半解析方法中圆形等效源法的前处理算法

应用计算机图形学的原理和方法,提出了一种求解数学上极值问题的扫描-生长算法,解决了二维场的圆形分割问题.该算法能够快速确定分割区域中多个极点(各分割圆的圆心)的位置和数量,达到了用尽量少的圆形数来最大限度地充满该分割区域,并能满足在需要处(如场量突变处)进行局部加密的要求.根据为广义多极技术(属半解析法范畴)创建的理论体系,这些极点确定了解函数在级数展开式中各变量的起点.正因为这些变量的准确定位,不仅克服了广义多极技术中极点位置设置的盲目性,而且提高了解的计算效率和计算精度.因此,扫描-生长算法还可推广应用于轴对称场的计算中.

Pre-Processing Algorithm of Circular Equivalent Source Method in Half-Analytical Method

Based on the principle and method of computer graphics, a "scan-and-grow" algorithm is proposed to solve circular cutting problems of a 2D-field, where the number and positions of the poles expressing the centers of cutting circles can be determined quickly and the goal of using the minimum circle number to cover the maximum field region surface can also be satisfied. Moreover, the number of circles near a singular point of the field can be increased locally. According to the theory created for the generalized multi-pole technique (in domain of half-analytical method), the center of each circle is determined as a starting point of each variable in a series expansion of the 2D-field solution function, and the arranging blank of the starting points in the generalized multi-pole technique can be filled up owing to the precise variable positioning. It is expected to extend this algorithm to the calculation of axisymmetrical fields.