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. Bespalov, Alex; Rocchi, Leonardo; Silvester, David: T-IFISS: a toolbox for adaptive FEM computation (2021)
  2. Choi, Gary P. T.; Rycroft, Chris H.: Volumetric density-equalizing reference map with applications (2021)
  3. Mohammadi, Vahid; Dehghan, Mehdi: A divergence-free generalized moving least squares approximation with its application (2021)
  4. Mohammadi, Vahid; Dehghan, Mehdi; De Marchi, Stefano: Numerical simulation of a prostate tumor growth model by the RBF-FD scheme and a semi-implicit time discretization (2021)
  5. Butler, T.; Jakeman, J. D.; Wildey, T.: Optimal experimental design for prediction based on push-forward probability measures (2020)
  6. Cai, Zhiqiang; Ku, JaEun: A dual finite element method for a singularly perturbed reaction-diffusion problem (2020)
  7. Chen, Meng; Ling, Leevan: Extrinsic meshless collocation methods for PDEs on manifolds (2020)
  8. Cho, Kanghun; Moon, Minam: Multiscale hybridizable discontinuous Galerkin method for elliptic problems in perforated domains (2020)
  9. Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P.: Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing (2020)
  10. Fok, Pak-Wing; Gou, Kun: Finite element simulation of intimal thickening in 2D multi-layered arterial cross sections by morphoelasticity (2020)
  11. Greco, F.; Arroyo, M.: High-order maximum-entropy collocation methods (2020)
  12. Gross, B. J.; Trask, N.; Kuberry, P.; Atzberger, P. J.: Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: a generalized moving least-squares (GMLS) approach (2020)
  13. Hesthaven, Jan S.; Mönkeberg, Fabian: Two-dimensional RBF-ENO method on unstructured grids (2020)
  14. Li, Ruo; Yang, Fanyi: A least squares method for linear elasticity using a patch reconstructed space (2020)
  15. Liu, Chun; Wang, Yiwei: On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach (2020)
  16. Liu, Chun; Wang, Yiwei: A variational Lagrangian scheme for a phase-field model: a discrete energetic variational approach (2020)
  17. Liu, Jun; Wu, Shu-Lin: A fast block (\alpha)-circulant preconditoner for all-at-once systems from wave equations (2020)
  18. Li, Xiangrong; Qi, Nan; Zhang, Weiwei; Nie, Yufeng: Provably size-guaranteed mesh generation with superconvergence (2020)
  19. Ma, Erfang: Integral formulation of the complete electrode model of electrical impedance tomography (2020)
  20. Muntean, Adrian; Nikolopoulos, Christos: Colloidal transport in locally periodic evolving porous media -- an upscaling exercise (2020)

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