Minimal surfaces and Sobolev gradients
SIAM Journal on Scientific Computing
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Nonlinear least squares and Sobolev gradients
Applied Numerical Mathematics
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Given a function f"0 defined on the unit square @W with values in R^3, we construct a piecewise linear function f on a triangulation of @W 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.