High Performance Earthquake Simulations
Alexander Breuer · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2015
i algorithm 7 2 numerics 9 2.1 Reference Coordinates 9 2.2 Basis Functions 11 2.3 Global Matrices 12 2.4 Elastic Wave Equations 13 2.5 Spatial Discretization 15 2.6 Weak Formulation 16 2.7 Time Prediction 16 2.8 Volume Integration 17 2.9 Surface Integration 18 2.10 Time Stepping 21 3 clustered local time stepping 23 3.1 LTS Relations 23 3.2 Clustering 27 3.3 Multiple Partitions 28 3.4 Time Management 33 3.5 Scheduling 36 ii supercomputing 47 4 systems 49 5 data structures 53 5.1 Matrix Structures 53 5.2 LTS Bitmask 56 5.3 Memory Layout 58 6 shared and distributed memory 65 6.1 OpenMP 65 6.2 Message Passing Interface 66 7 computational kernels 69 7.1 ADER-DG Kernels 69 7.2 Matrix Kernels 77 7.3 Arithmetic Intensity 80 7.4 Auto-Tuning 82 iii simulations 93 8 single node and small-scale 95 8.1 LOH.1 95 8.2 Global Time Stepping 95 8.3 Local Time Stepping 99 v vi contents 9 1+ trillion degrees of freedom 107 9.1 Cube 107 9.2 Weak Scaling 110 10 petascale multiphysics 115 10.1 1992 Landers 115 10.2 Strong Scaling 117 10.3 Production 121 11 petascale local time stepping 127 11.1 Mount Merapi 127 11.2 LTS in Theory 127 11.3 Strong Scaling 133 11.