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Computational Science and N Body algorithms Illustrated by GEM: General Earthquake Simulation Project CPS615 Introduction to Computational Science October 98 2
Abstract of GEM Analysis for Computational Science 3
Earthquakes are Worldwide 4
Northridge Earthquake 1994 (Southern California) 5
Southern California Earthquake Activity 6
We need to predict earthquakes! 7
Possible Special Features of Earthquake Simulation 8
Basic Computational Structure - I 9
Basic Computational Structure - II 10
Analysis of Computational Structure 11
First two Solutions of O(N2) Computational Complexity 12
Second two Solutions of O(N2) Computational Complexity 13
Basic Idea of Fast Multipole Algorithm 14
Intermediate results of a computation of 322 million particles on ASCI Red 15
Intermediate results of a computation of 9.7 million particles on PC Cluster loki 16
Some Performance Results of Interest from Salmon and Warren 17
Hierarchical Breakup of 2D Space 18
Simple Illustration of Tree Data Structure 19
Tree Structure for 10,000 bodies centrally clustered in a disk 20
Generation of Tree for a small number of particles 21
3 Approximations to Force on a Particle in Fast Multipole Approach 22
Parallelism in O(N2) N Body Approach I 23
Parallelism in O(N2) N Body Approach II 24
Parallelism in Cut Off Force Approach 25
Problems in Cut off Force Parallelism 26
Cyclic and Block Decomposition for Graphics Ray Tracing 27
Generation of Keys in Salmon Warren Method 28
Generation of 3D Key for Salmon Warren 29
Parallelism in Salmon Warren Approach 30
Two Space Filling Curves 31
Morton Curve split up into 8 processors represented by different gray levels 32
Space Filling Curve chopped up into equal length parts 33
Parallel Algorithm in Fast Multipole I 34
Locally essential Data for Processor in Bottom Left Hand Corner of Processor Array 35
Parallel Algorithm in Fast Multipole II 36
Scaling Ideas in GEM 37
Different Physical Scales in GEM 38
Lessons from Other Fields
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