Improvements in the reliability and element quality of parallel tetrahedral mesh generation. (English) Zbl 1352.65605

Summary: The paper presents a parallel tetrahedral mesh generation approach based on recursive bidivisions using triangular surfaces. Research was conducted for addressing issues concerning mesh generation reliability and element quality. A novel procedure employing local modification techniques is proposed for repairing the intersecting interdomain mesh instead of directly repeating the bidivision procedure, which improves the robustness of the complete meshing procedure significantly. In addition, a new parallel quality improvement scheme is suggested for optimizing the distributed volume meshes. The scheme is free of any communication cost and highly efficient. Finally, mesh experiments of hundreds of millions of elements are performed to demonstrate the reliability, effectiveness and efficiency of the proposed method and its potential applications to large-scale simulations of complex aerodynamics models.


65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65Y05 Parallel numerical computation


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[1] Weatherill, Aerospace simulations on parallel computers using unstructured grids, International Journal for Numerical Methods in Fluids 40 pp 171– (2002) · Zbl 1021.76030
[2] Cougny, Chapter 24 in CRC Handbook of Grid Generation pp 24.1– (1999)
[3] Chrisochoides, Chapter 7 in Numerical Solution of Partial Differential Equations on Parallel Computers pp 237– (2006)
[4] Alleaume A Francez L Loriot M Maman N Large out-of-core tetrahedral meshing Proceedings of the 16th International Meshing Roundtable 2006 461 476 · Zbl 1134.65312
[5] Linardakis, A static geometric medial axis domain decomposition in 2D Euclidean Space, ACM Transactions on Mathematical Software 10 pp 1– (2006) · Zbl 1291.65062
[6] Attali, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration (2007)
[7] Galtier J George PL Prepartitioning as a way to mesh subdomains in parallel Proceedings of the 5th International Meshing Roundtable 1996 107 122
[8] Larwood, Domain decomposition approach for parallel unstructured mesh generation, International Journal for Numerical Methods in Engineering 58 pp 177– (2003) · Zbl 1032.76667
[9] Boufflet J-P Breitkopf P Rassineux A Villon P A modular design for a parallel multifrontal mesh generator Proceedings of the 8th International Euro-Par Conference on Parallel Processing 2002 715 723 · Zbl 1068.65508
[10] Ivanov E Andrä H Kudryavtsev AN Domain decomposition approach for automatic parallel generation of tetrahedral grids Proceedings of the Conference on Numerical Geometry, Grid Generation and High Performance Computing 2006 115 124 · Zbl 1094.65017
[11] Zheng, Proceedings of the 2007 International Symposium on Computational Mechanics pp 22– (2007)
[12] Said, Distributed parallel Delaunay mesh generation, Computer Methods in Applied Mechanic Engineering 177 pp 109– (1999) · Zbl 0997.65137
[13] Chen, Three-dimensional constrained boundary recovery with an enhanced Steiner point suppression procedure, Computers and Structures 89 pp 455– (2011)
[14] ParMETIS - Parallel Graph Partitioning and Fill-reducing Matrix Ordering 2012 http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview
[15] Schloegel K Karypis G Kumar V Parallel multilevel algorithms for multi-constraint graph partitioning Proceeding of the 6th International Euro-Par Conference on Parallel Processing 2000 296 310 · Zbl 1012.68146
[16] de Cougny, Parallel volume meshing using face removals and hierarchical repartitioning, Computer Methods in Applied Mechanics and Engineering 174 pp 275– (1999) · Zbl 0963.76073
[17] Löhner, A parallel advancing front grid generation scheme, International Journal for Numerical Methods in Engineering 51 pp 663– (2001) · Zbl 1012.76077
[18] Si, Constrained Delaunay tetrahedral mesh generation and refinement, Finite Element in Analysis and Design 46 pp 33– (2010)
[19] Dijkstra, A note on two problems in connexion with graphs, Numerische Mathematik 1 pp 269– (1959) · Zbl 0092.16002
[20] Guigue, Fast and robust triangle-triangle overlap test using orientation predicates, Journal of Graphical Tools 8 pp 25– (2003)
[21] Yamakawa S Shimada K Removing self intersections of a triangular mesh by edge swapping, edge hammering, and face lifting Proceedings of the 18th International Meshing Roundtable 2009 13 30
[22] Ollivier-Gooch C GRUMMP 2012 http://tetra.mech.ubc.ca/GRUMMP/
[23] Freitag, Tetrahedral mesh improvement using swapping and smoothing, International Journal for Numerical Methods in Engineering 40 pp 3979– (1997) · Zbl 0897.65075
[24] Liu, Small polyhedron reconnection for mesh improvement and its implementation based on advancing front technique, International Journal for Numerical Methods in Engineering 79 pp 1004– (2009) · Zbl 1171.74472
[25] Xie, Enabling technologies in the problem solving environment HEDP, Communications in Computational Physics 4 pp 1170– (2008) · Zbl 1364.76007
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