JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11 doi: /jamstecr.23.1 A Performance Optimization of the Large-Scale Seismic Simulation on
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1 JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11 doi: /jamstecr.23.1 A Performance Optimization of the Large-Scale Seismic Simulation on the Earth Simulator (ES2) Yuichi Hirokawa 1, Toshiyuki Masatsuki 2, Noriaki Nishikawa 1, Misako Iwasawa 1, and Toshiyuki Asano 1 The understanding and prediction of influences caused by seismic wave ranges from low to high frequency is important to mitigate the disaster of earthquakes by multilateral preparations. The structure of undergrounds causes the complex behavior of seismic wave propagation. The numerical simulation is an effective tool to predict the wave propagation. For metropolises on a large plain such as Kanto basin, however, the simulation requires enormous computing resources as well as techniques of high-performance computing. In this paper, we have developed the optimization method for the seismic simulation code on the Earth Simulator (ES2). We assume the finite difference method code k-fdm3d developed by KOZO KEKAKU ENGINEERING Inc.. Because the code adopt a stencil computation with the structured grid, we have optimized the memory-access and communication of the computation. For the reasons, the optimization method has applicability to simulation code on the other fields. The method enables a 570 million grids seismic simulation on ES2. The method also allows the simulation to achieve approximately 30% to the peak performance of ES2. For the results, we have established the optimization method to calculate the high-accuracy prediction of seismic wave propagation applicable for a large plain. Keywords : Seismic wave, Simulation, The Earth Simulator, Parallelization, Optimization Received 9 March 2016 ; Revised 28 April 2016 ; Accepted 9 May Center for Earth Information Science and Technology (CEIST), Japan Agency for Marine-Earth Science and Technology (JAMSTEC) 2 KOZO KEIKAKU ENGINEERING Inc. Corresponding author: Yuichi Hirokawa Center for Earth Information Science and Technology, Japan Agency for Marine-Earth Science and Technology Showa-machi, Kanazawa-ku, Yokohama, Kanagawa , Japan y-hiroka@jamstec.go.jp Copyright by Japan Agency for Marine-Earth Science and Technology 1
2 ES2 A Performance Optimization of the Large-Scale Seismic Simulation on the Earth Simulator (ES2) doi: /jamstecr k-fdm3d ES2 ES y-hiroka@jamstec.go.jp 2 JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11
![Y. Hirokawa et al. 2 20[s] 0.5[Hz] 2[s] 0.5[Hz] 2012 2009 Seism3D3 Furumura and Chen, 2005; Furumura and Saito, 2009 2009a; 2010 1 2[](/docs-images/101/150283957/images/3-0.jpg "Hz] ES2 k-fdm3d ES2 3 2 3 4 5 6 2.1 2.")
3 Y. Hirokawa et al. 2 20[s] 0.5[Hz] 2[s] 0.5[Hz] Seism3D3 Furumura and Chen, 2005; Furumura and Saito, a; [Hz] ES2 k-fdm3d ES ES2 k-fdm3d 1 Navier ρü = (λ + μ) ( u) + μδu + F (1) ρ F λ μ ü Δ ü 4 ü ü Staggered 2 Verlet Leap Frog 2009b Fortran 90 MPI ES2 1 ES2 ES2 NEC SX9/E GByte/s JAMSTEC, 2008 Fig. 1. The configuration of the Earth Simulator (ES2). 1. ES2 JAMSTEC Rep. Res. Dev., Volume 23, September 2016,
4 ES2 A Performance Optimization of the Large-Scale Seismic Simulation on the Earth Simulator (ES2) 2 Fat-Tree 1 3 RTR CPU 128 GByte 8 KByte 64 1 MMU 16 RTR 256 MMU CPU 1 CPU GFLOPS 16 Byte 1 16,384 way 16,384 16,384 Load/Store 2.5 Byte/FLOP CPU Assignable Data Buffer ADB 256 KByte, 4 Byte/FLOP Nakazato et al., 2008 ADB Least Recently Used 2 Load 2009 ES2 k-fdm3d Fortran 90 3 ES Byte 16,384 8 Byte 32,768 4 Byte 65,536 ES2 16 Byte Load/Store Load/Store 4 1 Load/Store IDIM 1 i, j, k Load/Store 4 Bank Load/Store Load/Store 4 Bank00000 Load/Store Load/Store Load/Store Load/Store 4 1 ES2 16 Byte 1 Load/Store 2 Fig. 2. The architecture of the NEC SX9/E Fig. 3. The memory mapping of an array in Fortran JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11
