复杂边界单连通域共形映射解析建模研究

Analytically Modeling of Complicated Boundary Simply-connected Region Conformal Mapping

在工程实际中任意非规则复杂边界单连通域问题的数学模型建立难度大,导致求解和优化参数非常困难。根据共形映射原理,采用复变三角插值理论,利用法线迭代收敛方法,将任意复杂边界单连通域问题转化为单位圆域问题,系统地建立了二者间的共形映射函数,并对具有对称轴特性的单连通域问题进行了算法简化。

It is difficult to model the irregular geometry simply-connected region in engineering problems, which makes analytical solution and optimization of parameters very hard. Conformal mapping method is adopted to transform the complicated contact region to unit circle disk. To solve the conformal mapping function, complex triangular interpolation with iterative and normal convergence is presented. And FFT algorithm is used to solve the coefficients. For symmetrical region, a fast algorithm is realized by simplification. Using this method, it is possible to obtain analytical solution and optimized parameters. The method is realized by a computer program and its effect is presented with an example.