scholarly journals Quantization and centroidal Voronoi tessellations for probability measures on dyadic Cantor sets

2017 ◽  
Vol 4 (2) ◽  
pp. 127-146 ◽  
Author(s):  
Mrinal Kanti Roychowdhury
Keyword(s):  
Cantor Sets ◽  
Probability Measures ◽  
Voronoi Tessellations ◽  
Centroidal Voronoi Tessellations

Mahalanobis centroidal Voronoi tessellations

2015 ◽  
Vol 46 ◽  
pp. 48-54 ◽  
Author(s):  
Ronald Richter ◽  
Marc Alexa
Keyword(s):  
Voronoi Tessellations ◽  
Centroidal Voronoi Tessellations

Impact of Local Grid Refinements of Spherical Centroidal Voronoi Tessellations for Global Atmospheric Models

2017 ◽  
Vol 21 (5) ◽  
pp. 1310-1324 ◽  
Author(s):  
Yudi Liu ◽  
Taojin Yang
Keyword(s):  
Model Simulation ◽  
Horizontal Resolution ◽  
Global Model ◽  
Test Cases ◽  
Atmospheric Models ◽  
Voronoi Tessellations ◽  
Local Refinement ◽  
Reflected Waves ◽  
Centroidal Voronoi Tessellations ◽  
Local Grid

AbstractIn order to study the local refinement issue of the horizontal resolution for a global model with Spherical Centroidal Voronoi Tessellations (SCVTs), the SCVTs are set to 10242 cells and 40962 cells respectively using the density function. The ratio between the grid resolutions in the high and low resolution regions (hereafter RHL) is set to 1:2, 1:3 and 1:4 for 10242 cells and 40962 cells, and the width of the grid transition zone (for simplicity, WTZ) is set to 18° and 9° to investigate their impacts on the model simulation. The ideal test cases, i.e. the cosine bell and global steady-state nonlinear zonal geostrophic flow, are carried out with the above settings. Simulation results showthat the larger the RHL is, the larger the resulting error is. It is obvious that the 1:4 ratio gives rise to much larger errors than the 1:2 or 1:3 ratio; the errors resulting from the WTZ is much smaller than that from the RHL. No significant wave distortion or reflected waves are found when the fluctuation passes through the refinement region, and the error is significantly small in the refinement region. Therefore,when designing a local refinement scheme in the global model with SCVT, the RHL should be less than 1:4, i.e., the error is acceptable when the RHL is 1:2 or 1:3.

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