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 154 articles , 1 standard article )

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  1. Antonietti, Paola F.; Botti, Michele; Mazzieri, Ilario; Poltri, Simone Nati: A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids (2022)
  2. Antonietti, Paola F.; Mascotto, Lorenzo; Verani, Marco; Zonca, Stefano: Stability analysis of polytopic discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems (2022)
  3. Benvenuti, E.; Chiozzi, A.; Manzini, G.; Sukumar, N.: Extended virtual element method for two-dimensional linear elastic fracture (2022)
  4. Berrone, Stefano; Busetto, Martina: A virtual element method for the two-phase flow of immiscible fluids in porous media (2022)
  5. Feng, Fang; Han, Weimin; Huang, Jianguo: A nonconforming virtual element method for a fourth-order hemivariational inequality in Kirchhoff plate problem (2022)
  6. Gortsas, Theodore V.; Tsinopoulos, Stephanos V.; Polyzos, Demosthenes: A local domain boundary element method for solving the nonlinear Fisher KPP diffusion-reaction equation (2022)
  7. 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)
  8. Tushar, Jai; Kumar, Anil; Kumar, Sarvesh: Variational and virtual discretizations of optimal control problems governed by diffusion problems (2022)
  9. Yue Yu: mVEM: A MATLAB Software Package for the Virtual Element Methods (2022) arXiv
  10. Zhao, Lina; Kim, Dohyun; Park, Eun-Jae; Chung, Eric: Staggered DG method with small edges for Darcy flows in fractured porous media (2022)
  11. Bachini, Elena; Manzini, Gianmarco; Putti, Mario: Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces (2021)
  12. 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)
  13. Brenner, Susanne C.; Sung, Li-Yeng; Tan, Zhiyu: A (C^1) virtual element method for an elliptic distributed optimal control problem with pointwise state constraints (2021)
  14. Coelho, Karolinne O.; Devloo, Philippe R. B.; Gomes, Sônia M.: Error estimates for the scaled boundary finite element method (2021)
  15. Dassi, Franco; Lovadina, Carlo; Visinoni, Michele: Hybridization of the virtual element method for linear elasticity problems (2021)
  16. Dong, Zhaonan; Ern, Alexandre: Hybrid high-order method for singularly perturbed fourth-order problems on curved domains (2021)
  17. Feng, Fang; Han, Weimin; Huang, Jianguo: The virtual element method for an obstacle problem of a Kirchhoff-love plate (2021)
  18. Hackemack, Michael W.: Discontinuous Galerkin solutions for elliptic problems on polygonal grids using arbitrary-order Bernstein-Bézier functions (2021)
  19. Huang, Jianguo; Lin, Sen: A posteriori error analysis of a non-consistent virtual element method for reaction diffusion equations (2021)
  20. Lian, Yanjian; Bui, Ha H.; Nguyen, Giang D.; Tran, Hieu T.; Haque, Asadul: A general SPH framework for transient seepage flows through unsaturated porous media considering anisotropic diffusion (2021)

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