用二阶矢量位计算三维矢量磁位静磁场问题的多极理论

Multipole Theory for 3D Magnetic Vector Potential Magnetostatic Field Problems using the Second Order Vector Potential

提出了用二阶矢量磁位计算三维矢量位静磁场边值问题的多极理论方法。数学分析结果表明，对于具有唯一解的矢量磁位静磁场边值问题，多极理论所获得的解是唯一的。用多极理论求解三维矢量磁位的静磁场边值问题，既不需要离散场域或边界，又能获得整个场域内的连续级数解，且变量数较少，显著降低了计算机内存需要量。通过对两个实例的实际计算结果表明，三维矢量磁位静磁场分析的二阶矢量位多极理论方法是可行的，具有较高的计算精度，可以很方便地应用于三维矢量磁位静磁场边值问题的计算。

A MT(Multipole Theory) method for 3D magnetic vector potential magnetostatic field problems formulated in terms of the second order vector potential is presented in this paper.It is proven that the MT can get the unique solution for magnetic vector potential boundary value problems that has a unique solution.Using the MT method,it is unnecessary to discrete the field domain or the boundary,the number of the variables is much less than that of the other method and a minimum computer resource is needed.By calculating two examples,it is shown that the MT is reliable,has better computation accuracy and can be used to compute the 3D magnetic vector potential magnetostatic boundary value problems.