Commun. Comput. Phys., 13 (2013), pp. 1209-1226.

Retrieving Topological Information of Implicitly Represented Diffuse Interfaces with Adaptive Finite Element Discretization

Jian Zhang 1*, Qiang Du 2

1 Supercomputing center, Chinese Academy of Sciences, Beijing, P.R. China; and State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing, P.R. China.
2 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA.

Received 26 December 2011; Accepted (in revised version) 29 June 2012
Available online 8 October 2012


We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface framework. Utilizing an adaptive finite element implementation with effective gradient recovery techniques, we discuss how the Euler number can be accurately computed directly from the numerically solved phase field functions or order parameters. Numerical examples and applications to the topological analysis of point clouds are also presented.

AMS subject classifications: 65N30, 57M50, 74A50, 92C05

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Key words: Diffuse interface model, phase field method, Euler number, Gauss curvature, adaptive finite element, gradient recovery.

*Corresponding author.
Email: (J. Zhang), (Q. Du)

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