Keywords: mesh generation, parallel, mesh migration, refinement.

A parallel tetrahedral mesh generator is developed based on existing sequential mesh generation software. As sequential mesh generation software, the Netgen [1] mesh generator is used due to its availability as an LGPL open source software and its wide user base. The developed routines use the MPI communication libraries and the C++ language.

The parallel mesh generation algorithms developed proceed by decomposing the whole geometry into a number of sub-geometries sequentially on a master node at the beginning and then mesh each sub-geometry in parallel. When a mesh is generated for each sub-geometry by each processor, the partition boundary mesh faces of adjacent sub-geometries need to be conforming (i.e. matching). This is achieved during an initial phase on the master node by sequentially generating a surface mesh for the whole geometry including the sub-geometry faces after the geometry partitioning.

Another issue that needs to be addressed is load balancing. The parallel volume mesh generation phase should be load balanced. To achieve load balancing, a coarse volume mesh is generated which is partitioned in order to obtain sub-geometries with approximately the same number of tetrahedra.

Two mesh generation methods are implemented. The first decomposes the CAD geometry and produces conforming surface sub-meshes that are sent to other processors for volume mesh generation. The second method is a refinement based method that also makes use of the CAD geometry information. Advantages and disadvantages of each method are discussed. After the parallel volume mesh generation is performed, a distributed mesh results which has its partition boundary vertices duplicated on multiple processors. Global identifiers are used for each mesh entity. Hence, the duplicate partition boundary entities need to have the same identifiers.

Parallel repartitioning also has to be done as part of the first method. To facilitate distributed element movements in parallel, a migration algorithm that utilizes an "owner updates" rule [2] is developed. Timing results obtained on the European Curie supercomputer are presented. In particular, results show that by using the refinement based method, one can generate over a billion element meshes in under a minute.

1

J. Schöberl, "Netgen, an advancing front 2d/3d-mesh generator based on abstract rules", Computing and Visualization in Science, Vol.1, No. 1, p. 41-52, 1997.

2

M.S. Shephard, J.E. Flaherty, H.L. de Cougny, C. Ozturan, C.L. Bottasso, M.W. Beall, "Parallel Automated Adaptive Procedures for Unstructured Meshes", AGARD-FDP-VKI Special Course on "Parallel Computing in CFD", held at the VKI, Rhode-Saint-Genese, Belgium, May 1995 and at NASA Ames, USA , AGARD Report R-807. 1995. URL

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