Minimal surface computation using a finite element method on an embedded surface

作者：Cenanovic Mirza^*; Han**o Peter; Larson Mats G

来源：International Journal for Numerical Methods in Engineering, 2015, 104(7): 502-512.

DOI：10.1002/nme.4892

• mean curvature
• Laplace-Beltrami operator
• level set
• ghost penalty stabilization

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.

• 出版日期2015-11-16