Geodesic
Level set methods to compute minimal surfaces in a medium with exclusions (voids)
Monica Torres1 ; David Chopp2 ; Timothy Walsh3
1Purdue University, West Lafayette, USA
2Northwestern University, Evanston, USA
3Sandia National Laboratories, Albuquerque, USA
Interfaces and free boundaries, Tome 7 (2005) no. 2, pp. 161-185

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DOI

In [59], periodic minimal surfaces in a medium with exclusions (voids) are constructed and in this paper we present two algorithms for computing these minimal surfaces. The two algorithms use evolution of level sets by mean curvature. The first algorithm solves the governing nonlinear PDE directly and enforces numerically an orthogonality condition that the surfaces satisfy when they meet the boundaries of the exclusions. The second algorithm involves h-adaptive finite element approximations of a linear convection-diffusion equation, which has been shown to linearize the governing nonlinear PDE for weighted mean curvature flow.
DOI : 10.4171/ifb/119
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Monica Torres  1   ; David Chopp  2   ; Timothy Walsh  3

1 Purdue University, West Lafayette, USA
2 Northwestern University, Evanston, USA
3 Sandia National Laboratories, Albuquerque, USA 
Monica Torres; David Chopp; Timothy Walsh. Level set methods to compute minimal surfaces in a medium with exclusions (voids). Interfaces and free boundaries, Tome 7 (2005) no. 2, pp. 161-185. doi: 10.4171/ifb/119
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