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 121 articles , 1 standard article )

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  1. Duczek, Sascha; Gabbert, Ulrich: The finite cell method for polygonal meshes: poly-FCM (2016)
  2. Lai, Ming-Jun; Slavov, George: On recursive refinement of convex polygons (2016)
  3. Lopez, Luciano; Vacca, Giuseppe: Spectral properties and conservation laws in mimetic finite difference methods for PDEs (2016)
  4. Talebi, Hossein; Saputra, Albert; Song, Chongmin: Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements (2016)
  5. Beirão da Veiga, L.; Lovadina, C.; Mora, D.: A virtual element method for elastic and inelastic problems on polytope meshes (2015)
  6. Chi, Heng; Talischi, Cameron; Lopez-Pamies, Oscar; H. Paulino, Glaucio: Polygonal finite elements for finite elasticity (2015)
  7. Gain, Arun L.; Paulino, Glaucio H.; Duarte, Leonardo S.; Menezes, Ivan F. M.: Topology optimization using polytopes (2015)
  8. Giani, Stefano: Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods (2015)
  9. Mora, David; Rivera, Gonzalo; Rodríguez, Rodolfo: A virtual element method for the Steklov eigenvalue problem (2015)
  10. Mu, Lin; Wang, Xiaoshen; Wang, Yanqiu: Shape regularity conditions for polygonal/polyhedral meshes, exemplified in a discontinuous Galerkin discretization (2015)
  11. Vacca, Giuseppe; Beirão da Veiga, Lourenco: Virtual element methods for parabolic problems on polygonal meshes (2015)
  12. Chiong, Irene; Ooi, Ean Tat; Song, Chongmin; Tin-Loi, Francis: Scaled boundary polygons with application to fracture analysis of functionally graded materials (2014)
  13. Gain, Arun L.; Talischi, Cameron; Paulino, Glaucio H.: On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes (2014)
  14. Leon, S. E.; Spring, D. W.; Paulino, G. H.: Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements (2014)
  15. Manzini, Gianmarco; Russo, Alessandro; Sukumar, N.: New perspectives on polygonal and polyhedral finite element methods (2014)
  16. Talischi, Cameron; Paulino, Glaucio H.: Addressing integration error for polygonal finite elements through polynomial projections: a patch test connection (2014)
  17. Sukumar, N.: Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013)
  18. Vatanabe, S. L.; Paulino, G. H.; Silva, E. C. N.: Design of functionally graded piezocomposites using topology optimization and homogenization -- toward effective energy harvesting materials (2013)
  19. Gain, Arun L.; Paulino, Glaucio H.: Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation (2012)
  20. Talischi, Cameron; Paulino, Glaucio H.; Pereira Anderson; Menezes, Ivan F. M.: \textttPolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes (2012)