A Tutorial on Elliptic Pde Solvers and Their Parallelization

by Douglas, Craig C.; Haase, Gundolf; Langer, Ulrich

ISBN13:
9780898715415
ISBN10:
0898715415
Format: Paperback
Copyright: 2003-02-01
Publisher: Society for Industrial & Applied
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Summary

A Tutorial on Elliptic PDE Solvers and Their Parallelization is a valuable aid for learning about the possible errors and bottlenecks in parallel computing. One of the highlights of the tutorial is that the course material can run on a laptop, not just on a parallel computer or cluster of PCs, thus allowing readers to experience their first successes in parallel computing in a relatively short amount of time.
This tutorial is intended for advanced undergraduate and graduate students in computational sciences and engineering; however, it may also be helpful to professionals who use PDE-based parallel computer simulations in the field.

Author Biography

Ulrich Langer is Head of the Institute of Computational Mathematics at the Johannes Kepler University of Linz, Austria.

List of Figures	p. ix
List of Algorithms	p. xi
Abbreviations and Notation	p. xiii
Preface	p. xvii
Introduction	p. 1
A Simple Example	p. 5
The Poisson equation and its finite difference discretization	p. 5
Sequential solving	p. 8
Direct methods	p. 8
Iterative methods	p. 9
Parallel solving by means of DD	p. 11
Some other discretization methods	p. 13
Introduction to Parallelism	p. 15
Classifications of parallel computers	p. 15
Classification by Flynn	p. 15
Classification by memory access	p. 17
Communication topologies	p. 19
Specialties of parallel algorithms	p. 20
Synchronization	p. 20
Message passing	p. 21
Deadlock	p. 22
Data coherency	p. 23
Parallel extensions of operating systems and programming languages	p. 23
Basic global operations	p. 24
Send and Recv	p. 24
Exchange	p. 25
Gather-scatter operations	p. 25
Broadcast	p. 26
Reduce and reduce-all operations	p. 27
Synchronization by barriers	p. 27
Some remarks on portability	p. 27
Performance evaluation of parallel algorithms	p. 28
Speedup and scaleup	p. 28
Efficiency	p. 31
Communication expenditure	p. 33
Exercises	p. 33
Galerkin Finite Element Discretization of Elliptic Partial Differential Equations	p. 35
Variational formulation of elliptic BVPs	p. 35
Galerkin finite element discretization	p. 40
The Galerkin method	p. 41
The simplest finite element schemes	p. 42
Analysis of the Galerkin FEM	p. 62
Iterative solution of the Galerkin system	p. 64
Exercises	p. 68
Basic Numerical Routines in Parallel	p. 71
Storage of sparse matrices	p. 71
DD by nonoverlapping elements	p. 72
Vector-vector operations	p. 75
Matrix-vector operations	p. 76
Exercises	p. 79
Classical Solvers	p. 83
Direct methods	p. 84
LU factorization	p. 84
ILU factorization	p. 85
Smoothers	p. 90
[omega]-Jacobi iteration	p. 91
Gauss-Seidel iteration	p. 93
ADI methods	p. 97
Roughers	p. 103
CG method	p. 103
GMRES solver	p. 105
BICGSTAB solver	p. 107
Preconditioners	p. 108
Exercises	p. 108
Multigrid Methods	p. 111
Multigrid methods	p. 111
The multigrid algorithm	p. 112
Sequential algorithm	p. 112
Parallel components of multigrid	p. 113
Parallel algorithm	p. 116
Exercises	p. 117
Problems Not Addressed in This Book	p. 119
Internet Addresses	p. 121
Bibliography	p. 125
Index	p. 133
Table of Contents provided by Ingram. All Rights Reserved.

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A Tutorial on Elliptic Pde Solvers and Their Parallelization

9780898715415

0898715415

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Summary

Author Biography

Table of Contents

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