Parallelization of Topology Based Construction of Localization Map between Simplex Finite Element Meshes

摘要

This paper deals with the transfer of finite element data between simplex, mutually incompatible, finite element meshes representing the same geometrical model. The work focuses on a construction of the localization map defining for each node of the target mesh, onto which the data are to be transferred, the closest element of the original source mesh. Instead of adopting commonly applied strategies constructing the map using a spatial index based on various tree or dynamic cell data structures, a different approach utilising the topology of the mesh is introduced. The actual localization is performed using a walking algorithm, which is based on the traversal between neighbouring elements of the source mesh from an initial element towards the processed node. The individual nodes of the target mesh are processed in an appropriate order given by the nodal connectivity of the target mesh and controlled by a queue which ensures that only those target nodes that have a neighbouring processed node, are ready for localization. To make the algorithm efficient and reliable, its implementation also relies on the classification of the processed meshes to the underlying geometrical model. The paper also elaborates a simple strategy for the parallelization of the construction of the localization map using the domain decomposition concept. The performance of the proposed approach is demonstrated on a three-dimensional real-world example using a shared memory parallel computing architecture.