TriMe++: Multi-threaded triangular meshing in two dimensions

We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-sca...

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Vydané v:	Computer physics communications Ročník 308; s. 109442
Hlavní autori:	Lu, Jiayin, Rycroft, Chris H.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Elsevier B.V 01.03.2025 Elsevier
Predmet:	Centroidal Voronoi tessellation Computational geometry Delaunay triangulation DistMesh Geometric adaptivity Geometry meshing MATHEMATICS AND COMPUTING Multi-threaded programming Voro Voronoi tessellation DistMesh Computational geometry Geometric adaptivity Centroidal Voronoi tessellation Voronoi tessellation Delaunay triangulation Multi-threaded programming Geometry meshing Voro
ISSN:	0010-4655
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Abstract	We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in TriMe++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating large-scale meshes containing between 104 to 107 points. TriMe++ can handle complicated geometries and generates adaptive meshes of high quality. Program title:TriMe++ CPC Library link to program files:https://doi.org/10.17632/jxcsxtywtw.1 Developer's repository link:https://github.com/jiayinlu19960224/TriMe Licensing provisions: BSD 3-clause Programming language: C++ External routines/libraries: OpenMP, multi-threaded Voro++ Nature of problem: Multi-threaded geometry meshing in two dimension using the Delaunay triangulation Solution method: The TriMe++ library is built around several C++ classes that follows a structured meshing pipeline. During initialization, the shape_2d class reads the geometry input and generates a signed distance field using a grid-based data structure to represent the shape. The sizing_2d class subsequently produces adaptive element sizing and density fields for the mesh. It uses an adaptive quad-tree data structure, enabling efficient refinement of sizing and density values in areas with complex geometries. In the meshing procedure, the parallel_meshing_2d class iteratively improves point positions in the mesh. In each meshing iteration, the multi-threaded Voro++ library generates the Delaunay triangulation of the points. Users can select from three meshing algorithms, the DistMesh algorithm in the mesh_alg_2d_dm class, the centroidal Voronoi diagram meshing algorithm in the mesh_alg_2d_cvd class, and a hybrid method of the two in the mesh_alg_2d_hybrid class Throughout this meshing workflow, we use OpenMP for multi-threaded parallel computations.
AbstractList	We present TRIME++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in TRIME++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating large-scale meshes containing between 104 to 107 points. TRIME++ can handle complicated geometries and generates adaptive meshes of high quality. We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in TriMe++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating large-scale meshes containing between 104 to 107 points. TriMe++ can handle complicated geometries and generates adaptive meshes of high quality. Program title:TriMe++ CPC Library link to program files:https://doi.org/10.17632/jxcsxtywtw.1 Developer's repository link:https://github.com/jiayinlu19960224/TriMe Licensing provisions: BSD 3-clause Programming language: C++ External routines/libraries: OpenMP, multi-threaded Voro++ Nature of problem: Multi-threaded geometry meshing in two dimension using the Delaunay triangulation Solution method: The TriMe++ library is built around several C++ classes that follows a structured meshing pipeline. During initialization, the shape_2d class reads the geometry input and generates a signed distance field using a grid-based data structure to represent the shape. The sizing_2d class subsequently produces adaptive element sizing and density fields for the mesh. It uses an adaptive quad-tree data structure, enabling efficient refinement of sizing and density values in areas with complex geometries. In the meshing procedure, the parallel_meshing_2d class iteratively improves point positions in the mesh. In each meshing iteration, the multi-threaded Voro++ library generates the Delaunay triangulation of the points. Users can select from three meshing algorithms, the DistMesh algorithm in the mesh_alg_2d_dm class, the centroidal Voronoi diagram meshing algorithm in the mesh_alg_2d_cvd class, and a hybrid method of the two in the mesh_alg_2d_hybrid class Throughout this meshing workflow, we use OpenMP for multi-threaded parallel computations.
ArticleNumber	109442
Author	Rycroft, Chris H. Lu, Jiayin
Author_xml	– sequence: 1 givenname: Jiayin orcidid: 0000-0001-5590-1437 surname: Lu fullname: Lu, Jiayin email: jiayin_lu@math.ucla.edu organization: Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States – sequence: 2 givenname: Chris H. orcidid: 0000-0003-4677-6990 surname: Rycroft fullname: Rycroft, Chris H. organization: Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, United States
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Keywords	DistMesh Computational geometry Geometric adaptivity Centroidal Voronoi tessellation Voronoi tessellation Delaunay triangulation Multi-threaded programming Geometry meshing Voro
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Snippet	We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay... We present TRIME++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay...
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StartPage	109442
SubjectTerms	Centroidal Voronoi tessellation Computational geometry Delaunay triangulation DistMesh Geometric adaptivity Geometry meshing MATHEMATICS AND COMPUTING Multi-threaded programming Voro Voronoi tessellation
Title	TriMe++: Multi-threaded triangular meshing in two dimensions
URI	https://dx.doi.org/10.1016/j.cpc.2024.109442 https://www.osti.gov/servlets/purl/2546948
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