期刊
COMPUTER-AIDED DESIGN
卷 102, 期 -, 页码 52-60出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.cad.2018.04.007
关键词
Anisotropic meshing; Optimal power diagram; Optimal Voronoi tessellation; Function approximation
资金
- National Natural Science Foundation of China [61472332, 61572020, 61728206, U1605254]
- Natural Science Foundation of Fujian Province of China [2018101104]
- program of China Scholarship Council [201706315019, 201706315001]
- PECASE Award [N00014-16-1-2254]
- NSF CAREER Award [OCI-1149591]
In this paper, we present a novel method for generating cell complexes with anisotropy conforming to the Hessian of an arbitrary given function. This is done by variationally optimizing the discontinuous piecewise linear approximation of the given functions over power diagrams. The resulting cell complexes corresponding to the approximations are referred to as Optimal Power Diagram (OPD). A hybrid optimization technique, coupling a modified Monte Carlo method with a local search strategy, is tailored for effectively solving the specific optimization task. In contrast to the Optimal Voronoi Tessellation (OVT) method (Budninskiy et al., 2016), our OPD method does not restrict the target functions to be convex, providing more diverse classes of tessellations of the domain. Furthermore, our OPD method generally yields smaller approximation errors than the OVT method, which uses underlaid approximants. We conduct several experiments to demonstrate the efficacy of our optimization algorithm in finding good local minima and generating high-quality anisotropic polytopal meshes. (C) 2018 Elsevier Ltd. All rights reserved.
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