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N Body Problems using Data parallel Approach
Given by Geoffrey C. Fox at CPS615 Basic Simulation Track for Computational Science on 1998 Enhancements. Foils prepared 22 February 1998
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This uses the simple O(N2) Particle Dynamics Problem as a motivator to discuss solution of ordinary differential equations
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We discuss Euler, Runge Kutta and predictor corrector methods
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F90 and HPF Data parallel O(N2) algorithms are described with performance comments
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There is a related message parallel module sharing the same initial foils
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This mixed presentation uses parts of the following base foilsets which can also
be looked at on their own!
CPS615-95E CPS615 Foils -- set E: ODE's and Particle
Dynamics
CPS 615 1998 Update for N body Simple Algorithm with Data parallel F90/HPF
CPS615-95E 073 001 CPS 615 -- Computational Science in
Simulation Track
Data Parallel Module on ODE's and
Particle Dynamics
February 20, 1998
CPS615-95E 074 002 Abstract of Message Parallel ODE and
Particle Dynamics
Particle Dynamics as applications
CPS615-95E 003 003 Particle (N-Body) Applications and
Ordinary Differential Equations
(ODE's)
CPS615-95E 004 004 Particle Applications - Ordinary
Differential Equations (ODE's)
CPS615-95E 005 005 Particle Applications - the N-body
problem
CPS615-95E 006 006 Newton's First Law -- The
Gravitational Force on a Particle
CPS615-95E 007 007 Equations of Motion -- Newton's
Second Law
ODE Solution Techniques
CPS615-95E 008 008 Numerical techniques for solving
ODE's
CPS615-95E 009 009 Second and Higher Order Equations
CPS615-95E 010 010 Basic Discretization of Single First
Order Equation
CPS615-95E 011 011 Errors in numerical approximations
CPS615-95E 012 012 Runge-Kutta Methods: Euler's method
CPS615-95E 013 013 Estimate of Error in Euler's method
CPS615-95E 014 014 Relationship of Error to Computation
CPS615-95E 015 015 Example using Euler's method from
the CSEP book
CPS615-95E 016 016 Approximate solutions at t=1,using
Euler's method with different values
of h
CPS615-95E 017 017 Runge-Kutta Methods: Modified
Euler's method
CPS615-95E 018 018 Approximate solutions of the ODE for
et at t=1, using modified Euler's
method with different values of h
CPS615-95E 019 019 The Classical Runge-Kutta -- In
Words
CPS615-95E 020 020 The Classical Runge-Kutta --
Formally
CPS615-95E 021 021 The Classical Runge-Kutta
Pictorially
CPS615-95E 022 022 Predictor / Corrector Methods
CPS615-95E 023 023 Definition of Multi-step methods
CPS615-95E 024 024 Features of Multi-Step Methods
CPS615-95E 025 025 Comparison of Explicit and Implicit
Methods
Setup of N Body Problem
CPS615-95E 026 026 Solving the N-body equations of
motion
CPS615-95E 027 027 Representing the N-Body problem
CPS615-95E 028 028 Form of the Computation -- Data v.
Message Parallel
CPS615-95E 053 029 Summary of Parallel N-Body
Programming Methods and Algorithms
CPS615-95E 054 030 Status of Parallelism in Various N
Body Cases
CPS615-95E 055 031 Other N-Body Like Problems - I
CPS615-95E 056 032 Other N-Body Like Problems - II
Simple Data Parallel Approach
CPS615-95E 029 033 N-body Runge Kutta Routine in
Fortran90 - I
CPS615-95E 030 034 Runge Kutta Routine in Fortran90 -
II
CPS615-95E 031 035 Computation of accelerations - a
simple parallel array algorithm
CPS615-95E 032 036 Simple Data Parallel Version of N
Body Force Computation -- Grav -- I
CPS615-95E 033 037 The Grav Function in Data Parallel
Algorithm - II
Problems with Simple Method
CPS615-95E 034 038 Some Inefficiencies of the Data
Parallel N2 Algorithm - I
CPS615-95E 035 039 Some Inefficiencies of the Data
Parallel N2 Algorithm - II
Data Parallel Pipeline Algorithm
CPS615-95E 036 040 Better Data Parallel Pipeline
Algorithm for Computation of
Accelerations,
taking 1/2 the iterations of force
computation - I
CPS615-95E 037 041 Data Parallel Pipeline Algorithm in
detail
CPS615-95E 038 042 Basic Data Parallel pipeline
operation
CPS615-95E 039 043 Examples of Data Parallel Pipeline
Algorithm
CPS615-95E 040 044 Data Parallel Pipeline Algorithm
Grav -- Part I
CPS615-95E 041 045 Data Parallel Pipeline Algorithm for
Grav -- Part II
CPS615-95E 042 046 Data Parallel Grav Pipeline
Algorithm, concluded
Performance Issues
CPS615-95E 043 047 Data Parallel Parallel Decomposition
CPS615-95E 044 048 Data Parallel Parallel Execution
Time -I
CPS615-95E 045 049 Data Parallel Parallel Execution
Time -II
One Dimensional System Dimension
CPS615-95E 046 050 N-body Problem is a one dimensional
Algorithm
HPF Version
CPS615-95E 047 051 Excerpts from an HPF program for
this algorithm
CPS615-95E 048 052 HPF program excerpts - II
CPS615-95E 049 053 HPF program excerpts - finished
References
CPS615-95E 050 054 Notes and References
List of Foils Used as they occur
CPS615-95E CPS615 Foils -- set E: ODE's and Particle
Dynamics
73 74 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 53 54 55 56 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Sorted List of Foils Used
CPS615-95E CPS615 Foils -- set E: ODE's and Particle
Dynamics
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 53 54 55 56 73 74
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