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 16 articles , 1 standard article )

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  1. Cáceres, Ernesto; Gatica, Gabriel N.; Sequeira, Filánder A.: A mixed virtual element method for the Brinkman problem (2017)
  2. Da Veiga, Lourenco Beirão; Lovadina, Carlo; Vacca, Giuseppe: Divergence free virtual elements for the Stokes problem on polygonal meshes (2017)
  3. Beirão da Veiga, L.; Brezzi, F.; Marini, L.D.; Russo, A.: $H(\mathrmdiv)$ and $H(\mathbfcurl)$-conforming virtual element methods (2016)
  4. Boffi, Daniele; Botti, Michele; Di Pietro, Daniele A.: A nonconforming high-order method for the Biot problem on general meshes (2016)
  5. Duczek, Sascha; Gabbert, Ulrich: The finite cell method for polygonal meshes: poly-FCM (2016)
  6. Lopez, Luciano; Vacca, Giuseppe: Spectral properties and conservation laws in mimetic finite difference methods for PDEs (2016)
  7. Talebi, Hossein; Saputra, Albert; Song, Chongmin: Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements (2016)
  8. Mora, David; Rivera, Gonzalo; Rodríguez, Rodolfo: A virtual element method for the Steklov eigenvalue problem (2015)
  9. Mu, Lin; Wang, Xiaoshen; Wang, Yanqiu: Shape regularity conditions for polygonal/polyhedral meshes, exemplified in a discontinuous Galerkin discretization (2015)
  10. Manzini, Gianmarco; Russo, Alessandro; Sukumar, N.: New perspectives on polygonal and polyhedral finite element methods (2014)
  11. Talischi, Cameron; Paulino, Glaucio H.: Addressing integration error for polygonal finite elements through polynomial projections: a patch test connection (2014)
  12. Sukumar, N.: Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013)
  13. Vatanabe, S.L.; Paulino, G.H.; Silva, E.C.N.: Design of functionally graded piezocomposites using topology optimization and homogenization -- toward effective energy harvesting materials (2013)
  14. Gain, Arun L.; Paulino, Glaucio H.: Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation (2012)
  15. Talischi, Cameron; Paulino, Glaucio H.; Pereira Anderson; Menezes, Ivan F.M.: PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012)
  16. Talischi, Cameron; Paulino, Glaucio H.; Pereira Anderson; Menezes, Ivan F.M.: PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes (2012)