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. Bajars, Janis; Chappell, David J.; Hartmann, Timo; Tanner, Gregor: Improved approximation of phase-space densities on triangulated domains using discrete flow mapping with $p$-refinement (2017)
  3. Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael: Geometric constraints for shape and topology optimization in architectural design (2017)
  4. Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar: Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics (2017)
  5. Hudson, Thomas; Morandotti, Marco: Properties of screw dislocation dynamics: time estimates on boundary and interior collisions (2017)
  6. Jin, Bangti; Lazarov, Raytcho; Thomée, Vidar; Zhou, Zhi: On nonnegativity preservation in finite element methods for subdiffusion equations (2017)
  7. Koppenol, Daniël C.; Vermolen, Fred J.; Koppenol-Gonzalez, Gabriela V.; Niessen, Frank B.; van Zuijlen, Paul P.M.; Vuik, Kees: A mathematical model for the simulation of the contraction of burns (2017)
  8. Kuchment, Peter; Terzioglu, Fatma: Inversion of weighted divergent beam and cone transforms (2017)
  9. Lehto, Erik; Shankar, Varun; Wright, Grady B.: A radial basis function (RBF) compact finite difference (FD) scheme for reaction-diffusion equations on surfaces (2017)
  10. Le Louër, Frédérique; Rapún, María-Luisa: Topological sensitivity for solving inverse multiple scattering problems in three-dimensional electromagnetism. I: One step method (2017)
  11. Li, Jingzhi; Liu, Hongyu; Wang, Yuliang: Recovering an electromagnetic obstacle by a few phaseless backscattering measurements (2017)
  12. Lindsey, Michael; Rubinstein, Yanir A.: Optimal transport via a Monge-Ampère optimization problem (2017)
  13. Shankar, Varun: The overlapped radial basis function-finite difference (RBF-FD) method: a generalization of RBF-FD (2017)
  14. Zhang, Wenjuan; Al Kobaisi, Mohammed: A simplified enhanced MPFA formulation for the elliptic equation on general grids (2017)
  15. Belokrys-Fedotov, A.I.; Garanzha, V.A.; Kudryavtseva, L.N.: Generation of Delaunay meshes in implicit domains with edge sharpening (2016)
  16. Bogosel, Beniamin: The method of fundamental solutions applied to boundary eigenvalue problems (2016)
  17. Carpio, A.; Dimiduk, T.G.; Rapún, M.L.; Selgas, V.: Noninvasive imaging of three-dimensional micro and nanostructures by topological methods (2016)
  18. 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)
  19. Keuthen, M.; Kraft, D.: Shape optimization of a breakwater (2016)
  20. Kovács, Balázs; Power Guerra, Christian Andreas: Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces (2016)

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