A low-order implicit unstructured finite-element solver for Earth's crust deformation problem is proposed. The solver scales up to 294,912 CPU cores of K computer with 94.8% size-up efficiency, enabling solving a 504 billion degrees-of-freedom crust deformation problem with 126 billion second-order tetrahedral elements in 146.5 s at 0.970 PFLOPS (20.6% of peak) on 294,912 CPU cores. This is 11.1 times faster than a highly-tuned preconditioned conjugate gradient solver and 2.18 times faster than the state-of-the-art SC14 Gordon Bell Prize Finalist solver. With the proposed solver, we solved a practical 381 billion degrees-of-freedom Eastern Japan crust deformation problem (576 km x 800 km x 400 km area; resolution of 62.5 m) in 252.2 s using 294,912 CPU cores. Such high-resolution analysis assures the convergence of stress and strain required to evaluate nonlinear material constitutive models at plate boundaries and is expected to become a key tool for physics-based earthquake forecasting.

We present a scalable high-performance computing implementation of an agent-based economic model using distributed + shared-memory hybrid parallelization paradigms, capable of simulating 1:1 scale models of large economies like the eurozone. Agent-based economic models consist of millions of agents interacting over several graphs, which are either centralized or scale-free in nature. While most of the interactions are bi-directional, the interaction graphs are dense and random and keep evolving as the simulation progresses. These characteristics cause a very large and unknown number of random communications among MPI processes, posing challenges to developing scalable parallel extensions. Further, random access to large volume of data makes the algorithms highly memory-bound, severely degrading computational performance. Adopting various strategies inspired by the real-world functioning of economies, we reduce the large unknown number of communications to a known handful number. Memory-intensive algorithms are improved to make these cache-efficient, and advanced MPI functions are used to minimize communication overhead, thereby attaining higher performance and scalability. Further, an MPI + OpenMP hybrid model is developed to best utilize modern many-core computing nodes with low per-core memory capacity. It is demonstrated that our implementation can simulate a full fledged economic model with 331 million agents within 108 seconds using 128 CPU cores attaining 70 percent strong scalability.

We developed an unstructured finite element mesh generation method capable of modeling multiple-material complex geometry problems for large-scale seismic analysis of soil-structure systems. We used an octree structure to decompose the target domain into small subdomains and use the multiple material marching cubes method for robust and parallel tetrahedralization of each subdomain. By using the developed method on a 32 core shared memory machine, we could generate a 594,168,792 tetrahedral element soil-structure model of a power plant in 13 h 01 min. The validity of the generated model was confirmed by conducting a seismic response analysis on 2,304 compute nodes of the K computer at RIKEN. Although the model contains a small approximation in geometry (half of the minimum octree size) at present, we can expect fast and high quality meshing of large-scale models by making geometry correction in the future, which is expected to help improve the seismic safety of important structures and complex urban systems.