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 105 articles , 1 standard article )

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  1. Antonietti, Paola F.; Bonaldi, Francesco; Mazzieri, Ilario: A high-order discontinuous Galerkin approach to the elasto-acoustic problem (2020)
  2. Artioli, E.; Beirão da Veiga, L.; Dassi, F.: Curvilinear virtual elements for 2D solid mechanics applications (2020)
  3. Botti, Michele; Di Pietro, Daniele A.; Le Maître, Olivier; Sochala, Pierre: Numerical approximation of poroelasticity with random coefficients using polynomial chaos and hybrid high-order methods (2020)
  4. Guan, Qingguang: Weak Galerkin finite element method for Poisson’s equation on polytopal meshes with small edges or faces (2020)
  5. Huang, Jianguo; Lin, Sen: A (C^0 P_2) time-stepping virtual element method for linear wave equations on polygonal meshes (2020)
  6. Huynh, Hai D.; Zhuang, X.; Nguyen-Xuan, H.: A polytree-based adaptive scheme for modeling linear fracture mechanics using a coupled XFEM-SBFEM approach (2020)
  7. Li, Ruo; Yang, Fanyi: A sequential least squares method for Poisson equation using a patch reconstructed space (2020)
  8. Li, Ruo; Yang, Fanyi: A discontinuous Galerkin method by patch reconstruction for elliptic interface problem on unfitted mesh (2020)
  9. Liu, Jiangguo; Harper, Graham; Malluwawadu, Nolisa; Tavener, Simon: A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes (2020)
  10. Mathew, Tittu Varghese; Pramod, A. L. N.; Ooi, Ean Tat; Natarajan, Sundararajan: An efficient forward propagation of multiple random fields using a stochastic Galerkin scaled boundary finite element method (2020)
  11. Meng, Jian; Zhang, Yongchao; Mei, Liquan: A virtual element method for the Laplacian eigenvalue problem in mixed form (2020)
  12. Mora, David; Velásquez, Iván: Virtual element for the buckling problem of Kirchhoff-Love plates (2020)
  13. 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)
  14. Zhang, Bei; Zhao, Jikun; Chen, Shaochun: The nonconforming virtual element method for fourth-order singular perturbation problem (2020)
  15. Zhang, Yongchao; Mei, Liquan: A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes (2020)
  16. Zhang, Yongchao; Qian, Yanxia; Mei, Liquan: Discontinuous Galerkin methods for the Stokes equations with nonlinear damping term on general meshes (2020)
  17. Adak, D.; Natarajan, S.; Natarajan, E.: Virtual element method for semilinear elliptic problems on polygonal meshes (2019)
  18. Antonietti, Paola F.; Facciolà, Chiara; Russo, Alessandro; Verani, Marco: Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids (2019)
  19. Antonietti, P. F.; Pennesi, G.: (V)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes (2019)
  20. Bao, Feng; Mu, Lin; Wang, Jin: A fully computable a posteriori error estimate for the Stokes equations on polytopal meshes (2019)

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