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A numerical method for computing minimal surfaces in arbitrary dimension
- Source :
-
Journal of Computational Physics . Jul2005, Vol. 206 Issue 2, p650-660. 11p. - Publication Year :
- 2005
-
Abstract
- Abstract: 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 in 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) (1993) 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. [Copyright &y& Elsevier]
- Subjects :
- *NUMERICAL analysis
*ALGORITHMS
*BOUNDARY value problems
*DIFFERENTIAL equations
Subjects
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 206
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 17791352
- Full Text :
- https://doi.org/10.1016/j.jcp.2004.12.022