**
Parallelization of Topology Based Construction of Localization Map**

between Simplex Finite Element Meshes

**
Daniel Rypl
**

Department of Mechanics

Faculty of Civil Engineering

Czech Technical University in Prague

Thákurova 7, 166 29 Prague, Czech Republic

### Abstract:

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 as neighbour already 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.