【摘要】 应用分离变量法求解矩形域中拉普拉斯方程的边值问题可以得到一个无穷级数通解-该解的形式随着边界条件的不同而变化,称之为矩形等效源的基本解。在此基础上,提出了求解矩形外边界内多连通域中的恒定电磁场问题的矩形-圆形等效源混合新算法。在算法实施过程中综合应用可视化技术和场域边界校验点上的误差大小来选择等效源(包括其数目、位置安排及阶数等),确保解的可靠性,并极大提高了计算精度和效率。更多还原

【Abstract】 With the help of separation, a series expansion of the general solution of the boundary value problem for Laplace equation in a rectangular region has been derived. The expansion will change according to the change of the boundary conditions and is defined as the basic solution of the rectangu-lar equivalent source. The rectangular equivalent source-circul-ar equivalent source mixed method, which is suitable for calculating the electromagnetic static field in the multiply connected domain with a rectangular outer boundary, is systematically illustrated in this paper. The visualization of the solution combining with the calculation error at the checkpoin-ts in the boundaries of the field is applied to determine the nu-mber and position and order of the equivalent sources employ-ed. It makes the solution reliable, more accurate and efficient.更多还原