论文标题
2D傅立叶有限元公式用于曲线坐标的磁静态元素与对称方向
2D Fourier finite element formulation for magnetostatics in curvilinear coordinates with a symmetry direction
论文作者
论文摘要
我们提出了一种数值方法，用于在具有对称方向（包括轴向和翻译对称性）的域中线性磁静态问题解决方案。该方法使用沿对称方向的矢量电势配方的傅立叶串联分解，并涵盖了零（非振荡）和非零（振荡）谐波。对于后者，可以消除矢量电势的一个成分，从而产生与横向磁场的完全横向矢量电位。除了非振荡问题的纵向成分的泊松状方程外，横向问题的一般卷曲 - 曲线helmholtz方程涵盖了横向问题，涵盖了非振荡和振荡案例。该派生在与指标和渗透率张量的曲线渗透性和对称限制的曲线坐标的协变形式中进行。由纵向问题的通常的节点有限元法和横向问题的二维边缘元素方法对所得的变分形式进行处理。可以针对每个谐波独立计算数值解，这在记忆使用和并行化方面都是有利的。
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential formulation along the symmetry direction and covers both, zeroth (non-oscillatory) and non-zero (oscillatory) harmonics. For the latter it is possible to eliminate one component of the vector potential resulting in a fully transverse vector potential orthogonal to the transverse magnetic field. In addition to the Poisson-like equation for the longitudinal component of the non-oscillatory problem, a general curl-curl Helmholtz equation results for the transverse problem covering both, non-oscillatory and oscillatory case. The derivation is performed in the covariant formalism for curvilinear coordinates with a tensorial permeability and symmetry restrictions on metric and permeability tensor. The resulting variational forms are treated by the usual nodal finite element method for the longitudinal problem and by a two-dimensional edge element method for the transverse problem. The numerical solution can be computed independently for each harmonic which is favourable with regard to memory usage and parallelisation.
