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 106 articles )

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  1. Ammari, H.; Widlak, T.; Zhang, W.: Towards monitoring critical microscopic parameters for electropermeabilization (2017)
  2. Bogosel, Beniamin: The method of fundamental solutions applied to boundary eigenvalue problems (2016)
  3. Ko, William; Stockie, John M.: Parametric resonance in spherical immersed elastic shells (2016)
  4. Li, Yibao; Kim, Junseok: Three-dimensional simulations of the cell growth and cytokinesis using the immersed boundary method (2016)
  5. Stinner, Christian; Surulescu, Christina; Uatay, Aydar: Global existence for a go-or-grow multiscale model for tumor invasion with therapy (2016)
  6. Yang, Yidu; Bi, Hai; Li, Hao; Han, Jiayu: Mixed methods for the Helmholtz transmission eigenvalues (2016)
  7. Cochran, A.L.; Gao, Y.: A numerical method to detect soft tissue injuries from tissue displacements (2015)
  8. Gulizzi, V.; Milazzo, A.; Benedetti, I.: An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials (2015)
  9. Koko, Jonas: A Matlab mesh generator for the two-dimensional finite element method (2015)
  10. Li, Tiexiang; Huang, Wei-Qiang; Lin, Wen-Wei; Liu, Jijun: On spectral analysis and a novel algorithm for transmission eigenvalue problems (2015)
  11. Ray, Shannon; Miller, Warner A.; Alsing, Paul M.; Yau, Shing-Tung: Adiabatic isometric mapping algorithm for embedding 2-surfaces in Euclidean 3-space (2015)
  12. Sonon, B.; François, B.; Massart, T.J.: An advanced approach for the generation of complex cellular material representative volume elements using distance fields and level sets (2015)
  13. Wang, B.; Khoo, B.C.; Xie, Z.Q.; Tan, Z.J.: Fast centroidal Voronoi Delaunay triangulation for unstructured mesh generation (2015)
  14. Yang, Min; Liu, Jiangguo; Lin, Yanping: Pressure recovery for weakly over-penalized discontinuous Galerkin methods for the Stokes problem (2015)
  15. Zhang, Weiwei; Nie, Yufeng; Gu, Yuantong: Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation (2015)
  16. Zhou, Dong; Seibold, Benjamin; Shirokoff, David; Chidyagwai, Prince; Rosales, Rodolfo Ruben: Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions (2015)
  17. Hiltebrand, Andreas; Mishra, Siddhartha: Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws (2014)
  18. Hong, Youngjoon; Jung, Chang-Yeol; Temam, Roger: On the numerical approximations of stiff convection-diffusion equations in a circle (2014)
  19. Mahmood, Mohammed Shuker; Kovářik, Karel: Solution of double nonlinear problems in porous media by a combined finite volume-finite element algorithm (2014)
  20. Saye, Robert I.: High-order methods for computing distances to implicitly defined surfaces (2014)

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