线性等参单元逆变换的几何二分法及其修正

在证明线性等参单元的一个几何特性的基础上,提出了线性等参单元逆变换的几何二分法。几何二分法简单易行,避免求解高维高次非线性方程组。在几何二分法基础上,提出一种修正措施以消除畸形单元对所求结果的影响,几何二分法及其修正措施克服了以往方法存在的缺点,两个实例验证了由几何二分法及其修正措施进行等参逆变换的正确性。

Geometric dichotomy method for inverse isoparametric mapping in linear finite element and its correction measure

Geometric dichotomy method is innovated and used for inverse isoparametric mapping in linear finite element, of which a property is proved and served as the foundation. The geometric dichotomy method is easy and applicable, avoiding solving nonlinear equations with high dimensions and high orders. A correction measure is proposed to erase the effect of singular element on the result by the geometric dichotomy. The geometric dichotomy method and its correction measure overcome the disadvantages of the other existing methods. It is shown by two examples the correctness of the geometric dichotomy method and its correction measure for inverse isoparametric mapping in linear finite element.