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Minimal surface computation using a finite element method on an embedded surface
Author(s) -
Cenanovic Mirza,
Hansbo Peter,
Larson Mats G.
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4892
Subject(s) - isosurface , finite element method , discretization , mathematics , surface (topology) , piecewise , piecewise linear function , tetrahedron , mathematical analysis , signed distance function , mixed finite element method , extended finite element method , computation , curvature , minimal surface , mean curvature , geometry , algorithm , computer science , physics , artificial intelligence , visualization , thermodynamics
Summary We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace–Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three‐dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method. Copyright © 2015 John Wiley & Sons, Ltd.