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 119 articles , 1 standard article )

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  1. Gatica, Gabriel N.; Meddahi, Salim: On the coupling of VEM and BEM in two and three dimensions (2019)
  2. Guessab, Allal; Semisalov, Boris: Extended multidimensional integration formulas on polytope meshes (2019)
  3. Guo, Hailong; Xie, Cong; Zhao, Ren: Superconvergent gradient recovery for virtual element methods (2019)
  4. Ho-Nguyen-Tan, Thuan; Kim, Hyun-Gyu: Polygonal shell elements with assumed transverse shear and membrane strains (2019)
  5. Irisarri, Diego; Hauke, Guillermo: Stabilized virtual element methods for the unsteady incompressible Navier-Stokes equations (2019)
  6. Klinkel, S.; Reichel, R.: A finite element formulation in boundary representation for the analysis of nonlinear problems in solid mechanics (2019)
  7. Li, Ruo; Sun, Zhiyuan; Yang, Fanyi: Solving eigenvalue problems in a discontinuous approximation space by patch reconstruction (2019)
  8. Liu, Xin; Chen, Zhangxin: A virtual element method for the Cahn-Hilliard problem in mixed form (2019)
  9. Mascotto, Lorenzo; Perugia, Ilaria; Pichler, Alexander: A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects (2019)
  10. Mascotto, Lorenzo; Perugia, Ilaria; Pichler, Alexander: A nonconforming Trefftz virtual element method for the Helmholtz problem (2019)
  11. Mu, Lin: A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes (2019)
  12. Ortiz-Bernardin, A.; Alvarez, C.; Hitschfeld-Kahler, N.; Russo, A.; Silva-Valenzuela, R.; Olate-Sanzana, E.: Veamy: an extensible object-oriented C++ library for the virtual element method (2019)
  13. Vu-Huu, T.; Le-Thanh, C.; Nguyen-Xuan, H.; Abdel-Wahab, M.: A high-order mixed polygonal finite element for incompressible Stokes flow analysis (2019)
  14. Wang, Hui; Qin, Qing-Hua: Voronoi polygonal hybrid finite elements and their applications (2019)
  15. Wang, Hui; Qin, Qing-Hua; Lee, Cheuk-Yu: (n)-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization (2019)
  16. Xie, Shenglan; Zhu, Peng; Wang, Xiaoshen: Error analysis of weak Galerkin finite element methods for time-dependent convection-diffusion equations (2019)
  17. Zhang, Baiju; Yang, Yan; Feng, Minfu: Mixed virtual element methods for elastodynamics with weak symmetry (2019)
  18. Zhang, Bei; Zhao, Jikun; Yang, Yongqin; Chen, Shaochun: The nonconforming virtual element method for elasticity problems (2019)
  19. Zhao, Jikun; Zhang, Bei; Mao, Shipeng; Chen, Shaochun: The divergence-free nonconforming virtual element for the Stokes problem (2019)
  20. Zhao, Jikun; Zhang, Bei; Zhu, Xiaopeng: The nonconforming virtual element method for parabolic problems (2019)