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. Ammari, H.; Widlak, T.; Zhang, W.: Towards monitoring critical microscopic parameters for electropermeabilization (2017)
  2. Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar: Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics (2017)
  3. Belokrys-Fedotov, A.I.; Garanzha, V.A.; Kudryavtseva, L.N.: Generation of Delaunay meshes in implicit domains with edge sharpening (2016)
  4. Bogosel, Beniamin: The method of fundamental solutions applied to boundary eigenvalue problems (2016)
  5. Carpio, A.; Dimiduk, T.G.; Rapún, M.L.; Selgas, V.: Noninvasive imaging of three-dimensional micro and nanostructures by topological methods (2016)
  6. Galagusz, Ryan; Shirokoff, David; Nave, Jean-Christophe: A Fourier penalty method for solving the time-dependent Maxwell’s equations in domains with curved boundaries (2016)
  7. Ko, William; Stockie, John M.: Parametric resonance in spherical immersed elastic shells (2016)
  8. Kuchment, Peter; Terzioglu, Fatma: Three-dimensional image reconstruction from Compton camera data (2016)
  9. Liu, Jie: A second-order changing-connectivity ALE scheme and its application to FSI with large convection of fluids and near contact of structures (2016)
  10. Li, Yibao; Kim, Junseok: Three-dimensional simulations of the cell growth and cytokinesis using the immersed boundary method (2016)
  11. MacDonald, G.; Mackenzie, J.A.; Nolan, M.; Insall, R.H.: A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis (2016)
  12. Moura, R.C.; Silva, A.F.C.; Bigarella, E.D.V.; Fazenda, A.L.; Ortega, M.A.: Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme (2016)
  13. Saye, R.I.; Sethian, J.A.: Multiscale modelling of evolving foams (2016)
  14. Stinner, Christian; Surulescu, Christina; Uatay, Aydar: Global existence for a go-or-grow multiscale model for tumor invasion with therapy (2016)
  15. Yang, Yidu; Bi, Hai; Li, Hao; Han, Jiayu: Mixed methods for the Helmholtz transmission eigenvalues (2016)
  16. Zhigun, Anna; Surulescu, Christina; Uatay, Aydar: Global existence for a degenerate haptotaxis model of cancer invasion (2016)
  17. Cochran, A.L.; Gao, Y.: A numerical method to detect soft tissue injuries from tissue displacements (2015)
  18. Gulizzi, V.; Milazzo, A.; Benedetti, I.: An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials (2015)
  19. Koko, Jonas: A Matlab mesh generator for the two-dimensional finite element method (2015)
  20. Li, Tiexiang; Huang, Wei-Qiang; Lin, Wen-Wei; Liu, Jijun: On spectral analysis and a novel algorithm for transmission eigenvalue problems (2015)

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