A trust region method for constructing triangle-mesh approximations of parametric minimal surfaces

Given a function f 0 defined on the unit square Ω with values in R 3 , we construct a piecewise linear function f on a triangulation of Ω such that f agrees with f 0 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.