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CPS615 Foils -- set C: Laplace Example -- Programming Models and

Given by Geoffrey C. Fox at CPS615 Basic Simulation Track for Computational Science on Fall Semester 95. Foils prepared 2 October 1995

This takes Jacobi Iteration for Laplace's Equation in a 2D square and uses this to illustrate:
Programming in both Data Parallel (HPF) and Message Passing (MPI and a simplified Syntax)
SPMD -- Single Program Multiple Data -- Programming Model
Stencil dependence of Parallel Program and use of Guard Rings
Collective Communication
Basic Speed Up,Efficiency and Performance Analysis with edge over area dependence and consideration of load imbalance and communication overhead effects.

Table of Contents for CPS615 Foils -- set C: Laplace Example -- Programming Models and

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1 CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1995 --
Lecture Stream 3 --
The Laplace Example
Programming and Performance
2 Abstract of Laplace Example for CPS615
3 Parallel Computing
Algorithms and
Software --
Laplace Example
4 The Solution of Laplace's Equation
5 Discretized Form of Laplace'e Equation on a Parallel Processor
6 Basic Structure of Domain to be Updated in Parallel Version
7 Sequential and Introduction to Parallel Coding for the
Laplace Example
8 SEQUENTIAL LAPLACE PROGRAMMING
JACOBI ITERATION IN ONE DIMENSION
(constant in y direction)
9 SEQUENTIAL LAPLACE PROGRAMMING
JACOBI ITERATION IN TWO DIMENSIONS
10 Approaches to Parallel Programming
11 SPMD or SCMD
Single Program (code) Multiple Data
12 Data Parallel
Programming for
Laplace Example
13 Parallel Laplace Programming
Data Parallel for Jacobi Iteration in One Dimension
14 Notes on HPF Implementation of Lapace Solver
15 Message Passing Model
Used for Parallel
Programming for
Laplace Example
16 Basic Message Passing Approach
17 Message Passing Overview
18 Parallel Laplace Programming: Set Up of
Message Passing for Jacobi Iteration in One Dimension
19 Node Program: Message Passing for Laplace Sover
20 Collective Communication Primitives
21 Implementation of MPSHIFT(+1, SOURCE,DEST)
22 Possible Implementation of MPSHIFT in MPI
23 Implementation of SHIFT in MPI
24 Implementation of GLOBALMAX (TEST)
25 General Features
of
Laplace Example
26 What does the Laplace Update calculation look like?
27 The Various Stencil Special Cases
28 Communication Loads
29 What is the relation of sequential and parallel programming models ?
30 More on SPMD Programming Model and Sequential/Parallel Comparison
31 Programming with Guard Rings - Sequential
32 Programming with Guard Rings - Parallel
33 Special Case of Corner Processor
34 Analysis of Parallel Overheads
Efficiency and
Speedup
35 General Formalism for Speed Up
36 What Affects Speed Up ?
37 Load Imbalance and Speed-Up for Laplace Example -- I
38 Load Imbalance and Speed-Up for Laplace Example -- II
39 Analytical Analysis of Load Imbalance
40 Communication Overhead
41 Analytical Form of Speed Up for Communication Overhead
42 General Form of Efficiency
43 Communication to Calculation Ratio as a function of template
44 Performance for Increasing Stencil
45 Matrix Multiplication on the Hypercube
46 Efficiency of QCD Physics Simulation on JPL MarkIIIfp Hypercube
47 General Analysis of Overheads and Efficiency
48 Speed Up as a Function of Grain Size
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