Abstract:
A boundary conforming Delaunay mesh is a partitioning of a polyhedral domain into Delaunay simplices such that all boundary simplices satisfy the generalized Gabriel property. It's dual is a Voronoi
partition of the same domain which is preferable for Voronoi-box based finite volume schemes. For arbitrary 2D polygonal regions, such meshes can be generated in optimal time and size. For arbitrary
3D polyhedral domains, however, this problem remains a challenge. The main contribution of this paper is to show that boundary conforming Delaunay meshes for 3D polyhedral domains can be generated efficiently when the smallest input angle of the domain is bounded by arccos1/3≈70.53∘. In addition, well-shaped tetrahedra and appropriate mesh size can be obtained. Our new results are
achieved by reanalyzing a classical Delaunay refinement algorithm. Note that our theoretical guarantee on the input angle (70.53∘) is still too strong for many practical situations. We further discuss variants of the algorithm to relax the input angle restriction and to improve the mesh quality.
Key words:
Delaunay mesh, Voronoi partitions, partitions of polyhedra.
This publication is cited in the following 52 articles:
Patricio Farrell, Julien Moatti, Michael O'Donovan, Stefan Schulz, Thomas Koprucki, “Importance of satisfying thermodynamic consistency in optoelectronic device simulations for high carrier densities”, Opt Quant Electron, 55:11 (2023)
Hao-Yu Lin, Zai-Fa Zhou, Ji-Yang Liu, Su-Xin Bao, Qing-An Huang, 2023 International Symposium of Electronics Design Automation (ISEDA), 2023, 471
Abdallah Bradji, Daniel Lesnic, “Steady-state inhomogeneous diffusion with generalized oblique boundary conditions”, ESAIM: M2AN, 57:5 (2023), 2701
Xian-Yu Liu, An-Bo Li, Hao Chen, Yan-Qing Men, Yong-Liang Huang, “3D Modeling Method for Dome Structure Using Digital Geological Map and DEM”, IJGI, 11:6 (2022), 339
Durand R., Farias M.M., Pedroso D.M., Meschke G., “Reinforcing Bars Modelling Using a Rod-Solid Interface Element Without the Need For Mesh Compatibility”, Finite Elem. Anal. Des., 197 (2021), 103634
Jürgen Fuhrmann, Hang Si, Mathematics in Industry, 35, German Success Stories in Industrial Mathematics, 2021, 149
Selmer I., Farrell P., Smirnova I., Gurikov P., “Comparison of Finite Difference and Finite Volume Simulations For a Sc-Drying Mass Transport Model”, Gels, 6:4 (2020), 45
Kantner M., “Generalized Scharfetter-Gummel Schemes For Electro-Thermal Transport in Degenerate Semiconductors Using the Kelvin Formula For the Seebeck Coefficient”, J. Comput. Phys., 402 (2020), 109091
Markus Kantner, Springer Theses, Electrically Driven Quantum Dot Based Single-Photon Sources, 2020, 47
Markus Kantner, Theresa Höhne, Thomas Koprucki, Sven Burger, Hans-Jürgen Wünsche, Frank Schmidt, Alexander Mielke, Uwe Bandelow, Springer Series in Solid-State Sciences, 194, Semiconductor Nanophotonics, 2020, 241
Fuhrmann J., Guhlke C., Linke A., Merdon C., Mueller R., “Induced Charge Electroosmotic Flow With Finite Ion Size and Solvation Effects”, Electrochim. Acta, 317 (2019), 778–785
K. Gärtner, L. Kamenski, “Why do we need Voronoi cells and Delaunay meshes? Essential properties of the Voronoi finite volume method”, Comput. Math. Math. Phys., 59:12 (2019), 1930–1944
Jürgen Fuhrmann, Clemens Guhlke, Alexander Linke, Christian Merdon, Rüdiger Müller, Lecture Notes in Computational Science and Engineering, 131, Numerical Geometry, Grid Generation and Scientific Computing, 2019, 73
Bradji A., Fuhrmann J., “Convergence Order of a Finite Volume Scheme For the Time-Fractional Diffusion Equation”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. Dimov I., Farago I., Vulkov L., Springer International Publishing Ag, 2017, 33–45
Fuhrmann J., Glitzky A., Liero M., “Hybrid Finite-Volume/Finite-Element Schemes For P(X)-Laplace Thermistor Models”, Finite Volumes For Complex Applications Viii-Hyperbolic, Elliptic and Parabolic Problems, Springer Proceedings in Mathematics & Statistics, 200, eds. Cances C., Omnes P., Springer, 2017, 397–405
Fuhrmann J., Guhlke C., “A Finite Volume Scheme For Nernst-Planck-Poisson Systems With Ion Size and Solvation Effects”, Finite Volumes For Complex Applications Viii-Hyperbolic, Elliptic and Parabolic Problems, Springer Proceedings in Mathematics & Statistics, 200, eds. Cances C., Omnes P., Springer, 2017, 497–505
Farrell P., Linke A., “Uniform Second Order Convergence of a Complete Flux Scheme on Unstructured 1D Grids For a Singularly Perturbed Advection-Diffusion Equation and Some Multidimensional Extensions”, J. Sci. Comput., 72:1 (2017), 373–395
Jürgen Fuhrmann, Annegret Glitzky, Matthias Liero, “Electrothermal Description of Organic Semiconductor Devices by p(x)‐Laplace Thermistor Models”, Proc Appl Math and Mech, 17:1 (2017), 701
Series in Optics and Optoelectronics, Handbook of Optoelectronic Device Modeling and Simulation, 2017, 733
Citation in format AMSBIB
Contact us: