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.: Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory (2021)
  3. Choi, Gary P. T.; Rycroft, Chris H.: Volumetric density-equalizing reference map with applications (2021)
  4. 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)
  5. Edelmann, Dominik: Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains (2021)
  6. Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P.: Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers (2021)
  7. Ghosh, Sudeshna: Immersed boundary simulations of fluid shear-induced deformation of a cantilever beam (2021)
  8. Kim, Kwang-Yeon: Guaranteed and asymptotically exact a posteriori error estimator for lowest-order Raviart-Thomas mixed finite element method (2021)
  9. Li, Binjie; Wang, Tao; Xie, Xiaoping: Analysis of the L1 scheme for fractional wave equations with nonsmooth data (2021)
  10. Mackenzie, John; Rowlatt, Christopher; Insall, Robert: A conservative finite element ALE scheme for mass-conservative reaction-diffusion equations on evolving two-dimensional domains (2021)
  11. Mohammadi, Vahid; Dehghan, Mehdi: A divergence-free generalized moving least squares approximation with its application (2021)
  12. 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)
  13. Oh, Sahuck: A new mesh moving technique for a fluid-structure interaction problem using mesh deformation energy minimization (2021)
  14. Sun, Deyong; Dai, Rui; Liu, Xiangyang; Zhan, Yunsheng; Dong, Chunying: RI-IGABEM for 2D viscoelastic problems and its application to solid propellant grains (2021)
  15. Tominec, Igor; Larsson, Elisabeth; Heryudono, Alfa: A least squares radial basis function finite difference method with improved stability properties (2021)
  16. Wang, Chao; Li, Shaofan; Zeng, Danielle; Zhu, Xinhai: Quantification and compensation of thermal distortion in additive manufacturing: a computational statistics approach (2021)
  17. Butler, T.; Jakeman, J. D.; Wildey, T.: Optimal experimental design for prediction based on push-forward probability measures (2020)
  18. Cai, Zhiqiang; Ku, JaEun: A dual finite element method for a singularly perturbed reaction-diffusion problem (2020)
  19. Cenanovic, Mirza; Hansbo, Peter; Larson, Mats G.: Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement (2020)
  20. Chen, Meng; Ling, Leevan: Extrinsic meshless collocation methods for PDEs on manifolds (2020)

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