基于棱边元的三维定点谐波平衡有限元法及其在非线性问题中的应用

3-D Fixed-Point Harmonic Balance Finite Element Method Based on Edge Elements and Its Applications on Nonlinear Problems

为提升三维非线性电磁场仿真计算效率,提出了基于A、φ-A位组的三维定点谐波平衡有限元法。算法采用棱边元与节点元组合单元结构降低自由度,通过引入基于规范变换原则选取的标量位φ,保证矩阵方程的对称性。算法基于谐波平衡理论,实现了有限元方程系数矩阵的频域分解,使其适用于并行计算,并提出了直流分量定点磁阻率法及一种自适应的松弛因子选取方法,提升了算法非线性迭代的收敛速度。通过与传统时步有限元法及直流偏磁工况下的实验数据对比,验证了算法在三维涡流问题及考虑场路耦合的非线性问题上的有效性。在非线性工况下,分析了不同定点磁阻率选取方法对算法计算效率与收敛性能的影响。结果表明,在保证计算数值误差小于10-5时,相比其他定点磁阻率法,改进的定点磁阻率选取方法约降低31%的非线性迭代次数,29%的计算时间。

A 3-D fixed-point harmonic balance finite element method(FEM)based on the A,φ-A formulation is proposed for efficiently simulating the 3-D nonlinear electromagnetic field.The joint of edge and nodal elements is applied to reduce the degrees of freedom,while the gauge transformation is implemented for setting the scalar potential φ to guarantee the symmetrical property of the coefficient matrix.Based on the harmonic-balanced theory,the coefficient matrix is decomposed in the frequency domain for parallel computing,while the DC component fixed-point technique and a method of adaptively choosing the relaxation factor are proposed for decreasing the nonlinear iterations and the computing time.By comparing to the traditional time-domain FEM and the measurement results under DC-biased excitation,the method is validated for solving the 3-D eddy current problems and the nonlinear circuit-field coupling problems.The numerical properties,including the efficiency and the convergence of the 3-D harmonic balance method with different fixed-point reluctivities,are investigated in detail under nonlinear operating conditions.As indicated by the results,the improved fixed-point reluctivity method can reduce about 31%of nonlinear iterations and 29%of computing time compared to other methods when the numerical error is less than 10^(-5).