Title: Generation of Hexahedral Block-Structured Meshes using Fundamental Sheets Speaker: Franck Ledoux, CEA, France Date/Time: Tuesday, July 14, 2009, 11:00 a.m. Location: CSRI Building, Room 90 (Sandia NM) Brief Abstract: N. Kowalski1, F. Ledoux1, S. J. Owen2, M. L. Staten2 During last decade, numerous algorithms have been developed to automatically generate hexahedral meshes but, contrary to tetrahedral meshing, a generic algorithm that provides a satisfying hexahedral mesh for any 3D geometrical object does not exist. This situation is mainly due to the topological structure of hexahedral meshes which prevents algorithms to easily perform local topological modifications. A hexahedral mesh is structured as being a set of layers of hexahedra. In other words, the dual of a hexahedral mesh is structured as an arrangement of manifold surfaces, called sheets, which corresponds to layer of hexahedra in the primal mesh. Note that most of the people developing topological algorithms work in the dual mesh which has good properties to ease theoretical definitions and specific algorithms. Considering this topological constraint, some algorithms (like whisker-weaving) drive the mesh generation considering topology first. But a mesh is not just a topological object and the knowledge of geometry is necessary too. As a consequence the result of topology-driven algorithms is not always usable for a numerical simulation (negative Jacobian elements). Other promising algorithms, like unconstrained plastering, focus on the geometry and provide acceptable meshes for a wide range of geometries. Nevertheless, theoretical foundations are missing to ensure such an algorithm will work for any geometry. Recently, authors of [RS08] provide an atypical approach where a hexahedral block-structured mesh is generated by recovering a tetrahedral mesh using sheet reconstruction. In this work, we suggest a similar approach starting from an invalid hexahedral mesh. We think that geometry and topology must be considered simultaneously and we suggest an algorithm built on the theoretical notion of fundamental meshes [LS08]. A fundamental mesh is a hexahedral mesh which captures geometrical features via fundamental sheets and chords. Intuitively a fundamental sheet corresponds to a layer of hexahedra which are all adjacent to a geometrical surface, and a fundamental chord corresponds to one or more column of hexahedra which are adjacent to a geometrical curve. In other words, both geometrical and topological entities are important in a fundamental mesh. We give the results of a preliminary study to generate a block-structured hexahedral mesh using fundamental meshes (every obtained block is a hexahedron). We start from an existing hexahedral mesh where element quality is not satisfying and we modify it to obtain a fundamental mesh in which we remove most of the non-fundamental sheets to get a coarse block-structured mesh. Sheet operations like pillowing, inflating, and sheet extraction and chord contraction are intensively used. Future trends of this work will be depicted too. For instance, another option is to start from the geometry directly and not from an initial hexahedral mesh. References Over the last year we have been exploring the capabilities of FPGA’s, the design tools, and how to employ FPGAs to support HPC applications. The works has focused on using Xilinx hardware and the PowerPC, to accelerate basic matrix operations for the benchmark pHPCCG. In this presentation we will discuss FPGA basics and capabilities, the design tools and the various lessons learned. and the area’s where we see FPGA’s being able to contribute in the development of HPC. CSRI POC: Steve Owen, (505) 284-6599 |