Unstructured Mesh Generation and Its Parallelization

Our efforts to develop a serial Delaunay mesher and its parallel version are addressed. For the serial algorithm, focuses are put on its conformai and constrained boundary recovery procedures. Also, robustness and mesh quality issues are reviewed, and some typical resolutions are suggested. The final goal is to get a serial mesher with industry strength, in our opinion, which is also a prerequisite for a well performed parallel mesher.

[1]  R. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 3. Volume meshes , 1996 .

[2]  Nikos Chrisochoides,et al.  Parallel Delaunay mesh generation kernel , 2003 .

[3]  Jaime Peraire,et al.  Parallel unstructured mesh generation , 1996 .

[4]  Hugues de Cougny,et al.  Parallel Unstructured Grid Generation , 1998 .

[5]  Nikos Chrisochoides,et al.  Task Parallel Implementation of the Bowyer-Watson Algorithm , 1996 .

[6]  H. Borouchaki,et al.  Fast Delaunay triangulation in three dimensions , 1995 .

[7]  Nikos Chrisochoides,et al.  Simultaneous Mesh Generation and Partitioning for Delaunay Meshes , 2000, IMR.

[8]  Omar Ghattas,et al.  Parallel delaunay refinement mesh generation , 2004 .

[9]  P. George,et al.  ‘Ultimate’ robustness in meshing an arbitrary polyhedron , 2003 .

[10]  Roland W. Lewis,et al.  Aspects of adaptive mesh generation based on domain decomposition and Delaunay triangulation , 1995 .

[11]  L. Paul Chew,et al.  Guaranteed-quality Delaunay meshing in 3D (short version) , 1997, SCG '97.

[12]  Barry Joe,et al.  Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations , 1995, SIAM J. Sci. Comput..

[13]  Bharat K. Soni,et al.  Handbook of Grid Generation , 1998 .

[14]  Nikos Chrisochoides,et al.  Parallel Mesh Generation , 2006 .

[15]  Q. Du,et al.  Boundary recovery for three dimensional conforming Delaunay triangulation , 2004 .

[16]  D. White,et al.  6th International Meshing Roundtable '97 , 1997 .

[17]  Raimund Seidel,et al.  On the difficulty of triangulating three-dimensional Nonconvex Polyhedra , 1992, Discret. Comput. Geom..

[18]  B. G. Larwood,et al.  Domain decomposition approach for parallel unstructured mesh generation , 2003 .

[19]  Zhu Pei.  THREE-DIMENSIONAL UNSTRUCTURED MESH GENERATION , 2001 .

[20]  Zhen Yao,et al.  Redesign of a conformal boundary recovery algorithm for 3D Delaunay triangulation , 2006 .

[21]  Roland W. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 1. Fundamental aspects of triangulation and point creation , 1996 .

[22]  Yuanxian Gu,et al.  The boundary recovery and sliver elimination algorithms of three‐dimensional constrained Delaunay triangulation , 2006 .

[23]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[24]  Roland W. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 2. Surface meshes , 1996 .

[25]  T. Baker.  Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation , 1989, Engineering with Computers.

[26]  Nigel P. Weatherill,et al.  An interactive geometry utility environment for multi‐disciplinary computational engineering , 2002 .

[27]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

[28]  William H. Frey,et al.  An apporach to automatic three‐dimensional finite element mesh generation , 1985 .

[29]  Barry Joe,et al.  Construction of three-dimensional Delaunay triangulations using local transformations , 1991, Comput. Aided Geom. Des..

[30]  P. George,et al.  Automatic mesh generator with specified boundary , 1991 .

[31]  Qiang Du,et al.  Constrained boundary recovery for three dimensional Delaunay triangulations , 2004 .

[32]  Anwei Liu,et al.  How far flipping can go towards 3D conforming/constrained triangulation , 2000, IMR.

[33]  Carl Ollivier-Gooch,et al.  Tetrahedral mesh improvement using swapping and smoothing , 1997 .

[34]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[35]  Nigel P. Weatherill,et al.  Distributed parallel Delaunay mesh generation , 1999 .

[36]  Piotr Breitkopf,et al.  A Modular Design for a Parallel Multifrontal Mesh Generator , 2002, Euro-Par.

[37]  N. Weatherill,et al.  Efficient three‐dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints , 1994 .

[38]  P. George.  Improvements on Delaunay-based three-dimensional automatic mesh generator , 1997 .