5 Y. Hirokawa et al. Fig. 4. The memory access. left: original, right: optimized / upper: i-direction, middle: j-direction, lower: k-direction 図 4. メモリアクセス 左 オリジナル 右 最適化 / 上 i 方向 中 j 方向 下 k 方向 JAMSTEC Rep. Res. Dev., Volume 23, September 2016,
6 ES2 A Performance Optimization of the Large-Scale Seismic Simulation on the Earth Simulator (ES2) 1 16 Byte IDIM%(16 Byte/NByte) = 0 (2) N 1 Byte 8 Byte N = 8 1 IDIM IDIM/(16 Byte/NByte) %2 = 1 (3) 2 3 IDIM Bank00000 Load/Store Bank Bank00000 Load/Store Bank Z 5 V 3 K 3 5 dzv Z V!CDIR NEC SX NByte V 4 Load IDIM*JDIM*NByte i k j i j k k 16 5!CDIR OUTERUNROLL=16 2 Load V ADB 5!CDIR ON_ADB(V) j k ADB & ES ADB ADB ADB Load k k + 1 V 3 Load ADB Load ADB Read Only Memory Store Y 7 V J 7 dyv Y IDIM*NByte i j k j 16 7!CDIR OUTERUNROLL=16 2 Load V ADB 7!CDIR ON_ADB(V) Fig. 5. The optimized code in the direction Z. 5. Z Fortran 90 Fig. 6. The memory access in the direction Z. 6. Z 6 JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11
7 Y. Hirokawa et al. ADB ES2 & j j + 1 V 3 Load ADB X 9 V I 9 dxv X ES2 SX Load ADB 10 4 Load 2012 NEC SX-7 ADB Miss Status Handling Register MSHR ES2 11 j i k 11!CDIR NOLOOPCHG i 32 11!CDIR OUTERUNROLL=32 2 Load V ADB 11!CDIR ON_ADB(V) ES2 & j i i + 1 Fig. 9. The memory access in the direction X. 9. X Fig. 7. The optimized code in the direction Y. 7. Y Fortran 90 Fig. 10. The bank conflict in the direction X. 10. X Fig. 8. The memory access in the direction Y. 8. Y Fig. 11. The optimized code in the direction X. 11. X Fortran 90 JAMSTEC Rep. Res. Dev., Volume 23, September 2016,
8 ES2 A Performance Optimization of the Large-Scale Seismic Simulation on the Earth Simulator (ES2) 4 Load 3 ADB ES2 16 Byte Load 1 ADB 12 V i = 2 5 Load i = 1 6 Load i = 3 6 ADB 1 1 Non-blocking Non-blocking 2001 CPU 1 k-fdm3d IDIM = 1, 024 JDIM = 1, 280 KDIM = CPU Z 2.5 ADB k-fdm3d IDIM = 1, 024 JDIM = 1, 280 KDIM = CPU CPU CPU CPU Table 1. The performance comparison of optimization CPU Fig. 12. The memory access in the direction X. 12. X [s] GFLOPS (1CPU) JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11
9 Y. Hirokawa et al. k-fdm3d 1 CPU IDIM = 512, JDIM = 640, KDIM = 170 CPU CPU 1 16 CPU 8 CPU 14 CPU ES2 1,024 CPU CPU CPU CPU 3 8 CPU CPU [%] 1 8 CPU [%] MPI [%] Fig. 14. The scalability (weak scaling) 14. Table 3. The bank conflict caused by CPUs. 3. CPU Fig. 13. The speed-up ratio (strong scaling) 13. GFLOPS [s] [s] (1CPU) 8CPU 1NODE CPU 2NODE CPU 4NODE CPU 8NODE CPU 1NODE CPU 2NODE CPU 4NODE CPU 8NODE Table 2. The summary of optimization technique CPU [ ] Z Y X ( ) ( ) ( ) ( ) JAMSTEC Rep. Res. Dev., Volume 23, September 2016,
10 ES2 A Performance Optimization of the Large-Scale Seismic Simulation on the Earth Simulator (ES2) ES2 3 CPU CPU Load CPU CPU 2, CPU 1,024 CPU x y NEC/SX-9 NEC/SX-ACE MSHR CPU ES Fig. 15. The example of restricting bank allocation. 15. FlatMPI Furumura, T. and L. Chen (2005), Parallel simulation of strong ground motions during recent and historical damaging earthquake in Tokyo, Japan, Parallel Computing, 31, Furumura, T. and T. Saito (2009), Integrated Ground Motion and Tsunami Simulation for the 1944 Tonankai Earthquake Using High-Performance Superconputers, Journal of Disaster Research, 4(2), a 3 21 < furumura.pdf>. 2009b S83-S T2K < JAMSTEC (2008), The outline of the Earth Simulator (ES2), < system1.pdf> CFD - 42, SIG 9 (HPS3), Nakazato S., S. Tagaya, N. Nakagomi, T. Watai, A. Sawamura (2008), Hardware Technology of the SX-9 (1)- Main System -, NEC Technical Journal, 3(4), JAMSTEC Rep. Res. Dev., Volume 23, September 2016, 1 11
11 Y. Hirokawa et al. MSHR ARC-184(6), II JAMSTEC Rep. Res. Dev., Volume 23, September 2016,
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