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 134 articles , 1 standard article )

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  1. Li, Yibao; Liu, Rui; Xia, Qing; He, Chenxi; Li, Zhong: First- and second-order unconditionally stable direct discretization methods for multi-component Cahn-Hilliard system on surfaces (2022)
  2. Bachini, Elena; Manzini, Gianmarco; Putti, Mario: Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces (2021)
  3. Borio, Andrea; Hamon, François P.; Castelletto, Nicola; White, Joshua A.; Settgast, Randolph R.: Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics (2021)
  4. Coelho, Karolinne O.; Devloo, Philippe R. B.; Gomes, Sônia M.: Error estimates for the scaled boundary finite element method (2021)
  5. Huang, Jianguo; Lin, Sen: A posteriori error analysis of a non-consistent virtual element method for reaction diffusion equations (2021)
  6. Liu, Xin; Nie, Yufeng: A modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equations (2021)
  7. Mora, David; Velásquez, Iván: Virtual elements for the transmission eigenvalue problem on polytopal meshes (2021)
  8. Mora, David; Velásquez, Iván: A (C^1-C^0) conforming virtual element discretization for the transmission eigenvalue problem (2021)
  9. Osezua Ibhadode, Zhidong Zhang, Ali Bonakdar, Ehsan Toyserkani: IbIPP for topology optimization - An Image-based Initialization and Post-Processing code written in MATLAB (2021) not zbMATH
  10. Sreekumar, Abhilash; Triantafyllou, Savvas P.; Bécot, François-Xavier; Chevillotte, Fabien: Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains (2021)
  11. Wang, Gang; Wang, Ying; He, Yinnian: A weak Galerkin finite element method based on (\boldsymbolH(\operatornamediv)) virtual element for Darcy flow on polytopal meshes (2021)
  12. Wang, Qiming; Zhou, Zhaojie: Adaptive virtual element method for optimal control problem governed by general elliptic equation (2021)
  13. Wang, Ying; Wang, Gang; Wang, Feng: An adaptive virtual element method for incompressible flow (2021)
  14. Yang, Di; He, Yinnian: A discontinuous Galerkin method by patch reconstruction for convection-diffusion-reaction problems over polytopic meshes (2021)
  15. Zhang, Xiaojia Shelly; Chi, Heng; Zhao, Zhi: Topology optimization of hyperelastic structures with anisotropic fiber reinforcement under large deformations (2021)
  16. Zhao, Jikun; Zhang, Bei: The curl-curl conforming virtual element method for the quad-curl problem (2021)
  17. Adak, D.; Natarajan, S.: Virtual element method for semilinear sine-Gordon equation over polygonal mesh using product approximation technique (2020)
  18. Antonietti, Paola F.; Bonaldi, Francesco; Mazzieri, Ilario: A high-order discontinuous Galerkin approach to the elasto-acoustic problem (2020)
  19. Antonietti, Paola Francesca; Bertoluzza, Silvia; Prada, Daniele; Verani, Marco: The virtual element method for a minimal surface problem (2020)
  20. Artioli, E.; Beirão da Veiga, L.; Dassi, F.: Curvilinear virtual elements for 2D solid mechanics applications (2020)

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