摘要
针对含任意形状闭围线区域的无限大平面中分区调和函数边界值问题,先通过保角变换将任意形状闭围线映射为单位圆,再将变换域中单位圆内的解析函数展开为Faber级数,最后利用单位圆上的连续性边界条件,对其进行了研究和计算.通过数值算例,得到了正方形闭围线的数值解.结果表明,将Faber级数展开、保角变换技术应用到复变函数分析中,可有效解决一些复杂区域中非均匀调和函数的边界值问题.
The problems of harmonic equations are studied with multi-region in the infinite plane. Firstly, the arbitrary closed contour was mapped to a unit circle in the infinite region by conformal transform;Then the analytical functions in the unite circle were expanded to Faber Series, with unknown coefficients in transformed plane;finally, the coeffi- cients were determined by the boundary conditions on the interface. Numerical results were presented and graphically were shown for the case of square contours. The evidences confirmed that the Faber expansion is an efficient tool for the two-dimension harmonic equation in infinite plane containing an arbitrarily shaped region.
出处
《南通大学学报（自然科学版）》
CAS
2014年第1期81-85,共5页
Journal of Nantong University(Natural Science Edition)
基金
国家自然科学基金项目(10902055)
江苏省研究生培养创新工程项目(CXLX12_0882)
南通大学研究生科研计划创新项目(YKC12077)
