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 119 articles , 1 standard article )

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  1. Mora, David; Velásquez, Iván: Virtual element for the buckling problem of Kirchhoff-Love plates (2020)
  2. Vu-Huu, T.; Le-Thanh, C.; Nguyen-Xuan, H.; Abdel-Wahab, M.: An equal-order mixed polygonal finite element for two-dimensional incompressible Stokes flows (2020)
  3. Wang, Gang; Wang, Ying; He, Yinnian: A posteriori error estimates for the virtual element method for the Stokes problem (2020)
  4. Wang, Ying; Wang, Gang: A least-squares virtual element method for second-order elliptic problems (2020)
  5. Zhang, Bei; Zhao, Jikun; Chen, Shaochun: The nonconforming virtual element method for fourth-order singular perturbation problem (2020)
  6. Zhang, Yongchao; Mei, Liquan: A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes (2020)
  7. Zhang, Yongchao; Mei, Liquan; Li, Rui: A hybrid high-order method for a coupled Stokes-Darcy problem on general meshes (2020)
  8. Zhang, Yongchao; Qian, Yanxia; Mei, Liquan: Discontinuous Galerkin methods for the Stokes equations with nonlinear damping term on general meshes (2020)
  9. Zhao, Jikun; Zhang, Bei; Mao, Shipeng; Chen, Shaochun: The nonconforming virtual element method for the Darcy-Stokes problem (2020)
  10. Adak, D.; Natarajan, S.; Natarajan, E.: Virtual element method for semilinear elliptic problems on polygonal meshes (2019)
  11. Antonietti, Paola F.; Facciolà, Chiara; Russo, Alessandro; Verani, Marco: Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids (2019)
  12. Antonietti, P. F.; Pennesi, G.: (V)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes (2019)
  13. Bao, Feng; Mu, Lin; Wang, Jin: A fully computable a posteriori error estimate for the Stokes equations on polytopal meshes (2019)
  14. Beirão da Veiga, L.; Mora, D.; Vacca, G.: The Stokes complex for virtual elements with application to Navier-Stokes flows (2019)
  15. Benvenuti, E.; Chiozzi, A.; Manzini, G.; Sukumar, N.: Extended virtual element method for the Laplace problem with singularities and discontinuities (2019)
  16. Chen, Long; Wang, Feng: A divergence free weak virtual element method for the Stokes problem on polytopal meshes (2019)
  17. Chi, Heng; Beirão da Veiga, Lourenço; Paulino, Glaucio H.: A simple and effective gradient recovery scheme and \textitaposteriori error estimator for the virtual element method (VEM) (2019)
  18. Feng, Fang; Han, Weimin; Huang, Jianguo: Virtual element methods for elliptic variational inequalities of the second kind (2019)
  19. Feng, Fang; Han, Weimin; Huang, Jianguo: Virtual element method for an elliptic hemivariational inequality with applications to contact mechanics (2019)
  20. Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe: The nonconforming virtual element method for eigenvalue problems (2019)