PolyMesher

PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab. We present a simple and robust Matlab code for polygonal mesh generation that relies on an implicit description of the domain geometry. The mesh generator can provide, among other things, the input needed for finite element and optimization codes that use linear convex polygons. In topology optimization, polygonal discretizations have been shown not to be susceptible to numerical instabilities such as checkerboard patterns in contrast to lower order triangular and quadrilaterial meshes. Also, the use of polygonal elements makes possible meshing of complicated geometries with a self-contained Matlab code. The main ingredients of the present mesh generator are the implicit description of the domain and the centroidal Voronoi diagrams used for its discretization. The signed distance function provides all the essential information about the domain geometry and offers great flexibility to construct a large class of domains via algebraic expressions. Examples are provided to illustrate the capabilities of the code, which is compact and has fewer than 135 lines.


References in zbMATH (referenced in 121 articles , 1 standard article )

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  1. Antonietti, Paola F.; Houston, Paul; Hu, Xiaozhe; Sarti, Marco; Verani, Marco: Multigrid algorithms for (hp)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes (2017)
  2. Artioli, E.; Beirão da Veiga, Lourenço; Lovadina, Carlo; Sacco, E.: Arbitrary order 2D virtual elements for polygonal meshes. II: Inelastic problem (2017)
  3. Bachar, Mostafa; Guessab, Allal; Mohammed, Osama; Zaim, Yassine: New cubature formulas and Hermite-Hadamard type inequalities using integrals over some hyperplanes in the (d)-dimensional hyper-rectangle (2017)
  4. Beirão da Veiga, Lourenco; Lopez, Luciano; Vacca, Giuseppe: Mimetic finite difference methods for Hamiltonian wave equations in 2D (2017)
  5. Beirão da Veiga, Lourenço; Lovadina, Carlo; Vacca, Giuseppe: Divergence free virtual elements for the Stokes problem on polygonal meshes (2017)
  6. Berrone, Stefano; Borio, Andrea: A residual a posteriori error estimate for the virtual element method (2017)
  7. Botti, Michele; Di Pietro, Daniele A.; Sochala, Pierre: A hybrid high-order method for nonlinear elasticity (2017)
  8. Cáceres, Ernesto; Gatica, Gabriel N.; Sequeira, Filánder A.: A mixed virtual element method for the Brinkman problem (2017)
  9. Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.: (hp)-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes (2017)
  10. Chi, H.; da Veiga, L. Beirão; Paulino, G. H.: Some basic formulations of the virtual element method (VEM) for finite deformations (2017)
  11. Li, Yibao; Kim, Junseok; Wang, Nan: An unconditionally energy-stable second-order time-accurate scheme for the Cahn-Hilliard equation on surfaces (2017)
  12. Nguyen-Xuan, H.; Nguyen-Hoang, Son; Rabczuk, T.; Hackl, K.: A polytree-based adaptive approach to limit analysis of cracked structures (2017)
  13. Sutton, Oliver J.: The virtual element method in 50 lines of MATLAB (2017)
  14. Vacca, Giuseppe: Virtual element methods for hyperbolic problems on polygonal meshes (2017)
  15. Beirão da Veiga, L.; Brezzi, F.; Marini, L. D.; Russo, A.: (H(\mathrmdiv)) and (H(\mathbfcurl))-conforming virtual element methods (2016)
  16. Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro: Virtual element implementation for general elliptic equations (2016)
  17. Bellomo, N.; Berrone, S.; Gibelli, L.; Pieri, A. B.: Macroscopic first order models of multicomponent human crowds with behavioral dynamics (2016)
  18. Benedetto, M. F.; Berrone, S.; Borio, A.; Pieraccini, S.; Scialò, S.: Order preserving SUPG stabilization for the virtual element formulation of advection-diffusion problems (2016)
  19. Boffi, Daniele; Botti, Michele; Di Pietro, Daniele A.: A nonconforming high-order method for the Biot problem on general meshes (2016)
  20. Chi, Heng; Talischi, Cameron; Lopez-Pamies, Oscar; Paulino, Glaucio H.: A paradigm for higher-order polygonal elements in finite elasticity using a gradient correction scheme (2016)