有理宏单元法求解泊松方程

基于有理超限插值,提出了一种在求解域边界布点的全域求解数值方法——有理宏单元法。推导出了三角形及四边形单元的有理混合函数,划分单元各边的节点并选定各边上的插值函数,建立了三角形及四边形母单元的形函数。利用等参变换,将求解域影射到相应的母单元上,得到了求解泊松方程边值问题的有理宏单元方程组。通过将求解域划分为一个或多个宏单元,有理宏单元法可对任意形状的二维区域求解。作有理宏单元法解泊松方程边值问题的算例,验证了本文方法的有效性。

Rational Macro-Element Method Applied in Poisson's Equation

In this paper, based on the rational transfinite interpolation, a set of global approximation method namely rational macro-element method was proposed. The rational blending function of triangular or rectangular elements was deduced, and the dots and interpolational functions were established at every boundries. The shape functions of triangular or rectangular macro-elements were obtained. Then, following the idea of isoparametric element, the element was extend to computational zone. The rational macroelement method was given to solve Poisson's equation. Through divided to several zone, the method can solve in any shape 2D zone. Finally, the rational macro-element method was programmed to solve Poisson equation and verifies the validity of this mefhod.