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. Anjuna, D.; Sakthivel, K.; Hasanov, A.: Determination of a spatial load in a damped Kirchhoff-Love plate equation from final time measured data (2022)
  2. Bakharev, F.; Enin, A.; Groman, A.; Kalyuzhnyuk, A.; Matveenko, S.; Petrova, Yu.; Starkov, I.; Tikhomirov, S.: Velocity of viscous fingers in miscible displacement: comparison with analytical models (2022)
  3. Domokos, Gábor; Lángi, Zsolt; Sipos, András A.: Tracking critical points on evolving curves and surfaces (2022)
  4. Ferrero, Andrea; Taddei, Tommaso; Zhang, Lei: Registration-based model reduction of parameterized two-dimensional conservation laws (2022)
  5. Ghosh, Sudeshna; Yadav, Pooja: Study of gravitational settling of single semi-torus shaped particle using immersed boundary method (2022)
  6. Gross, B. J.; Kuberry, P.; Atzberger, P. J.: First-passage time statistics on surfaces of general shape: surface PDE solvers using generalized moving least squares (GMLS) (2022)
  7. Huang, Tianci; Zahr, Matthew J.: A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows (2022)
  8. Kao, Chiu-Yen; Mohammadi, Seyyed Abbas: A rearrangement minimization problem corresponding to p-Laplacian equation (2022)
  9. Li, Yibao; Liu, Rui; Xia, Qing; He, Chenxi; Li, Zhong: First- and second-order unconditionally stable direct discretization methods for multi-component Cahn-Hilliard system on surfaces (2022)
  10. Lockerby, Duncan A.: Integration over discrete closed surfaces using the method of fundamental solutions (2022)
  11. Sukumar, N.; Srivastava, Ankit: Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks (2022)
  12. Yang, Wei; Wang, Tiancheng: Isotropic cloak materials design based on the numerical optimization method of the inverse medium problem (2022)
  13. Zhang, Ying; Li, Chong-Jun; Jia, Yan-Mei; Liu, Zhen-Yi; Chen, Juan: Revised SBFEM on arbitrary polygons and faceted polyhedrons with the second order completeness by elimination of bubble functions (2022)
  14. Bespalov, Alex; Rocchi, Leonardo; Silvester, David: T-IFISS: a toolbox for adaptive FEM computation (2021)
  15. Chappell, David; Crofts, Jonathan J.; Richter, Martin; Tanner, Gregor: A direction preserving discretization for computing phase-space densities (2021)
  16. Choi, Gary P. T.: Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory (2021)
  17. Choi, Gary P. T.; Rycroft, Chris H.: Volumetric density-equalizing reference map with applications (2021)
  18. Drake, Kathryn P.; Fuselier, Edward J.; Wright, Grady B.: A partition of unity method for divergence-free or curl-free radial basis function approximation (2021)
  19. Edelmann, Dominik: Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains (2021)
  20. Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P.: Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers (2021)

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