an:00829978
Zbl 0857.35004
Renka, R. J.; Neuberger, J. W.
Minimal surfaces and Sobolev gradients
EN
SIAM J. Sci. Comput. 16, No. 6, 1412-1427 (1995).
00030122
1995
j
35A15 65N06 65M99 65N99
preconditioning; parametric minimal surfaces; Sobolev metric method
The authors treat the problem of computing triangle-based piecewise linear approximations to parametric minimal surfaces in the Euclidean 3-space. They employ the Sobolev metric method to descend the surface-area functional at each iteration. Test results show that, starting with extremely poor initial estimates, a few descent iterations produce approximations in the vicinity of the solution. They also introduce a new characterization of minimal surfaces that eliminates the potential problem of triangle area approaching zero. In place of the surface area functional, they minimize a functional whose critical points are uniformly parametrized minimal surfaces. This leads to both rapid convergence of the descent method and simplifying the expressions for gradients and Hessians.
Ma Li (New Brunswick)