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 76 articles , 1 standard article )

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  1. Guan, Qingguang: Weak Galerkin finite element method for Poisson’s equation on polytopal meshes with small edges or faces (2020)
  2. Li, Ruo; Yang, Fanyi: A sequential least squares method for Poisson equation using a patch reconstructed space (2020)
  3. Liu, Jiangguo; Harper, Graham; Malluwawadu, Nolisa; Tavener, Simon: A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes (2020)
  4. Zhang, Yongchao; Mei, Liquan: A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes (2020)
  5. Adak, D.; Natarajan, S.; Natarajan, E.: Virtual element method for semilinear elliptic problems on polygonal meshes (2019)
  6. Antonietti, Paola F.; Facciolà, Chiara; Russo, Alessandro; Verani, Marco: Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids (2019)
  7. Antonietti, P. F.; Pennesi, G.: (V)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes (2019)
  8. Bao, Feng; Mu, Lin; Wang, Jin: A fully computable a posteriori error estimate for the Stokes equations on polytopal meshes (2019)
  9. Chen, Long; Wang, Feng: A divergence free weak virtual element method for the Stokes problem on polytopal meshes (2019)
  10. Feng, Fang; Han, Weimin; Huang, Jianguo: Virtual element method for an elliptic hemivariational inequality with applications to contact mechanics (2019)
  11. Feng, Fang; Han, Weimin; Huang, Jianguo: Virtual element methods for elliptic variational inequalities of the second kind (2019)
  12. Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe: The nonconforming virtual element method for eigenvalue problems (2019)
  13. Guessab, Allal; Semisalov, Boris: Extended multidimensional integration formulas on polytope meshes (2019)
  14. Guo, Hailong; Xie, Cong; Zhao, Ren: Superconvergent gradient recovery for virtual element methods (2019)
  15. Irisarri, Diego; Hauke, Guillermo: Stabilized virtual element methods for the unsteady incompressible Navier-Stokes equations (2019)
  16. Li, Ruo; Sun, Zhiyuan; Yang, Fanyi: Solving eigenvalue problems in a discontinuous approximation space by patch Reconstruction (2019)
  17. Liu, Xin; Chen, Zhangxin: A virtual element method for the Cahn-Hilliard problem in mixed form (2019)
  18. Mascotto, Lorenzo; Perugia, Ilaria; Pichler, Alexander: A nonconforming Trefftz virtual element method for the Helmholtz problem (2019)
  19. Mu, Lin: A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes (2019)
  20. Ortiz-Bernardin, A.; Alvarez, C.; Hitschfeld-Kahler, N.; Russo, A.; Silva-Valenzuela, R.; Olate-Sanzana, E.: Veamy: an extensible object-oriented C++ library for the virtual element method (2019)

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