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.

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  1. Antonietti, P. F.; Pennesi, G.: (V)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes (2019)
  2. Borsche, R.; Meurer, A.: Microscopic and macroscopic models for coupled car traffic and pedestrian flow (2019)
  3. Vasconcelos, Artur G. R.; Albuquerque, Duarte M. S.; Pereira, José C. F.: A very high-order finite volume method based on weighted least squares for elliptic operators on polyhedral unstructured grids (2019)
  4. Ye, Huilin; Shen, Zhiqiang; Li, Ying: Interplay of deformability and adhesion on localization of elastic micro-particles in blood flow (2019)
  5. Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew: Iterative updating of model error for Bayesian inversion (2018)
  6. Copos, Calina A.; Guy, Robert D.: A porous viscoelastic model for the cell cytoskeleton (2018)
  7. Frittelli, Massimo; Sgura, Ivonne: Virtual element method for the Laplace-Beltrami equation on surfaces (2018)
  8. Guessab, Allal; Semisalov, Boris: Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope (2018)
  9. Guevara Vasquez, Fernando; Mauck, China: Approximation by Herglotz wave functions (2018)
  10. Kim, Eugenia; Wilkening, Jon: Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation (2018)
  11. Ku, Jaeun; Reichel, Lothar: Simple efficient solvers for certain ill-conditioned systems of linear equations, including (H(\operatornamediv)) problems (2018)
  12. Lu, Jiajun; Baginski, Frank; Ren, Xiaofeng: Equilibrium configurations of boundary droplets in a self-organizing inhibitory system (2018)
  13. Martin, R.; Chappell, D. J.; Chuzhanova, N.; Crofts, Jonathan J.: A numerical simulation of neural fields on curved geometries (2018)
  14. Martins, Diogo M. C.; Albuquerque, Duarte M. S.; Pereira, José C. F.: On the use of polyhedral unstructured grids with a moving immersed boundary method (2018)
  15. Meng, Liang; Breitkopf, Piotr; Le Quilliec, Guénhaël; Raghavan, Balaji; Villon, Pierre: Nonlinear shape-manifold learning approach: concepts, tools and applications (2018)
  16. Reeger, Jonah A.; Fornberg, Bengt: Numerical quadrature over smooth surfaces with boundaries (2018)
  17. Sarfaraz, Wakil; Madzvamuse, Anotida: Domain-dependent stability analysis of a reaction-diffusion model on compact circular geometries (2018)
  18. Shankar, Varun; Kirby, Robert M.; Fogelson, Aaron L.: Robust node generation for mesh-free discretizations on irregular domains and surfaces (2018)
  19. Zala, Vidhi; Shankar, Varun; Sastry, Shankar P.; Kirby, Robert M.: Curvilinear mesh adaptation using radial basis function interpolation and smoothing (2018)
  20. Zhu, Shengfeng; Hu, Xianliang; Wu, Qingbiao: A level set method for shape optimization in semilinear elliptic problems (2018)

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