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 28 articles , 1 standard article )

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  1. Li, Rui; Gao, Yali; Li, Jian; Chen, Zhangxin: A weak Galerkin finite element method for a coupled Stokes-Darcy problem on general meshes (2018)
  2. Aghili, Joubine; Di Pietro, Daniele A.; Ruffini, Berardo: An $hp$-hybrid high-order method for variable diffusion on general meshes (2017)
  3. Berrone, Stefano; Borio, Andrea: A residual a posteriori error estimate for the virtual element method (2017)
  4. Botti, Michele; Di Pietro, Daniele A.; Sochala, Pierre: A hybrid high-order method for nonlinear elasticity (2017)
  5. Cáceres, Ernesto; Gatica, Gabriel N.; Sequeira, Filánder A.: A mixed virtual element method for the Brinkman problem (2017)
  6. Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.: $hp$-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes (2017)
  7. Da Veiga, Lourenco Beirão; Lovadina, Carlo; Vacca, Giuseppe: Divergence free virtual elements for the Stokes problem on polygonal meshes (2017)
  8. Sutton, Oliver J.: The virtual element method in 50 lines of MATLAB (2017)
  9. Beirão da Veiga, L.; Brezzi, F.; Marini, L.D.; Russo, A.: $H(\mathrmdiv)$ and $H(\mathbfcurl)$-conforming virtual element methods (2016)
  10. Beirão da Veiga, Lourenco; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro: Virtual element implementation for general elliptic equations (2016)
  11. Bellomo, N.; Berrone, S.; Gibelli, L.; Pieri, A.B.: Macroscopic first order models of multicomponent human crowds with behavioral dynamics (2016)
  12. Boffi, Daniele; Botti, Michele; Di Pietro, Daniele A.: A nonconforming high-order method for the Biot problem on general meshes (2016)
  13. Duczek, Sascha; Gabbert, Ulrich: The finite cell method for polygonal meshes: poly-FCM (2016)
  14. Lopez, Luciano; Vacca, Giuseppe: Spectral properties and conservation laws in mimetic finite difference methods for PDEs (2016)
  15. Talebi, Hossein; Saputra, Albert; Song, Chongmin: Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements (2016)
  16. Chi, Heng; Talischi, Cameron; Lopez-Pamies, Oscar; H.Paulino, Glaucio: Polygonal finite elements for finite elasticity (2015)
  17. Mora, David; Rivera, Gonzalo; Rodríguez, Rodolfo: A virtual element method for the Steklov eigenvalue problem (2015)
  18. Mu, Lin; Wang, Xiaoshen; Wang, Yanqiu: Shape regularity conditions for polygonal/polyhedral meshes, exemplified in a discontinuous Galerkin discretization (2015)
  19. Vacca, Giuseppe; Beirão da Veiga, Lourenco: Virtual element methods for parabolic problems on polygonal meshes (2015)
  20. Chiong, Irene; Ooi, Ean Tat; Song, Chongmin; Tin-Loi, Francis: Scaled boundary polygons with application to fracture analysis of functionally graded materials (2014)

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