A numerical method for computing minimal surfaces in arbitrary dimension

被引：13

作者：

Cecil, T ^{[1
]}

机构：

[1] Univ Texas, ICES, Univ Stn, Austin, TX 78712 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2005年 / 206卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/j.jcp.2004.12.022

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper we propose a numerical method for computing minimal surfaces with fixed boundaries, The level set method is used to evolve a codimension-1 surface with fixed codimension-2 boundary ill R-n under mean curvature flow. For n = 3 the problem has been approached in D, L. Chopp, 1993 and L.-T. Cheng [D. L Chopp, Computing minimal surfaces via level set curvature flow, J. Comput. Phys. 106(1) (199.1) 77 91 and L.-T. Cheng, The level set method applied to geometrically based motion, materials science, and image processing, UCLA CAM Report, 00-20] using the level set method, but with a more complicated boundary conditions, The method we present can be generalized straightforward to arbitrary dimension, and the framework in which it is presented is dimension independent, Examples are shown for n = 2, 3, 4. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：650 / 660

页数：11

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