用二阶矢量位计算三维涡流问题的多极理论

The Multipole Theory for 3 D Eddy Current Problems by using the Second Order Vector Potential

本文提出用二阶矢量位计算三维涡流问题的多极理论，数学分析结果表明：多极理论解自动满足三维涡流问题的Ａ＊－Ψ数学模型，从而保证Ａ＊是唯一的。用多极理论求解三维涡流问题，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，显著降低了内存需要量。通过两个实例的实际计算结果表明，三维涡流分析的多极理论是可行的，具有较高的计算精度，可以很方便地应用于三维涡流场问题的计算。

The MT (Multipole Theory) method for 3 Deddy current problems formulated in terms of the second order vector potential is presented in this paper.By the mathematical analysis,it is proven that the MT solution automatically satisfies A * Ψ formulation of 3 D eddy current field and the modified magnetic vector potential A[DD(-*4] * is unique.By using the MT to compute the 3 D eddy current field,it is unnecessary to discrete the field domain or the boundary.Moreover,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 proven that the MT of 3 D eddy current field computation is reliable and has better cmputation accuracy,it can be used to compute 3 D eddy current field problems.