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 238 articles )

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  1. Cai, Zhiqiang; Ku, JaEun: A dual finite element method for a singularly perturbed reaction-diffusion problem (2020)
  2. Chen, Meng; Ling, Leevan: Extrinsic meshless collocation methods for PDEs on manifolds (2020)
  3. Cho, Kanghun; Moon, Minam: Multiscale hybridizable discontinuous Galerkin method for elliptic problems in perforated domains (2020)
  4. Fok, Pak-Wing; Gou, Kun: Finite element simulation of intimal thickening in 2D multi-layered arterial cross sections by morphoelasticity (2020)
  5. Greco, F.; Arroyo, M.: High-order maximum-entropy collocation methods (2020)
  6. 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)
  7. Hesthaven, Jan S.; Mönkeberg, Fabian: Two-dimensional RBF-ENO method on unstructured grids (2020)
  8. Li, Ruo; Yang, Fanyi: A least squares method for linear elasticity using a patch reconstructed space (2020)
  9. Ma, Erfang: Integral formulation of the complete electrode model of electrical impedance tomography (2020)
  10. Muntean, Adrian; Nikolopoulos, Christos: Colloidal transport in locally periodic evolving porous media -- an upscaling exercise (2020)
  11. Reeger, Jonah A.: Approximate integrals over the volume of the ball (2020)
  12. Vasyliv, Yaroslav; Alexeev, Alexander: Simulating incompressible flow on moving meshfree grids (2020)
  13. Zahr, M. J.; Shi, A.; Persson, P.-O.: Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method (2020)
  14. Antonietti, P. F.; Pennesi, G.: (V)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes (2019)
  15. Barg, Michael C.; Mangum, Amanda J.: A phase separation problem and geodesic disks on Cassinian oval surfaces (2019)
  16. Berge, Runar Lie; Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas: Unstructured Voronoi grids conforming to lower dimensional objects (2019)
  17. Borsche, R.; Meurer, A.: Microscopic and macroscopic models for coupled car traffic and pedestrian flow (2019)
  18. Brus, S. R.; Wirasaet, D.; Kubatko, E. J.; Westerink, J. J.; Dawson, C.: High-order discontinuous Galerkin methods for coastal hydrodynamics applications (2019)
  19. Calvetti, D.; Nakkireddy, S.; Somersalo, Erkki: Approximation of continuous EIT data from electrode measurements with Bayesian methods (2019)
  20. Dehghan, Mehdi; Mohammadi, Vahid: Two-dimensional simulation of the damped Kuramoto-Sivashinsky equation via radial basis function-generated finite difference scheme combined with an exponential time discretization (2019)

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