はじめに・有限要素法入門（Ⅰ） - nkl.cc.u ...

1 I I 2011 I 4820-1027 I 4810-1204 Intro-01 2 ? Intro-01 3 I 4820-1027 I 4810-1204 I 48101204 Intro-01 4 2007 3F 27219 3F 27219 il e-mail 1/2 5

2 ECCS2008 Intro-01 2/2 6 SMASH Science-Modeling- SMASH ScienceModelingAlgorithm-Software-Hardwa re Intro-01 7 Intro-01 1/2 8 Intro-01 2/2 9

3 Intro-01 10 HPC HPC 2008 2 1990 21 COE 21 Intro-01 HPC High-Performance Computing 11 HPC HighPerformance Computing T2K Intro-01 12 HPC Intro-01 13 HPC 4S HPC 4S ppOpen-HPC ppOpen-HPC

4 One-domain meshUtilitiesPluggable Analysis Modules Static linear DynamicStructureFluidWaveOne-domain meshUtilitiesPluggable Analysis Modules Static linear DynamicStructureFluidWaveiiFDMFEMBEMDEMp pOpen-APPLFVMUser s ProgramPartitioner Dynamic linear Contact Dynamic linear Contact meshPEEquationsolversVisualizerParallelI /OPartitioned meshiiFTCOMMppOpen-SYSppOpen-HPCV isualization dataGPPViewPEsVisualization dataGPPViewPEsOptimized Application with Optimized ppOpen-APPL, ppOpen-MATHI ntro-014S4S 44 SS SystemSystemStageStageStatus StyleStatus Style14 44 SS SystemSystem StageStage, Status, Style, Status.

5 Style System Stage 4 System SMASH Stage 4 AASSMM dlidliSSciencecience AASSHH AAlgorithmlgorithmMModelingodeling SSMMAASSHHSS oftwareoftwareAAlgorithmlgorithm SSMMAASSHHHH ardwareardwareIntro-014S4S 44 SS SystemSystemStageStageStatus StyleStatus Style15 44 SS SystemSystem Stage, Stage, Status, StyleStatus.

6 Style System Stage 4 System SMASH Stage 4 St t Status HPC Style Style e-Learning Intro-01 16 3 Intro-01 17 SMASH

7 4 Intro-01 2/2 18 Intro-01 19 2008 I I I II FEM FEM 2009 2009 I II II 2010 I II 2011 I I II IIIntro-0120 ?

8 Intro-01 21 Taylor Taylor Intro-01 1/3 22 1/3 =12xxdxdxBFdxdmax22@0,0@0,0=====+ xxBFxBFmax221+ = BF =0 =0 Intro-01 2/3 23 2/3 xxBFxBFmax221+ = X=X XXmax =0X=0X=0 x= =50 Xmax= X 49 0 BF 1 0d0 12255985051200495494912+ + X BF= + = + = Intro-01 24 Finite Difference Method Finite Difference Method i-1 i i+1 x xIntro-01

9 25 i i+1 i i+1 i-1 i i+1d x x xdxdiii ++ 12/1 x 0 i 11112/12/122xxdxddxddiiiiiiiii+ = = + + + 22xxxdxi = = Intro-01 Taylor 1/3 26 Taylor 1/3 i-1 i i+1 x x()()Kiixxx + + +=+3332221 iiiiixxx +321!3!2 ()()Kiiiiixxxxxx + = 3332221!3!2 iii Intro-01 Taylor 2/3 27 Taylor 2/3 i-1 i i+1 x x()()xx 3322 ()()Kiiiiixxxxxx + + +=+321!

10 3!2 ()() 322 ()()Kiiiiixxxxxx + + = +332221!3!2 x ()()xx 3322 ()()Kiiiiixxxxxx + = 321!3!2 ()()iixx 3221 ()()Kiiiiixxxxxx + + = 321!3!2 x Intro-01 Taylor 3/3 28 Taylor 3/3 i-1 i i+1 x x()() 3322 ()()Kiiiiixxxxxx + + +=+3332221!3!2 ()()Kiixxxxxx + = 3332221!