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. Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio: Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods (2018)
  2. Benedetto, Matías Fernando; Caggiano, Antonio; Etse, Guillermo: Virtual elements and zero thickness interface-based approach for fracture analysis of heterogeneous materials (2018)
  3. Cao, Shuhao; Chen, Long: Anisotropic error estimates of the linear virtual element method on polygonal meshes (2018)
  4. Chau, Khai N.; Chau, Khanh N.; Ngo, Tuan; Hackl, Klaus; Nguyen-Xuan, H.: A polytree-based adaptive polygonal finite element method for multi-material topology optimization (2018)
  5. da Veiga, L. Beirão; Lovadina, C.; Vacca, G.: Virtual elements for the Navier-Stokes problem on polygonal meshes (2018)
  6. Hackemack, Michael W.; Ragusa, Jean C.: Quadratic serendipity discontinuous finite element discretization for (S_N) transport on arbitrary polygonal grids (2018)
  7. Li, Rui; Gao, Yali; Li, Jian; Chen, Zhangxin: A weak Galerkin finite element method for a coupled Stokes-Darcy problem on general meshes (2018)
  8. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: Lowest-order weak Galerkin finite element method for Darcy flow on convex polygonal meshes (2018)
  9. Mora, David; Velásquez, Iván: A virtual element method for the transmission eigenvalue problem (2018)
  10. Perumal, Logah: A brief review on polygonal/polyhedral finite element methods (2018)
  11. Vacca, Giuseppe: An (H^1)-conforming virtual element for Darcy and Brinkman equations (2018)
  12. Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime; Demkowicz, Leszek: High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations (2018)
  13. Vu-Huu, T.; Phung-Van, P.; Nguyen-Xuan, H.; Abdel Wahab, M.: A polytree-based adaptive polygonal finite element method for topology optimization of fluid-submerged breakwater interaction (2018)
  14. Wang, Gang; He, Yinnian; Yang, Jinjin: Weak Galerkin finite element methods for the simulation of single-phase flow in fractured porous media (2018)
  15. Zhang, Baiju; Feng, Minfu: Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation (2018)
  16. Aghili, Joubine; Di Pietro, Daniele A.; Ruffini, Berardo: An (hp)-hybrid high-order method for variable diffusion on general meshes (2017)
  17. Alejandro Ortiz-Bernardin, Catalina Alvarez, Nancy Hitschfeld-Kahler, Alessandro Russo, Rodrigo Silva-Valenzuela, Edgardo Olate-Sanzana: Veamy: an extensible object-oriented C++ library for the virtual element method (2017) arXiv
  18. Antonietti, Paola F.; Bruggi, Matteo; Scacchi, Simone; Verani, Marco: On the virtual element method for topology optimization on polygonal meshes: a numerical study (2017)
  19. 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)
  20. Artioli, E.; Beirão da Veiga, Lourenço; Lovadina, Carlo; Sacco, E.: Arbitrary order 2D virtual elements for polygonal meshes. II: Inelastic problem (2017)