Computational Homogenization with Million-way Parallelism using Domain Decomposition Methods

Parallel computational homogenization using the well-known FE2 approach is described and combined with fast domain decomposition and algebraic multigrid solvers. It is the purpose of this paper to show that and how the FE2 method can take advantage of the largest supercomputers available and those of the upcoming exascale era for virtual material testing of micro-heterogeneous materials such as advanced steel. The FE2 method is a computational micro-macro homogenization approach which incorporates micromechanical finite element simulations into macroscopic finite element simulations. In this approach, at each Gauß integration point of the macroscopic finite element problem a microscopic finite element problem, defined on a representative volume element (RVE), is attached. Note that the FE2 method is not embarassingly parallel since the RVE problems are coupled through the macroscopic problem. Numerical results are presented considering different grids on both, the macroscopic and microscopic level. Unstructured as well as structured grids with different irregular domain decompositions are considered on the microscale. Finally, weak scaling results from a few nodes up to a million parallel processes are presented