同伦迭代法在触模算法中的应用

Homotopy algorithm and its applications to the die-touching problem

加工过程仿真中的触模处理 ,实际上是射线与曲面求交的问题 ,即非线性方程组的求解问题。广泛应用的Newton迭代法的收敛性取决于迭代初始值的选取 ,是局部收敛的方法。基于同伦映射的同伦算法 ,具有大范围收敛性。文中尝试将同伦迭代应用于触模算法中 。

The die\|touching problem in the FEM analysis in forming process,is factually to calculate the crossing point between a ray and surface.Also,this problem can be induced to compute the non\|linear equations,which is frequently solved by Newton iteration.However,the convergence of Newton algorithm is greatly dependent on the initial point,that means the method is locally convergent.The homotopy algorithm,basing on homotopy mapping,is convergent with wide range.This paper applies the homotopy iteration to the die\|touching problem and the examples show its feasibility and effectiveness.