problems with dominated motional terms accurately and effectively. A numerical method for analyzing eddy-current magnetic field in high-speed rotating solid conductors using operator splitting finite element method (OSFEM) is presented. An artificial example and a benchmark transient eddy-current field problem, the problems 30A and 30B in testing electromagnetic analysis methods (TEAM) workshop, are used to test the accuracy and performance of the method. It is demonstrated that the numerical solution using the proposed method is nonoscillatory even for convection dominated cases. Besides, the calculated torque values are more accurate using the proposed OSFEM when compared with those obtained using SGFEM. It is concluded that the OSFEM can solve eddy-current problems with high-speed rotating conductors efficiently and accurately.

An Adaptive Mesh Method in Transient Finite Element Analysis of Magnetic Field Using a Novel Error Estimator

A novel error estimator for adaptive mesh refinement in finite element analysis (FEA) of magnetic field using quadratic finite elements is presented. The method uses a novel heuristic a posteriori error estimator, which is easy to compute and simple to implement, as an indicator of the numerical errors of the computed solution. The proposed error estimator is the L2 norm of the difference between the computed quadratic finite element solution and the interpolated linear solution. Throughout the time-stepping process for problems excited by periodic sinusoidal excitations, this error estimator can also be used to efficiently compute the numerical error at each time step and guide the adaptive mesh refinement in transient FEA. A multi-time-step adaptive mesh refinement method is also proposed in this paper for transient problems. The proposed method does not need to interpolate the solution from old mesh to a new adaptively refined mesh in transient FEA and hence there is no interpolation error. The effectiveness of the proposed error estimator is illustrated through several numerical examples being reported in this paper.