任意边界下的极小曲面造型问题

Approximating to Minimal Surface with Weighted B-Spline Surface

讨论了任意边界下的极小曲面造型问题,提出了一个用B-样条函数做任意有界区域上极小曲面造型的新方法。基本思想是:对B-样条函数加权,权函数为节点到区域边界的距离函数,使用加权的B-样条函数空间作为有限元子空间,从而可以得到极小曲面在任意边界上的B-样条曲面近似解。结果表明,新方法得到的极小曲面具有良好的光顺性,且计算精度高。

This paper discusses minimal surface in arbitrary boundary and describes a new method for approximating to minimal surface with B-spline surface in arbitrary bounded domain. The basic idea of the new method can be described as follows ： multiplying B-spline basis by a weight function which is the distance function to эΩ, then, discussing the approximation to minimal surface in arbitrary bounded domain by using the span of weighted B-spline as the finite element subspace. The results show that the new method yields high orderly and accurate approximations.