## TetGen

 swMATH ID: 4046 Software Authors: Hang Si Description: TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator. TetGen is a C++ program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available. This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other softwares are presented. Homepage: http://wias-berlin.de/software/tetgen/?lang=1 Programming Languages: C++ Operating Systems: Unix/Linux, MacOS, Windows Keywords: tetrahedral mesh; quality mesh generation; boundary mesh generation; Delaunay tetrahedralization; constrained Delaunaytetrahedralization Related Software: Triangle; Gmsh; Netgen; CGAL; PETSc; Matlab; DistMesh; CGALmesh; ParaView; Qhull; FreeFem++; Voro++; Python; METIS; TMSmesh; deal.ii; GitHub; SimVascular; Trilinos; SIERRA Referenced in: 181 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
TetGen, a Delaunay-based quality tetrahedral mesh generator. Zbl 1369.65157
Si, Hang
2015
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### Referenced by 484 Authors

 6 Dassi, Franco 5 Lu, Benzhuo 5 Sequeira, Filánder A. 5 Si, Hang 4 Kamenski, Lennard 4 Linke, Alexander 3 Araya, Rodolfo A. 3 de Hoop, Maarten V. 3 Formaggia, Luca 3 Fuhrmann, Jürgen 3 Gatica, Gabriel N. 3 Levy, Bruno 3 Marsden, Alison L. 3 Rudolf, Florian 3 Rupp, Karl 3 Selberherr, Siegfried 3 Weinbub, Josef 2 Adams, Nikolaus A. 2 Beirão da Veiga, Lourenço 2 Burstedde, Carsten 2 Candiani, Valentina 2 Chen, Minxin 2 Cohen, Elaine 2 Edwards, Michael G. 2 Ehab Moustafa Kamel, Karim 2 Fu, Lin 2 Garanzha, Vladimir A. 2 Gärtner, Klaus 2 Gatica, Luis F. 2 Geuzaine, Christophe A. 2 Gu, David Xianfeng 2 Guo, Jianwei 2 Holke, Johannes 2 Hu, Xiangyu 2 Hyvönen, Nuutti 2 Jeon, Kiwan 2 Ji, Zhe 2 Knepley, Matthew G. 2 Kosturski, Nikola 2 Kraus, Johannes K. 2 Kudryavtseva, Lyudmila N. 2 Langmach, Hartmut 2 Lee, Chang-Ock 2 Lei, Na 2 Liu, Ju 2 Massart, Thierry Jacques 2 Morhammer, Andreas 2 Nakov, Svetoslav 2 Remacle, Jean-François 2 Repin, Sergeĭ Igorevich 2 Scott, Larkin Ridgway 2 Shi, Jia 2 Sohn, Dongwoo 2 Sonon, Bernard 2 Wall, Wolfgang A. 2 Yan, Dongming 2 Zhang, Linbo 2 Zhang, Qianru 2 Zhang, Yongjie Jessica 2 Zheng, Xiaopeng 2 Zonca, Stefano 1 Adams, Marvin L. 1 Adams, Michael P. 1 Aguayo, Jorge 1 Ahmed, Raheel 1 Al-Shaalan, Tareq M. 1 Alkämper, Martin 1 Allen, William J. 1 Alliez, Pierre 1 Aman, Aytek 1 Andrä, Heiko 1 Aragón, Alejandro M. 1 Ayhan, Ali O. 1 Badia, Santiago 1 Bajc, Iztok 1 Bänsch, Eberhard 1 Barter, Garrett E. 1 Basri, Ronen 1 Bastarrica, María Cecilia 1 Bauernöppel, Frank 1 Belokrys-Fedotov, Aleksei I. 1 Bennett, Janine C. 1 Beretta, Elena 1 Berge, Runar Lie 1 Berre, Inga 1 Berrone, Stefano 1 Bhattacharjee, Anirban 1 Biasotti, Silvia 1 Bihlo, Alex 1 Bilous, M. V. 1 Bin Zubair Syed, H. 1 Boffi, Daniele 1 Boissonnat, Jean-Daniel 1 Bombace, Nicola 1 Bonfiglioli, Aldo 1 Bosma, Sebastian B. M. 1 Brakhage, Karl-Heinz 1 Bravo-Castillero, Julián 1 Bremer, Peer-Timo 1 Brenner, Konstantin ...and 384 more Authors
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### Referenced in 54 Serials

 22 Journal of Computational Physics 17 SIAM Journal on Scientific Computing 16 Computer Methods in Applied Mechanics and Engineering 10 Computers & Mathematics with Applications 9 Computer Aided Geometric Design 6 Journal of Scientific Computing 6 Computational Geosciences 5 International Journal for Numerical Methods in Engineering 5 Journal of Computational and Applied Mathematics 5 Applied Numerical Mathematics 5 Computational Mechanics 4 Computer Physics Communications 3 Mathematics and Computers in Simulation 3 Computational Mathematics and Mathematical Physics 3 European Journal of Mechanics. A. Solids 3 Computational Methods in Applied Mathematics 2 Computers and Fluids 2 ACM Transactions on Mathematical Software 2 ACM Transactions on Graphics 2 Computational Geometry 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Journal of Mathematical Imaging and Vision 2 Advances in Computational Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Inverse Problems 1 Journal of Fluid Mechanics 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 BIT 1 SIAM Journal on Numerical Analysis 1 Moscow University Computational Mathematics and Cybernetics 1 Computers & Operations Research 1 Mathematical and Computer Modelling 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Advances in Engineering Software 1 Cybernetics and Systems Analysis 1 Mathematica Montisnigri 1 Numerical Linear Algebra with Applications 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Computing and Visualization in Science 1 Matematicheskoe Modelirovanie 1 Archives of Computational Methods in Engineering 1 International Journal of Computational Methods 1 Inverse Problems in Science and Engineering 1 SIAM Journal on Imaging Sciences 1 Mathematical Geosciences 1 International Journal for Numerical Methods in Biomedical Engineering 1 GEM - International Journal on Geomathematics 1 Journal of Mathematics in Industry 1 Molecular Based Mathematical Biology
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### Referenced in 26 Fields

 140 Numerical analysis (65-XX) 36 Mechanics of deformable solids (74-XX) 36 Fluid mechanics (76-XX) 25 Partial differential equations (35-XX) 20 Computer science (68-XX) 15 Biology and other natural sciences (92-XX) 10 Optics, electromagnetic theory (78-XX) 10 Geophysics (86-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Statistical mechanics, structure of matter (82-XX) 4 Operations research, mathematical programming (90-XX) 3 Information and communication theory, circuits (94-XX) 2 Functions of a complex variable (30-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Probability theory and stochastic processes (60-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)