Fu, Lin; Han, Luhui; Hu, Xiangyu Y.; Adams, Nikolaus A. An isotropic unstructured mesh generation method based on a fluid relaxation analogy. (English) Zbl 1441.65075 Comput. Methods Appl. Mech. Eng. 350, 396-431 (2019). Summary: In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three characteristic fields based on three modeling equations are computed to define the target mesh-vertex distribution, i.e. target feature-size function and density function. The modeling solutions are computed on a multi-resolution Cartesian background mesh. Second, with a target particle density and a local smoothing-length interpolated from the target field on the background mesh, a set of physically-motivated model equations is developed and solved by an adaptive-smoothing-length Smoothed Particle Hydrodynamics (SPH) method. The relaxed particle distribution conforms well with the target functions while maintaining isotropy and smoothness inherently. Third, a parallel fast Delaunay triangulation method is developed based on the observation that a set of neighboring particles generates a locally valid Voronoi diagram at the interior of the domain. The incompleteness of near domain boundaries is handled by enforcing a symmetry boundary condition. A set of two-dimensional test cases shows the feasibility of the method. Numerical results demonstrate that the proposed method produces high-quality globally optimized adaptive isotropic meshes even for high geometric complexity. Cited in 1 ReviewCited in 10 Documents MSC: 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry Keywords:unstructured mesh; level-set; SPH; Delaunay triangulation; Voronoi diagram Software:DualSPHysics; DistMesh; Boost C++ Libraries; Boost; Triangle PDFBibTeX XMLCite \textit{L. Fu} et al., Comput. Methods Appl. Mech. Eng. 350, 396--431 (2019; Zbl 1441.65075) Full Text: DOI References: [1] Chew, L. P., Guaranteed-Quality Triangular MeshesTech. Rep. (1989), Cornell University [2] Křížek, M.; Neittaanmäki, P., Superconvergence phenomenon in the finite element method arising from averaging gradients, Numer. Math., 45, 1, 105-116 (1984) · Zbl 0575.65104 [3] Huang, Y.; Qin, H.; Wang, D., Centroidal Voronoi tessellation-based finite element superconvergence, Internat. J. Numer. 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