## DistMesh

 swMATH ID: 12766 Software Authors: P.-O. Persson; G. Strang Description: A Simple Mesh Generator in MATLAB. Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple MATLAB code, described in more detail than usual, so the reader can experiment (and add to the code) knowing the underlying principles. We find the node locations by solving for equilibrium in a truss structure (using piecewise linear force-displacement relations) and reset the topology by the Delaunay algorithm. The geometry is described implicitly by its distance function. In addition to being much shorter and simpler than other meshing techniques, our algorithm typically produces meshes of very high quality. We discuss ways to improve the robustness and the performance, but our aim here is simplicity. Readers can download (and edit) the codes from http://math.mit.edu/ persson/mesh. Homepage: http://persson.berkeley.edu/distmesh/ Dependencies: Matlab Related Software: Matlab; Triangle; rbf_qr; Gmsh; iFEM; TetGen; top.m; FreeFem++; COMSOL; PolyMesher; Netgen; GitHub; Qhull; na14; LAPACK; Mesquite; CGAL; IIMPACK; MRST; FEAPpv Cited in: 316 Publications
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### Cited by 670 Authors

 7 Persson, Per-Olof 6 Liu, Jie 6 Shankar, Varun 5 Dapogny, Charles 5 Dehghan Takht Fooladi, Mehdi 5 Fornberg, Bengt 5 Garanzha, Vladimir A. 5 Kim, Junseok 5 Kudryavtseva, Lyudmila N. 5 Li, Yibao 4 Allaire, Grégoire 4 Chappell, David J. 4 Chen, Long 4 Flyer, Natasha 4 Ju, Lili 4 Liu, Chun 4 Menezes, Ivan F. M. 4 Mohammadi, Vahid 4 Paulino, Glaucio H. 4 Wright, Grady B. 3 Calvetti, Daniela 3 Crofts, Jonathan J. 3 Groenwold, Albert A. 3 Gunzburger, Max D. 3 Kok, Schalk 3 Kovács, Balázs 3 Larsson, Elisabeth 3 Lehto, Erik 3 Li, Buyang 3 Ling, Leevan 3 Massart, Thierry Jacques 3 Somersalo, Erkki 3 Sonon, Bernard 3 Talischi, Cameron 3 Wilke, Daniel Nicolas 3 Wu, Qingbiao 3 Yamasaki, Shintaro 3 Zhang, Zhimin 3 Zhu, Shengfeng 2 Albuquerque, Duarte M. S. 2 Atzberger, Paul J. 2 Baginski, Frank E. 2 Bakushinskĭ, Anatoliĭ Borisovich B. 2 Balachandar, S. Raja 2 Belokrys-Fedotov, Aleksei I. 2 Bendito, Enrique 2 Bogoşel, Beniamin 2 Cai, Zhiqiang 2 Carmona, Ángeles 2 Chen, Minxin 2 Choi, Gary Pui-Tung 2 Chuzhanova, N. 2 Copos, Calina A. 2 de Hoop, Maarten V. 2 Diele, Fasma 2 Duan, Beiping 2 Ehab Moustafa Kamel, Karim 2 Encinas, Andrés M. 2 Feppon, Florian 2 Fernandes Pereira, José Carlos 2 Frey, Pascal Jean 2 Fuselier, Edward J. 2 Galagusz, Ryan 2 Gesto, J. M. 2 Ghosh, Sudeshna 2 Govindjee, Sanjay 2 Gross, B. J. 2 Guy, Robert D. 2 Heryudono, Alfa R. H. 2 Hysing, Shuren 2 Jeong, Darae 2 Jolivet, Pierre 2 Kawamoto, Atsushi 2 Khoo, Boo Cheong 2 Kirby, Robert M. II 2 Ku, Jaeun 2 Kuberry, Paul Allen 2 Kuchment, Peter A. 2 Li, Jingzhi 2 Li, Peijun 2 Liu, Chunxiao 2 Lubich, Christian 2 Majd, Sheereen 2 Marangi, Carmela 2 Nakkireddy, S. 2 Nie, Yufeng 2 Nikolopoulos, Christos V. 2 Nomura, Tsuyoshi 2 Peraire, Jaime 2 Pereira Anderson 2 Ragni, Stefania 2 Rapún, María-Luisa 2 Reeger, Jonah A. 2 Saye, Robert I. 2 Shin, Jaemin 2 Shirokoff, David 2 Shuker Mahmood, Mohammed 2 Smirnova, Alexandra B. 2 Song, Lunji 2 Strang, William Gilbert ...and 570 more Authors
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### Cited in 82 Serials

