Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4645181 | Applied Numerical Mathematics | 2014 | 8 Pages |
Abstract
Given a function f0f0 defined on the unit square Ω with values in R3R3, we construct a piecewise linear function f on a triangulation of Ω such that f agrees with f0f0 on the boundary nodes, and the image of f has minimal surface area. The problem is formulated as that of minimizing a discretization of a least squares functional whose critical points are uniformly parameterized minimal surfaces. The nonlinear least squares problem is treated by a trust region method in which the trust region radius is defined by a stepwise-variable Sobolev metric. Test results demonstrate the effectiveness of the method.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Robert J. Renka,