An approximation method based on MRA for the quasi-Plateau problem

作者：Hao, Yong-Xia; Li, Chong-Jun^*; Wang, Ren-Hong

来源：BIT Numerical Mathematics, 2013, 53(2): 411-442.

DOI：10.1007/s10543-012-0412-2

• Plateau problem
• Minimal surface
• Dirichlet functional
• Multiresolution analysis
• Approximation

In this paper, we discuss how to obtain the parametric surface of minimal area defined on a rectangular parameter domain among all the surfaces with prescribed entire or partial borders, i.e, the quasi-Plateau problem. An approximation method is presented based on the Multiresolution Analysis (MRA) using B-splines. Four algorithms are proposed according to different cases of the boundary conditions. The solution surfaces can be obtained by solving a system of linear equations of simple and sparse structure. Examples are provided to illustrate that the proposed method is effective and flexible.

• 出版日期2013-6
• 单位大连理工大学