 50 Journal of Computational Physics 31 Computer Methods in Applied Mechanics and Engineering 18 SIAM Journal on Scientific Computing 13 International Journal for Numerical Methods in Engineering 12 Journal of Scientific Computing 11 Computers & Mathematics with Applications 10 Journal of Computational and Applied Mathematics 9 Computers and Fluids 9 Applied Mathematics and Computation 7 Inverse Problems 6 Mathematics and Computers in Simulation 6 Engineering Analysis with Boundary Elements 6 Structural and Multidisciplinary Optimization 5 Journal of Fluid Mechanics 5 Numerische Mathematik 5 SIAM Journal on Numerical Analysis 5 Computational Mechanics 4 Applied Numerical Mathematics 4 SIAM Journal on Applied Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Computational Geosciences 4 SIAM Journal on Imaging Sciences 3 Computational Mathematics and Mathematical Physics 3 Applied Mathematical Modelling 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Quarterly of Applied Mathematics 2 Numerical Methods for Partial Differential Equations 2 SIAM Journal on Matrix Analysis and Applications 2 SIAM Journal on Mathematical Analysis 2 Discrete and Continuous Dynamical Systems. Series B 2 International Journal of Numerical Analysis and Modeling 2 Inverse Problems in Science and Engineering 2 Journal of Physics A: Mathematical and Theoretical 2 Communications in Computational Physics 2 Inverse Problems and Imaging 2 SMAI Journal of Computational Mathematics 1 Classical and Quantum Gravity 1 IMA Journal of Numerical Analysis 1 International Journal for Numerical Methods in Fluids 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 BIT 1 Computing 1 Applied Mathematics Letters 1 European Journal of Applied Mathematics 1 Computational Geometry 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Review 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Experimental Mathematics 1 Electronic Journal of Differential Equations (EJDE) 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 ETNA. Electronic Transactions on Numerical Analysis 1 Statistica Sinica 1 Journal of Computational Neuroscience 1 International Journal of Computational Fluid Dynamics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Journal of Mechanics. A. Solids 1 The ANZIAM Journal 1 Archives of Computational Methods in Engineering 1 Foundations of Computational Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 International Journal of Computational Methods 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Communications in Applied Mathematics and Computational Science 1 Numerical Mathematics: Theory, Methods and Applications 1 Advances in Applied Mathematics and Mechanics 1 Science China. Mathematics 1 Science China. Technological Sciences 1 Inverse and Ill-Posed Problems Series 1 ISRN Applied Mathematics 1 Journal of Theoretical Biology 1 Molecular Based Mathematical Biology 1 Annals of Applied Mathematics 1 Lecture Notes in Electrical Engineering 1 Computational and Mathematical Biophysics 1 International Journal on Finite Volumes
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### Cited in 34 Fields

 213 Numerical analysis (65-XX) 90 Partial differential equations (35-XX) 79 Fluid mechanics (76-XX) 71 Mechanics of deformable solids (74-XX) 38 Biology and other natural sciences (92-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 17 Optics, electromagnetic theory (78-XX) 10 Computer science (68-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Operations research, mathematical programming (90-XX) 7 Approximations and expansions (41-XX) 7 Statistics (62-XX) 6 Differential geometry (53-XX) 6 Geophysics (86-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Operator theory (47-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Convex and discrete geometry (52-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of particles and systems (70-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)