科研之友
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摘要
Given a function fo defined on the unit square Omega with values in R-3, we construct a piecewise linear function f on a triangulation of Omega such that f agrees with fo 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.
- 出版日期2014-2
