A Parallel Approach for the Generation of Unstructured Meshes with Billions of Elements on Distributed-Memory Supercomputers

This paper describes a parallel approach for the rapid generation of ultra-large-scale unstructured meshes on distributed-memory supercomputers. A medium-sized initial mesh is prepared first. Afterwards, a two-level domain decomposition (DD) strategy is used to split and distribute the initial mesh to different cores. Finally, the parallel mesh generation, comprising a recursive procedure which includes parallel surface recovery, parallel boundary updating, and parallel mesh multiplication, is performed. The two-level DD differentiates the intra-node and inter-node communication to reduce communication overheads. A global indexing and updating scheme is used to make the mesh multiplication devoid of communication. A new parallel surface recovery algorithm without communication is developed to maintain the fidelity of the resulting mesh model to the original geometric model. Tests of the parallel approach for some real-life problems on supercomputers (Dawning-5000A and Tianhe-2) are presented. Issues regarding the speedup, parallel efficiency, and mesh quality are discussed. Results show that the proposed parallel approach has a reasonably good scalability, that the quality of the resulting mesh is improved, and that ultra-large-scale meshes with billions of elements can be generated quickly.

[1]  Timothy J. Tautges,et al.  Creating geometry and mesh models for nuclear reactor core geometries using a lattice hierarchy-based approach , 2012, Engineering with Computers.

[2]  G. Houzeaux,et al.  Alya: Computational Solid Mechanics for Supercomputers , 2014, Archives of Computational Methods in Engineering.

[3]  Erdal Yilmaz,et al.  Application of surface conformed linear mesh and data subdivision technique to a spinning projectile , 2013 .

[4]  Mark S. Shephard,et al.  PARALLEL MESH GENERATION AND ADAPTATION FOR CAD GEOMETRIES , 2011 .

[5]  Heiko Andrä,et al.  Domain Decomposition Approach for Automatic Parallel Generation of Tetrahedral Grids , 2006 .

[6]  Andrey N. Chernikov,et al.  Towards Exascale Parallel Delaunay Mesh Generation , 2009, IMR.

[7]  Guillaume Houzeaux,et al.  Parallel uniform mesh multiplication applied to a Navier–Stokes solver , 2013 .

[8]  Kazuhiro Nakahashi,et al.  Parallel unstructured mesh generation by an advancing front method , 2007, Math. Comput. Simul..

[9]  Yasin Yilmaz,et al.  Using sequential NETGEN as a component for a parallel mesh generator , 2015, Adv. Eng. Softw..

[10]  Jalal Abedi,et al.  High Performance Computing of Fluid-Structure Interactions in Hydrodynamics Applications Using Unstructured Meshes with More than One Billion Elements , 2002, HiPC.

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

[12]  Heiko Andrä,et al.  Automatic parallel generation of tetrahedral grids by using a domain decomposition approach , 2008 .

[13]  R. J. Alves de Sousa,et al.  On the use of EAS solid‐shell formulations in the numerical simulation of incremental forming processes , 2011 .

[14]  Jack Dongarra,et al.  Applied Mathematics Research for Exascale Computing , 2014 .

[15]  Kazuhiro Nakahashi,et al.  Direct Surface Triangulation Using Stereolithography Data , 2002 .

[16]  Erdal Yilmaz,et al.  Variable Intensity Computational Mesh And Data Technique: A Practical Approach For Large-Scale Flow Simulation and Visualization , 2010 .

[17]  Chen Ji,et al.  A 14.6 billion degrees of freedom, 5 teraflops, 2.5 terabyte earthquake simulation on the Earth Simulator , 2003, ACM/IEEE SC 2003 Conference (SC'03).

[18]  R. Löhner.  Regridding Surface Triangulations , 1996 .

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

[20]  Seren Soner,et al.  Parallel Mesh Generation, Migration and Partitioning for the Elmer Application , 2022 .

[21]  Erdal Yilmaz,et al.  Surface conformed linear mesh and data subdivision technique for large-scale flow simulation and visualization in Variable Intensity Computational Environment , 2013 .

[22]  Onkar Sahni,et al.  Tools to support mesh adaptation on massively parallel computers , 2011, Engineering with Computers.

[23]  Dhabaleswar K. Panda,et al.  High performance and scalable mpi intra-node communication middleware for multi-core clusters , 2009 .