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CPS615-End of N-Body Discussion and Beginning of Numerical Integration

Given by Geoffrey C. Fox at Delivered Lectures of CPS615 Basic Simulation Track for Computational Science on 15 October 96. Foils prepared 12 November 1996

This finishes the last part of N body and ODE discussion fociussing on pipeline data parallel algorithm
Note several foils were changed after presentation and so discussion is a little disconnected from foils at times
We start Numerical Integration with a basic discussion of Newton-Cotes formulae (including Trapezoidal and Simpson's rule)
We illustrate them pictorially


This mixed presentation uses parts of the following base foilsets which can also be looked at on their own!
Master Set of Foils for 1996 Session of CPS615
CPS615 Foils -- set E: ODE's and Particle Dynamics
CPS615 Numerical Integration Module

Table of Contents for CPS615-End of N-Body Discussion and Beginning of Numerical Integration

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CPS 615 Lectures 1996 Fall Semester -- October 15
1 Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1996 --
Lecture of October 15 - 1996
2 Abstract of Oct 15 1996 CPS615 Lecture

Last Part of N Body Discussion
3 Simple Data Parallel Version of N Body Force Computation -- Grav -- I
4 The Grav Function in Data Parallel Algorithm - II
5 Some Inefficiencies of the N2 Algorithm - I
6 Some Inefficiencies of the N2 Algorithm - II
7 Better Pipeline Algorithm for Computation of Accelerations,
taking 1/2 the iterations of force computation - I
8 Pipeline Algorithm in detail
9 Basic pipeline operation
10 Examples of Pipeline Algorithm
11 Pipeline Algorithm Grav -- Part I
12 Pipeline Algorithm for Grav -- Part II
13 Grav Pipeline Algorithm, concluded
14 Parallel Implementation - I
15 Parallel Execution Time -I
16 Parallel Execution Time -II
17 N-body Problem is a one dimensional Algorithm

Start of Numerical Integration
18 1:Introduction to Numerical Integration
19 2:NI.1: Newton-Cotes Formulae
20 3:Linear Equations for Coefficients
21 4:Examples of Newton Cotes Rules I
22 5:Examples of Newton Cotes Rules II
23 6:Formulae for Examples: Trapezoidal and Simpson's Rules
24 7:Summary of Newton Cotes Rules
25 8:Errors in Newton Cotes Formulae
26 9:Use of High Order Newton Cotes

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