## PolyMesher

 swMATH ID: 13340 Software Authors: Talischi, Cameron; Paulino, Glaucio H.; Pereira Anderson; Menezes, Ivan F.M. Description: 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. Homepage: http://rd.springer.com/article/10.1007%2Fs00158-011-0706-z Dependencies: Matlab Keywords: topology optimization; polygonal elements; centroidal Voronoi tessellations; implicit geometries; { t PolyMesher}; Matlab Related Software: PolyTop; Matlab; Triangle; DistMesh; iFEM; Gmsh; Veamy; MRST; top.m; FEAPpv; Eigen; FreeFem++; FEniCS; top88.m; Clipper; Feel++; Voro++; Delynoi; XFEM; METIS Referenced in: 163 Publications
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### Referenced by 260 Authors

 12 Beirão da Veiga, Lourenço 12 Paulino, Glaucio H. 11 Antonietti, Paola Francesca 9 Vacca, Giuseppe 7 Huang, Jianguo 7 Mora, David 7 Zhang, Bei 7 Zhao, Jikun 6 Manzini, Gianmarco 6 Nguyen-Xuan, Hung 6 Talischi, Cameron 6 Verani, Marco 5 Berrone, Stefano 5 Chi, Heng 5 Lovadina, Carlo 4 Borio, Andrea 4 Botti, Michele 4 Chen, Shaochun 4 Di Pietro, Daniele Antonio 4 Feng, Fang 4 Han, Weimin 4 He, Yinnian 4 Mei, Liquan 4 Mu, Lin 4 Russo, Alessandro 4 Sukumar, Natarajan 4 Velásquez, Iván G. 4 Zhang, Yongchao 3 Adak, Dibyendu 3 Dong, Zhaonan 3 Feng, Minfu 3 Gain, Arun L. 3 Guessab, Allal 3 Li, Ruo 3 Lin, Sen 3 Mascotto, Lorenzo 3 Menezes, Ivan F. M. 3 Natarajan, Sundararajan 3 Song, Chongmin 3 Vu-Huu, T. 3 Wahab, M. Abdel 3 Wang, Gang 3 Yang, Fanyi 2 Artioli, Edoardo 2 Benedetto, Matías Fernando 2 Benvenuti, Elena 2 Brezzi, Franco 2 Chen, Long 2 Chen, Zhangxin 2 Chiozzi, Andrea 2 Dassi, Franco 2 Ern, Alexandre 2 Facciolà, Chiara 2 Gatica, Gabriel N. 2 Georgoulis, Emmanuil H. 2 Hackemack, Michael W. 2 Hackl, Klaus 2 Houston, Paul 2 Kumar, Sarvesh 2 Le-Thanh, C. 2 Li, Yibao 2 Liu, Jiangguo 2 Lopez-Pamies, Oscar 2 Lopez, Luciano 2 Mao, Shipeng 2 Marini, Luisa Donatella 2 Mazzieri, Ilario 2 Natarajan, E. Palamadai 2 Nie, Yufeng 2 Ooi, Ean Tat 2 Pennesi, Giorgio 2 Pereira Anderson 2 Perugia, Ilaria 2 Pichler, Alexander 2 Qin, Qinghua 2 Sochala, Pierre 2 Sun, Zhiyuan 2 Tavener, Simon J. 2 Tin-Loi, Francis 2 Wang, Gang 2 Wang, Hui 2 Wang, Qiming 2 Wang, Xiaoshen 2 Zhang, Baiju 2 Zhou, Zhaojie 1 Abedi-Shahri, Seyed Sadjad 1 Aghili, Joubine 1 Alabdali, Osama 1 Asem, Rodrigo Véjar 1 Bachar, Mostafa 1 Bachini, Elena 1 Bao, Feng 1 Bécot, François-Xavier 1 Bellomo, Nicola 1 Bertoluzza, Silvia 1 Boffi, Daniele 1 Bonaldi, Francesco 1 Brenner, Susanne Cecelia 1 Bruggi, Matteo 1 Bui, Ha H. ...and 160 more Authors
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### Referenced in 40 Serials

 32 Computer Methods in Applied Mechanics and Engineering 14 Journal of Scientific Computing 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 10 Computers & Mathematics with Applications 9 SIAM Journal on Scientific Computing 8 Journal of Computational and Applied Mathematics 7 SIAM Journal on Numerical Analysis 6 Journal of Computational Physics 5 Applied Mathematics and Computation 5 Applied Numerical Mathematics 4 Calcolo 4 Numerical Algorithms 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 International Journal for Numerical Methods in Engineering 3 Computational Mechanics 3 Applied Mathematics Letters 3 Engineering Analysis with Boundary Elements 3 Structural and Multidisciplinary Optimization 2 Numerical Methods for Partial Differential Equations 2 Applied Mathematical Modelling 2 Communications in Nonlinear Science and Numerical Simulation 1 Applied Mathematics and Optimization 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Computer Aided Geometric Design 1 Communications in Partial Differential Equations 1 International Journal of Computer Mathematics 1 Filomat 1 Advances in Computational Mathematics 1 Mathematical Problems in Engineering 1 European Journal of Mechanics. A. Solids 1 European Journal of Mechanics. B. Fluids 1 Computational Geosciences 1 Computational Methods in Applied Mathematics 1 Communications in Computational Physics 1 Advances in Applied Mathematics and Mechanics 1 Research in the Mathematical Sciences 1 Mathematics in Engineering 1 Communications on Applied Mathematics and Computation 1 Electronic Research Archive
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### Referenced in 13 Fields

 148 Numerical analysis (65-XX) 56 Mechanics of deformable solids (74-XX) 54 Partial differential equations (35-XX) 46 Fluid mechanics (76-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 3 Optics, electromagnetic theory (78-XX) 2 Real functions (26-XX) 2 Approximations and expansions (41-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)