We have used data learning and low-precision computation to develop an implicit solver that demonstrates high performance up to 152,352 computer nodes (609,408 MPI processes × 12 OpenMP threads = 7,312,896 parallel computation) and conducted an unprecedented ultra-large-scale analysis of ultra-high-fidelity fault-structure systems using nonlinear dynamic finite element analysis on three-dimensional low-order unstructured elements. The developed solver achieved 25.45-fold speedup from the state of the art solver on Fugaku and attained weak scaling efficiency of 93.7% from 9.391 billion [email protected] computer nodes to 1.201 trillion [email protected],984 computer nodes on performance measurement problems. Moreover, a realistic 324 billion DOF application example, which is difficult to obtain performance for, was computed in high performance. Since the developed solver is based on a highly generalizable algorithm, it is expected to contribute not only to earthquake simulation on Fugaku but also to the enhancement of similar applications in other fields and on other supercomputers.

To realize numerical towing-tank tests by substantially shortening the time to the solution, a general-purpose Finite-Element flow solver, named FrontFlow/blue (FFB), has been fully optimized so as to achieve maximum possible sustained memory throughputs with three of its four hot kernels. A single-node sustained performance of 179.0 GFLOPS, which corresponds to 5.3% of the peak performance, has been achieved on Fugaku, the next flagship computer of Japan. A weak-scale benchmark test has confirmed that FFB runs with a parallel efficiency of over 85% up to 5,505,024 compute cores, and an overall sustained performance of16.7 PFLOPS has been achieved. As a result, the time needed for large-eddy simulation using 32 billion grids has been significantly reduced from almost two days to only 37 min., or by a factor of 71. This has clearly indicated that a numerical towing-tank could actually be built for ship hydrodynamics within a few years.

Numerical weather prediction (NWP) supports our daily lives. Weather models require higher spatiotemporal resolutions to prepare for extreme weather disasters and reduce the uncertainty of predictions. The accuracy of the initial state of the weather simulation is also critical; thus, we need more advanced data assimilation (DA) technology. By combining resolution and ensemble size, we have achieved the world’s largest weather DA experiment using a global cloud-resolving model and an ensemble Kalman filter method. The number of grid points was $\sim$4.4 trillion, and 1.3 PiB of data was passed from the model simulation part to the DA part. We adopted a data-centric application design and approximate computing to speed up the overall system of DA. Our DA system, named NICAM-LETKF, scales to 131,072 nodes (6,291,456 cores) of the supercomputer Fugaku with a sustained performance of 29 PFLOPS and 79 PFLOPS for the simulation and DA parts, respectively.

The general-purpose fluid simulation software FrontFlow/blue (FFB) is based on the finite element method (FEM). It was designed to accept extremely large-scale simulations and is an important application in the manufacturing field in Japan. Moreover, since this application is significant in both the manufacturing field and the development of the post-K supercomputer, it is employed as an important application for the new post-K supercomputer that is under development. The K computer is still the important infrastructure in Japan. And there are some supercomputers having the same architecture to the K computer. Therefore we continue to improve the performance of the FFB on the K computer. On significant subroutines, several improvement techniques, store order based loop modification decreasing total load and store operations, unrolled loop rerolling to employ SIMD load instruction, adjusting number of arrays in loop, using sector cache function, and so on, were employed. As a result, an improvement of 160% was obtained on a single CPU performance. This paper shows and discusses the detail of these improvements.

The process of performance tuning is time consuming and costly even if it is carried out automatically. It is crucial to learn from the experience of experts. Our long-term goal is to construct a database of facts extracted from specific performance tuning histories of computation-intensive applications such that we can search the database for promising optimization patterns that fit a given kernel.

