A parallel approach to the variational transfer of discrete fields between arbitrarily distributed unstructured finite element meshes

An essential ingredient for the discretization and numerical solution of coupled multiphysics or multiscale problems is stable and efficient techniques for the transfer of discrete fields between nonmatching volume or surface meshes. Here, we present and investigate a new and completely parallel approach. It allows for the transfer of discrete fields between unstructured volume and surface meshes, which can be arbitrarily distributed among different processors. No a priori information on the relation between the different meshes is required. Our inherently parallel approach is general in the sense that it can deal with both classical interpolation and variational transfer operators, e.g., the L²-projection and the pseudo-L2-projection. It includes a parallel search strategy, output dependent load-balancing, and the computation of element intersections, as well as the parallel assembling of the algebraic representation of the respective transfer operator. We describe our algorithmic framework and its implementation in the library MOONoLith. Furthermore, we investigate the efficiency and parallel scalability of our new approach using different examples in three dimensions. This includes the computation of a volume transfer operator between 2 meshes with 2 billion elements in total and the computation of a surface transfer operator between 14 different meshes with 5:9 billion elements in total. The experiments have been performed with up to 12;288 cores.