本征值问题和可视化技术在电磁场计算中的应用

齐次边界条件或周期性边界条件下的Laplace场构成Sturm-Liouville型本征值问题。求解本征值问题可得一系列的本征值和对应的本征函数。由这些本征函数构成了对应的Laplace边值问题的级数通解。揭示了用于计算电磁场问题的新型等效源方法（包括圆形等效源方法、矩形等效源方法和矩形－圆形等新源混合算法）和本征值问题之间的内在联系，也即阐明了本征值问题是新等效源方法的理论基础。应用模拟电荷法、多极子法、多极理论和新型等效源方法等方法求解计算电磁场时，有关参数（诸如模拟电荷、内外极或者等效源的数目和位置安排，尤其是模拟电荷电量的大小、内外极的次数或者等效源的阶数等）的选择问题是影响这些方法应用的瓶颈。在计算过程中综合应用解的图形显示和校核点处的计算值的误差大小来确定有关参数，既可以确保解的正确性，又可以极大地提高计算效率和计算精度。

The Application of Eigenvalue Problem and Visualization Technology in Calculation of Electro-magneto Static Field

The Laplace equation with homogeneous or periodic boundary condition constructs the eigenvalue problem of Sturm Liouville equations and the solving of the eigenvalue problem will obtain a series of eigenvalues and corresponding eigenfunctions. The intrinsic relation between the new style equivalent source method (NEMS, including circular equivalent source method, rectangular equivalent source method and rectangular circular equivalent source hybrid method) in electro magneto static field and eigenvalue problem is revealed in this paper, i.e. the eigenvalue problem is the theoretical basis of NESM. When charge simulation method (CSM), multiple multi pole method (MMP), multi pole theory or the NESM is applied, the selection of parameters such as number, position, charging volume or orders of inner or outer poles and equivalent sources is the bottleneck of affecting the application of these methods. The comprehensive application of solution visualization and calculation errors at check points on field boundaries to determine relevant parameters would not only make solution correct, but also increase the precision and efficiency of calculation.