Computational homogenization at extreme scales

Abstract

Multi-scale simulations at extreme scales in terms of both physical length scales and computational resources are presented. In this letter, we introduce a hierarchically parallel computational homogenization solver that employs hundreds of thousands of computing cores and resolves O(10 5) in material length scales (from O(cm) to O(100 nm)). Simulations of this kind are essential in understanding the multi-scale essence of many natural and synthetically made materials. Thus, we present a simulation consisting of 53.8 Billion finite elements with 28.1 Billion nonlinear equations that is solved on 393,216 computing cores (786,432 threads). The excellent parallel performance of the computational homogenization solver is demonstrated by a strong scaling test from 4,096 to 262,114 cores. A fully coupled multi-scale damage simulation shows a complex crack profile at the micro-scale and the macroscopic crack tunneling phenomenon. Such large and predictive simulations are an important step towards Virtual Materials Testing and can aid in development of new material formulations with extreme properties. Furthermore, the high computational efficiency of our computational homogenization solver holds great promise for utilizing the next generation of exascale parallel computing platforms that are expected to accelerate computations through orders of magnitude increase in parallelism rather than speed of each processor.

Large-scale simulations of quasi-brittle microcracking in realistic highly heterogeneous microstructures obtained from micro CT imaging

“…It shows that the presented simulations can be conducted on classical machines, but that a very large space for improvement of computational times is possible, by using massively parallel computers, such as e.g. in [15,17].…”

“…all pores, gravels, sand grains, initial microcracks... present, for instance, in a concrete sample, is nowadays still out of reach. In [17,16], Mosby and Matouš developed hierarchically parallel solvers based on multi-scale simulations on extreme scales in terms of both physical length scales and computed capabilities resources, and show the ability to efficiently compute the failure of heterogeneous samples from sub-micrometer to centimeter scales in damage mechanics problems of particle-reinforced adhesives. In [24], another multiscale framework using large-scale simulations at the microstructural level has been proposed to study cracking in a ultra-high strength steel.…”

“…Such simulations can be either used within multiscale simulations such as in [17,16,24], or in combined experiments/simulations sub-volume techniques as described in [18] to accurately describe the damage due to microscale cracking.…”

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

“…In particular, we demonstrate this ideal scaling behavior through simulation of a patch test (see schematic inset of Figure 12) using the Vulcan supercomputer at Lawrence Livermore National Laboratory (LLNL) (Mosby and Matouš, 2016).…”

“…The complete multiscale simulation contains 747M finite elements and 396M DOFs. This scaling study was performed using the Vulcan machine at LLNL (from Mosby and Matouš, 2016). …”