Basic IMAGE version of Foils prepared 22 February 1998

Foil 7 Equations of Motion -- Newton's Second Law

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- 1998 Enhancements. by Geoffrey C. Fox
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Table of Contents for N Body Problems using Data parallel Approach

CPS 615 1998 Update for N body Simple Algorithm with Data parallel F90/HPF
1 CPS 615 -- Computational Science in
Simulation Track
Data Parallel Module on ODE's and Particle Dynamics
February 20, 1998
2 Abstract of Message Parallel ODE and Particle Dynamics
Particle Dynamics as applications
3 Particle (N-Body) Applications and Ordinary Differential Equations (ODE's)
4 Particle Applications - Ordinary Differential Equations (ODE's)
5 Particle Applications - the N-body problem
6 Newton's First Law -- The Gravitational Force on a Particle
7 Equations of Motion -- Newton's Second Law
ODE Solution Techniques
8 Numerical techniques for solving ODE's
9 Second and Higher Order Equations
10 Basic Discretization of Single First Order Equation
11 Errors in numerical approximations
12 Runge-Kutta Methods: Euler's method
13 Estimate of Error in Euler's method
14 Relationship of Error to Computation
15 Example using Euler's method from the CSEP book
16 Approximate solutions at t=1,using Euler's method with different values of h
17 Runge-Kutta Methods: Modified Euler's method
18 Approximate solutions of the ODE for et at t=1, using modified Euler's method with different values of h
19 The Classical Runge-Kutta -- In Words
20 The Classical Runge-Kutta -- Formally
21 The Classical Runge-Kutta Pictorially
22 Predictor / Corrector Methods
23 Definition of Multi-step methods
24 Features of Multi-Step Methods
25 Comparison of Explicit and Implicit Methods
Setup of N Body Problem
26 Solving the N-body equations of motion
27 Representing the Data Parallel N-Body problem
28 Form of the Computation -- Data v. Message Parallel
29 Summary of Parallel N-Body Programming Methods and Algorithms
30 Status of Parallelism in Various N Body Cases
31 Other N-Body Like Problems - I
32 Other N-Body Like Problems - II
Simple Data Parallel Approach
33 N-body Runge Kutta Routine in Fortran90 - I
34 Runge Kutta Routine in Fortran90 - II
35 Computation of accelerations - a simple parallel array algorithm
36 Simple Data Parallel Version of N Body Force Computation -- Grav -- I
37 The Grav Function in Data Parallel Algorithm - II
Problems with Simple Method
38 Some Inefficiencies of the Data Parallel N2 Algorithm - I
39 Some Inefficiencies of the Data Parallel N2 Algorithm - II
Data Parallel Pipeline Algorithm
40 Better Data Parallel Pipeline Algorithm for Computation of Accelerations,
taking 1/2 the time for iterations over force computation
41 Data Parallel Pipeline Algorithm in detail
42 Basic Data Parallel pipeline operation
43 Examples of Data Parallel Pipeline Algorithm
44 Data Parallel Pipeline Algorithm Grav -- Part I
45 Data Parallel Pipeline Algorithm for Grav -- Part II
46 Data Parallel Grav Pipeline Algorithm, concluded
Performance Issues
47 Data Parallel Parallel Decomposition
48 Data Parallel Parallel Execution Time -I
49 Data Parallel Parallel Execution Time -II
One Dimensional System Dimension
50 N-body Problem is a one dimensional Algorithm
HPF Version
51 Excerpts from an HPF program for this algorithm
52 HPF program excerpts - II
53 HPF program excerpts - finished
References
54 Notes and References
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