Computer Methods in Applied Mechanics and Engineering
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
A Parallel Algorithm for Mesh Smoothing
SIAM Journal on Scientific Computing
IEEE Transactions on Information Theory
Multi-atomic Young measure and artificial boundary in approximation of micromagnetics
Applied Numerical Mathematics
Centroidal Voronoi Tessellation Based Algorithms for Vector Fields Visualization and Segmentation
VIS '04 Proceedings of the conference on Visualization '04
Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
A geometric approach to non-parametric density estimation
Pattern Recognition
Constrained CVT meshes and a comparison of triangular mesh generators
Computational Geometry: Theory and Applications
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Computers & Mathematics with Applications
ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method
Journal of Computational Physics
Proper general decomposition (PGD) for the resolution of Navier-Stokes equations
Journal of Computational Physics
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab
Structural and Multidisciplinary Optimization
An algorithm for discrete booleans with applications to finite element modeling of complex systems
Finite Elements in Analysis and Design
Original article: Mesh generation for FEM based on centroidal Voronoi tessellations
Mathematics and Computers in Simulation
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Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, and optimal allocation of resources. In this paper, we explore the use of CVTs in grid generation in connection with finite element approximations of partial differential equations. We being by describing these tessellations and methods for their determination. We then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations.