کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645829 | 1342066 | 2009 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On the numerical solution of Plateau's problem On the numerical solution of Plateau's problem](/preview/png/4645829.png)
The present paper is dedicated to the numerical computation of minimal surfaces by the boundary element method. Having a parametrization γ of the boundary curve over the unit circle at hand, the problem is reduced to seeking a reparametrization κ of the unit circle. The Dirichlet energy of the harmonic extension of γ○κ has to be minimized among all reparametrizations. The energy functional is calculated as boundary integral that involves the Dirichlet-to-Neumann map. First and second order necessary optimality conditions of the underlying minimization problem are formulated. Existence and convergence of approximate solutions is proven. An efficient algorithm is proposed for the computation of minimal surfaces and numerical results are presented.
Journal: Applied Numerical Mathematics - Volume 59, Issue 11, November 2009, Pages 2785-2800