DistMesh

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.


References in zbMATH (referenced in 172 articles )

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  1. Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew: Iterative updating of model error for Bayesian inversion (2018)
  2. Copos, Calina A.; Guy, Robert D.: A porous viscoelastic model for the cell cytoskeleton (2018)
  3. Guessab, Allal; Semisalov, Boris: Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope (2018)
  4. Guevara Vasquez, Fernando; Mauck, China: Approximation by Herglotz wave functions (2018)
  5. Kim, Eugenia; Wilkening, Jon: Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation (2018)
  6. Ku, Jaeun; Reichel, Lothar: Simple efficient solvers for certain ill-conditioned systems of linear equations, including $H(\operatornamediv)$ problems (2018)
  7. Lu, Jiajun; Baginski, Frank; Ren, Xiaofeng: Equilibrium configurations of boundary droplets in a self-organizing inhibitory system (2018)
  8. Meng, Liang; Breitkopf, Piotr; Le Quilliec, Guénhaël; Raghavan, Balaji; Villon, Pierre: Nonlinear shape-manifold learning approach: concepts, tools and applications (2018)
  9. Reeger, Jonah A.; Fornberg, Bengt: Numerical quadrature over smooth surfaces with boundaries (2018)
  10. Sarfaraz, Wakil; Madzvamuse, Anotida: Domain-dependent stability analysis of a reaction-diffusion model on compact circular geometries (2018)
  11. Shankar, Varun; Kirby, Robert M.; Fogelson, Aaron L.: Robust node generation for mesh-free discretizations on irregular domains and surfaces (2018)
  12. Zhu, Shengfeng; Hu, Xianliang; Wu, Qingbiao: A level set method for shape optimization in semilinear elliptic problems (2018)
  13. Ammari, H.; Widlak, T.; Zhang, W.: Towards monitoring critical microscopic parameters for electropermeabilization (2017)
  14. 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)
  15. Bayona, Victor; Flyer, Natasha; Fornberg, Bengt; Barnett, Gregory A.: On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs (2017)
  16. Chen, Long; Wei, Huayi; Wen, Min: An interface-fitted mesh generator and virtual element methods for elliptic interface problems (2017)
  17. Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael: Geometric constraints for shape and topology optimization in architectural design (2017)
  18. Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar: Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics (2017)
  19. Erdmanis, J.; Kitenbergs, G.; Perzynski, R.; Cēbers, A.: Magnetic micro-droplet in rotating field: numerical simulation and comparison with experiment (2017)
  20. Hudson, Thomas; Morandotti, Marco: Properties of screw dislocation dynamics: time estimates on boundary and interior collisions (2017)

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