Computational homogenization with million-way parallelism using domain decomposition methods

Abstract

Parallel computational homogenization using the well-known FE 2 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 FE 2 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 FE 2 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 FE 2 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 micro-This work was supported in part by Deutsche Forschungsgemeinschaft (DFG) through the Priority Programme 1648 "Software for Exascale Computing" (SPPEXA) under grants KL 2094/4-1, KL 2094/4-2, RH 122/2-1, and RH 122/3-2.

Exa-Dune—Flexible PDE Solvers, Numerical Methods and Applications

“…The global macro grid T H can be any MPI-enabled DUNE grid manager with adjustable overlap size for the domain decomposition, we currently use DUNE-YASPGRID. The fine grids τ h (T ) are constructed using the same grid manager as on the macro scale, with MPI subcom-municators.These are currently limited to a size of one (rank-local), however the overall scalability could benefit from dynamically sizing these subcommunicators to balance communication overhead and computational intensity as demonstrated in [36,Sec. 2.2].…”

Fully-coupled micro–macro finite element simulations of the Nakajima test using parallel computational homogenization

“…In this article, we consider the numerical simulation of the Nakajima test on high-performance computers using our highly scalable software package FE2TI [26], which combines an implementation of the computational homogenization approach FE 2 [17,39,45,54,56] with different and sparse direct solver packages such as PARDISO [52], MUMPS [1], and UMFPACK [11].…”

“…This motivates the use of homogenization methods. Here, the FE 2 computational homogenization method was chosen; see also our earlier publications [26,32] on the use of FE 2 within the EXASTEEL project, which was part of the DFG priority program 1648 "Software for Exascale Computing" (SPPEXA, [12]); see Sect. 2 and the acknowledgements.…”

“…In this paper, we will describe the software enhancements that were necessary to perform the simulation of the Nakajima test using our FE2TI software package [26]. This includes the implementation of a frictionless contact formulation on the macroscopic level using a penalty method, the incorporation of the blank holder and the die into the simulation to approximate the real test setup as good as possible, and the choice of suitable boundary conditions.…”

“…Furthermore, we highlight the effects of improved initial guesses for each load step using an extrapolation strategy as well as using an adaptive load step strategy. Our further advances, compared to [26] and [32] include a parallel Newton-Krylov-BDDC (NK-BDDC) approach (based on [27]) applied to the macroscopic problem, which replaces Newton-Krylov-BoomerAMG used earlier.…”