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Anisotropic Mesh Adaptation for Evolving Triangulated Surfaces

Jiao, Xiangmin, Andrew Colombi, Xinlai Ni, and John C. Hart

Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.173-190, September 17-20 2006


15th International Meshing Roundtable
Birmingham, Alabama, U.S.A.
September 17-20, 2006

Xiangmin Jiao
College of Computing, Georgia Institute of Technology, Atlanta, GA 30332

Andrew Colombi, Xinlai Ni, and John C. Hart
Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Dynamic surfaces arise in many applications, such as free surfaces in multiphase flows and moving interfaces in fluid-solid interactions. In many applications, an explicit surface triangulation is used to track the dynamic surfaces, posing significant challenges in adapting their meshes, especially if large curvatures and sharp features may dynamically appear or vanish as the surfaces evolve. In this paper, we present an anisotropic mesh adaptation technique to meet these challenges. Our technique strives for optimal aspect ratios of the triangulation to reduce interpolation errors and to capture geometric features based on a novel extension of the quadric-based surface analysis. Our adaptation algorithm combines the operations of vertex redistribution, edge flipping, edge contraction, and edge splitting. Experimental results demonstrate the effectiveness of our anisotropic adaptation techniques for static and dynamic surfaces.

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