Optimal power diagrams via function approximation

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 co...

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Vydáno v:Computer aided design Ročník 102; s. 52 - 60
Hlavní autoři: Xiao, Yanyang, Chen, Zhonggui, Cao, Juan, Zhang, Yongjie Jessica, Wang, Cheng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Ltd 01.09.2018
Elsevier BV
Témata:
Anisotropic meshing
Anisotropy
Approximants
Approximation
CAD
Computer aided design
Diagrams
Discrete element method
Function approximation
Mathematical analysis
Mathematical functions
Monte Carlo simulation
Optimal power diagram
Optimal Voronoi tessellation
Optimization
Tessellation
Anisotropic meshing
Optimal power diagram
Function approximation
Optimal Voronoi tessellation
ISSN:0010-4485, 1879-2685
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Shrnutí: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. [Display omitted] •A novel optimal power diagram (OPD) method is proposed for generating high-quality cell complexes.•The anisotropy of the resulting power cells conforms to the Hessian of an arbitrary given function.•A modified Monte Carlo method with a local search strategy is tailored for effective optimization.
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ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2018.04.007