Parallel Computing in Quantum Chemistry / Edition 1

by Curtis L. Janssen, Ida M. B. Nielsen

Overview

An In-Depth View of Hardware Issues, Programming Practices, and Implementation of Key Methods

Exploring the challenges of parallel programming from the perspective of quantum chemists, Parallel Computing in Quantum Chemistry thoroughly covers topics relevant to designing and implementing parallel quantum chemistry programs.

Focusing on good parallel program design and performance analysis, the first part of the book deals with parallel computer architectures and parallel computing concepts and terminology. The authors discuss trends in hardware, methods, and algorithms; parallel computer architectures and the overall system view of a parallel computer; message-passing; parallelization via multi-threading; measures for predicting and assessing the performance of parallel algorithms; and fundamental issues of designing and implementing parallel programs.

The second part contains detailed discussions and performance analyses of parallel algorithms for a number of important and widely used quantum chemistry procedures and methods. The book presents schemes for the parallel computation of two-electron integrals, details the Hartree–Fock procedure, considers the parallel computation of second-order Møller–Plesset energies, and examines the difficulties of parallelizing local correlation methods.

Through a solid assessment of parallel computing hardware issues, parallel programming practices, and implementation of key methods, this invaluable book enables readers to develop efficient quantum chemistry software capable of utilizing large-scale parallel computers.

Product Details

ISBN-13:	9780367387501
Publisher:	Taylor & Francis
Publication date:	09/19/2019
Pages:	232
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Janssen, Curtis L.; Nielsen, Ida M. B.

Table of Contents

I Parallel Computing Concepts and Terminology

1 Introduction 3

1.1 Parallel Computing in Quantum Chemistry: Past and Present 4

1.2 Trends in Hardware Development 5

1.2.1 Moore's Law 5

1.2.2 Clock Speed and Performance 6

1.2.3 Bandwidth and Latency 7

1.2.4 Supercomputer Performance 8

1.3 Trends in Parallel Software Development 10

1.3.1 Responding to Changes in Hardware 10

1.3.2 New Algorithms and Methods 10

1.3.3 New Programming Models 12

References 13

2 Parallel Computer Architectures 17

2.1 Flynn's Classification Scheme 17

2.1.1 Single-Instruction, Single-Data 17

2.1.2 Single-Instruction, Multiple-Data 18

2.1.3 Multiple-Instruction, Multiple-Data 18

2.2 Network Architecture 19

2.2.1 Direct and Indirect Networks 19

2.2.2 Routing 20

2.2.3 Network Performance 23

2.2.4 Network Topology 25

2.2.4.1 Crossbar 26

2.2.4.2 Ring 27

2.2.4.3 Mesh and Torus 27

2.2.4.4 Hypercube 28

2.2.4.5 Fat Tree 28

2.2.4.6 Bus 30

2.2.4.7 Ad Hoc Grid 31

2.3 Node Architecture 31

2.4 MIMD System Architecture 34

2.4.1 Memory Hierarchy 35

2.4.2 Persistent Storage 35

2.4.2.1 Local Storage 37

2.4.2.2 Network Storage 37

2.4.2.3 Trends in Storage 38

2.4.3 Reliability 38

2.4.4 Homogeneity and Heterogeneity 39

2.4.5 Commodity versus Custom Computers 40

2.5 Further Reading 42

References 43

3 Communication via Message-Passing 45

3.1 Point-to-Point Communication Operations 46

3.1.1 Blocking Point-to-Point Operations 46

3.1.2 Non-Blocking Point-to-Point Operations 47

3.2 Collective Communication Operations 49

3.2.1 One-to-All Broadcast 50

3.2.2 All-to-All Broadcast 51

3.2.3 All-to-One Reduction and All-Reduce 54

3.3 One-Sided Communication Operations 55

3.4 Further Reading 56

References 56

4 Multi-Threading 59

4.1 Pitfalls of Multi-Threading 61

4.2 Thread-Safety 64

4.3 Comparison of Multi-Threading and Message-Passing 65

4.4 Hybrid Programming 66

4.5 Further Reading 69

References 70

5 Parallel Performance Evaluation 71

5.1 Network Performance Characteristics 71

5.2 Performance Measures for Parallel Programs 74

5.2.1 Speedup and Efficiency 74

5.2.2 Scalability 79

5.3 Performance Modeling 80

5.3.1 Modeling the Execution Time 80

5.3.2 Performance Model Example: Matrix-Vector Multiplication 83

5.4 Presenting and Evaluating Performance Data: A Few Caveats 86

5.5 Further Reading 90

References 90

6 Parallel Program Design 93

6.1 Distribution of Work 94

6.1.1 Static Task Distribution 95

6.1.1.1 Round-Robin and Recursive Task Distributions 96

6.1.2 Dynamic Task Distribution 99

6.1.2.1 Manager-Worker Model 99

6.1.2.2 Decentralized Task Distribution 101

6.2 Distribution of Data 101

6.3 Designing a Communication Scheme 104

6.3.1 Using Collective Communication 104

6.3.2 Using Point-to-Point Communication 105

6.4 Design Example: Matrix-Vector Multiplication 107

6.4.1 Using a Row-Distributed Matrix 108

6.4.2 Using a Block-Distributed Matrix 109

6.5 Summary of Key Points of Parallel Program Design 112

6.6 Further Reading 114

References 114

II Applications of Parallel Programming in Quantum Chemistry

7 Two-Electron Integral Evaluation 117

7.1 Basics of Integral Computation 117

7.2 Parallel Implementation Using Static Load Balancing 119

7.2.1 Parallel Algorithms Distributing Shell Quartets and Pairs 119

7.2.2 Performance Analysis 121

7.2.2.1 Determination of the Load Imbalance Factor k(p) 122

7.2.2.2 Determination of μ and σ for Integral Computation 123

7.2.2.3 Predicted and Measured Efficiencies 124

7.3 Parallel Implementation Using Dynamic Load Balancing 125

7.3.1 Parallel Algorithm Distributing Shell Pairs 126

7.3.2 Performance Analysis 128

7.3.2.1 Load Imbalance 128

7.3.2.2 Communication Time 128

7.3.2.3 Predicted and Measured Efficiencies 129

References 130

8 The Hartree-Fock Method 131

8.1 The Hartree-Fock Equations 131

8.2 The Hartree-Fock Procedure 133

8.3 Parallel Fock Matrix Formation with Replicated Data 135

8.4 Parallel Fock Matrix Formation with Distributed Data 138

8.5 Further Reading 145

References 146

9 Second-Order Møller-Plesset Perturbation Theory 147

9.1 The Canonical MP2 Equations 147

9.2 A Scalar Direct MP2 Algorithm 149

9.3 Parallelization with Minimal Modifications 151

9.4 High-Performance Parallelization 154

9.5 Performance of the Parallel Algorithms 158

9.6 Further Reading 164

References 164

10 Local Møller-Plesset Perturbation Theory 167

10.1 The LMP2 Equations 167

10.2 A Scalar LMP2 Algorithm 169

10.3 Parallel LMP2 170

10.3.1 Two-Electron Integral Transformation 171

10.3.2 Computation of the Residual 173

10.3.3 Parallel Performance 174

References 177

Appendices

A A Brief Introduction to MPI 181

B Pthreads: Explicit Use of Threads 189

C OpenMP: Compiler Extensions for Multi-Threading 195

Index 205