In finite element simulations, the handling of geometrical objects is a critical aspect in both serial and parallel software environments.
The main focus of my research is to investigate two topics related to this aspect, information transfer and parametric finite elements.
The first topic is about stable and efficient techniques for the transfer of discrete fields between non matching volume or surface meshes are an essential ingredient for the discretization and numerical solution of coupled multi-physics or multi-scale problems, and mesh refinement or remeshing. In particular, L2-projections allows for the transfer of discrete fields between unstructured meshes, both in the volume and on the surface. We developed an algorithm for parallelizing the assembly of the L2-transfer operator for unstructured meshes which are arbitrarily distributed among different processes. This algorithm requires no a priori information on the geometrical relationship between the different meshes.
The second topic is about the possible applications of mixing parametric finite-elements together with methods from geometry-processing, such as barycentric coordinates and bijective mappings between polygons or polyhedra.
These ideas are to be developed within MOONoLith (Multipurpose Object Oriented Numerics Library).
A Parallel Approach to the Variational Transfer of Discrete Fields between Arbitrarily Distributed Finite Element Meshes;