To improve performance of large-scale scientific applications, scientists or tuning experts make various empirical attempts to change compiler options, program parameters or even the syntactic structure of programs. Those attempts followed by performance evaluation are repeated until satisfactory results are obtained. The task of performance tuning requires a great deal of time and effort. On account of combinatorial explosion of possible attempts, scientists/tuning experts have a tendency to make decisions on what to be explored just based on their intuition or good sense of tuning. We advocate evidence-based performance tuning (EBT) that facilitates the use of database of facts extracted from tuning histories of applications to guide the exploration of the search space. However, in general, performance tuning is conducted as transient tasks without version control systems. Tuning histories may lack explicit facts about what kind of program transformation contributed to the better performance or even about the chronological order of the source code snapshots. For reconstructing the missing information, we employ a state-of-the-art fine-grained change pattern identification tool for inferring applied transformation patterns only from an unordered set of source code snapshots. The extracted facts are intended to be stored and queried for further data mining. This paper reports on experiments of tuning pattern identification followed by predictive model construction conducted for a few scientific applications tuned for the K supercomputer.

This paper presents a new heroic computing method for unstructured, low-order, finite-element, implicit nonlinear wave simulation: 1.97 PFLOPS (18.6% of peak) was attained on the full K computer when solving a 1.08T degrees-of-freedom (DOF) and 0.270T-element problem. This is 40.1 times more DOF and elements, a 2.68-fold improvement in peak performance, and 3.67 times faster in time-to-solution compared to the SC14 Gordon Bell finalist's state-of-the-art simulation. The method scales up to the full K computer with 663,552 CPU cores with 96.6% sizeup efficiency, enabling solving of a 1.08T DOF problem in 29.7 s per time step. Using such heroic computing, we solved a practical problem involving an area 23.7 times larger than the state-of-the-art, and conducted a comprehensive earthquake simulation by combining earthquake wave propagation analysis and evacuation analysis. Application at such scale is a groundbreaking accomplishment and is expected to change the quality of earthquake disaster estimation and contribute to society.

In this paper, we develop a rank-mapping algorithm for an icosahedral grid system on a massive parallel computer with the 3-D torus network topology, specifically on the K computer. Our aim is to improve the weak scaling performance of the point-to-point communications for exchanging grid-point values between adjacent grid regions on a sphere. We formulate a new rank-mapping algorithm to reduce the maximum number of hops for the point-to-point communications. We evaluate both the new algorithm and the standard ones on the K computer, using the communication kernel of the Nonhydrostatic Icosahedral Atmospheric Model (NICAM), a global atmospheric model with an icosahedral grid system. We confirm that, unlike the standard algorithms, the new one achieves almost perfect performance in the weak scaling on the K computer, even for 10,240 nodes. Results of additional experiments imply that the high scalability of the new rank-mapping algorithm on the K computer is achieved by reducing network congestion in the links between adjacent nodes.

Real space DFT (RSDFT) is a simulation technique most suitable for massively-parallel architectures to perform first-principles electronic-structure calculations based on density functional theory. We here report unprecedented simulations on the electron states of silicon nanowires with up to 107,292 atoms carried out during the initial performance evaluation phase of the K computer being developed at RIKEN.

Abstract In this research, we focus on improving the performance of GeoFEM on a single processor using a common data structure and coding approach in order to optimize GeoFEM for implementation on various computer architectures including parallel systems. A new data structure and direct access coding are developed for fluid analysis and they are implemented on scalar, vector, and pseudovector architectures. A 17% increase in peak performance is obtained on pseudovector and scalar architectures, and a 20% peak performance improvement is achieved on vector architecture. By applying a new direct access coding approach, the peak performance of the structure solver is increased by 23% on pseudovector architecture and 28% on vector architecture. Architecture‐independent matrix assembly coding is developed and evaluated on vector and scalar machines. A performance of 736.8 flops is obtained for the matrix assembly process and 900.7 Mflops for the entire code on an NEC SX‐4 supercomputer. An average of 2.06 Gflops performance is obtained on a Fujitsu VPP5000 (peak: 9.6 Gflops), and 124 Mflops is obtained for the matrix assembling process on a 533‐MHz 21164 Alpha system. Copyright © 2002 John Wiley & Sons, Ltd.