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目次

List of Contributors xiii Preface xvii Acknowledgments xix Glossary xxi Abbreviations xxv 1. Why Graphics Processing Units 1” Perri Needham, Andreas W. Götz and Ross C. Walker 1.1 A Historical Perspective of Parallel Computing 1 1.2 The Rise of the GPU 5 1.3 Parallel Computing on Central Processing Units 7 1.4 Parallel Computing on Graphics Processing Units 12 1.5 GPU–Accelerated Applications 15 References 19 2. GPUs: Hardware to Software 23 Perri Needham, Andreas W. Götz and Ross C. Walker 2.1 Basic GPU Terminology 24 2.2 Architecture of GPUs 24 2.3 CUDA Programming Model 26 2.4 Programming and Optimization Concepts 30 2.5 Software Libraries for GPUs 34 2.6 Special Features of CUDA–Enabled GPUs 35 References 36 3. Overview of Electronic Structure Methods 39 Andreas W. Götz 3.1 Introduction 39 3.2 Hartree–Fock Theory 42 3.3 Density Functional Theory 46 3.4 Basis Sets 49 3.5 Semiempirical Methods 53 3.6 Density Functional Tight Binding 56 3.7 Wave Function–Based Electron Correlation Methods 57 Acknowledgments 60 References 61 4. Gaussian Basis Set Hartree–Fock, Density Functional Theory, and Beyond on GPUs 67 Nathan Luehr, Aaron Sisto and Todd J. Martínez 4.1 Quantum Chemistry Review 68 4.2 Hardware and CUDA Overview 72 4.3 GPU ERI Evaluation 73 4.4 Integral–Direct Fock Construction on GPUs 78 4.5 Precision Considerations 88 4.6 Post–SCF Methods 91 4.7 Example Calculations 93 4.8 Conclusions and Outlook 97 References 98 5. GPU Acceleration for Density Functional Theory with Slater–Type Orbitals 101 Hans van Schoot and Lucas Visscher 5.1 Background 101 5.2 Theory and CPU Implementation 102 5.3 GPU Implementation 105 5.4 Conclusion 112 References 113 6. Wavelet–Based Density Functional Theory on Massively Parallel Hybrid Architectures 115 Luigi Genovese, Brice Videau, Damien Caliste, Jean–François Méhaut, Stefan Goedecker and Thierry Deutsch 6.1 Introductory Remarks on Wavelet Basis Sets for Density Functional Theory Implementations 115 6.2 Operators in Wavelet Basis Sets 117 6.3 Parallelization 123 6.4 GPU Architecture 124 6.5 Conclusions and Outlook 132 References 133 7. Plane–Wave Density Functional Theory 135 Maxwell Hutchinson, Paul Fleurat–Lessard, Ani Anciaux–Sedrakian, Dusan Stosic, Jeroen Bédorf and Sarah Tariq 7.1 Introduction 135 7.2 Theoretical Background 136 7.3 Implementation 143 7.4 Optimizations 148 7.5 Performance Examples 151 7.6 Exact Exchange with Plane Waves 159 7.7 Summary and Outlook 165 Acknowledgments 165 References 165 Appendix A: Definitions and Conventions 168 Appendix B: Example Kernels 168 8. GPU–Accelerated Sparse Matrix–Matrix Multiplication for Linear Scaling Density Functional Theory 173 Ole Schütt, Peter Messmer, Jürg Hutter and Joost VandeVondele 8.1 Introduction 173 8.2 Software Architecture for GPU–Acceleration 177 8.3 Maximizing Asynchronous Progress 180 8.4 Libcusmm: GPU Accelerated Small Matrix Multiplications 183 8.5 Benchmarks and Conclusions 186 Acknowledgments 189 References 189 9. Grid–Based Projector–Augmented Wave Method 191 Samuli Hakala, Jussi Enkovaara, Ville Havu, Jun Yan, Lin Li, Chris O’Grady and Risto M. Nieminen 9.1 Introduction 191 9.2 General Overview 193 9.3 Using GPUs in Ground–State Calculations 196 9.4 Time–Dependent Density Functional Theory 202 9.5 Random Phase Approximation for the Correlation Energy 203 9.6 Summary and Outlook 207 Acknowledgments 208 References 208 10. Application of Graphics Processing Units to Accelerate Real–Space Density Functional Theory and Time–Dependent Density Functional Theory Calculations 211 Xavier Andrade and Alán Aspuru–Guzik 10.1 Introduction 212 10.2 The Real–Space Representation 213 10.3 Numerical Aspects of the Real–Space Approach 214 10.4 General GPU Optimization Strategy 216 10.5 Kohn–Sham Hamiltonian 217 10.6 Orthogonalization and Subspace Diagonalization 221 10.7 Exponentiation 222 10.8 The Hartree Potential 223 10.9 Other Operations 224 10.10 Numerical Performance 225 10.11 Conclusions 228 10.12 Computational Methods 228 Acknowledgments 229 References 229 11. Semiempirical Quantum Chemistry 239 Xin Wu, Axel Koslowski and Walter Thiel 11.1 Introduction 239 11.2 Overview of Semiempirical Methods 240 11.3 Computational Bottlenecks 241 11.4 Profile–Guided Optimization for the Hybrid Platform 244 11.5 Performance 249 11.6 Applications 251 11.7 Conclusion 252 Acknowledgement 253 References 253 12. GPU Acceleration of Second–Order Møller–Plesset Perturbation Theory with Resolution of Identity 259 Roberto Olivares–Amaya, Adrian Jinich, Mark A. Watson and Alán Aspuru–Guzik 12.1 Møller–Plesset Perturbation Theory with Resolution of Identity Approximation (RI–MP2) 259 12.2 A Mixed–Precision Matrix Multiplication Library 263 12.3 Performance of Accelerated RI–MP2 266 12.4 Example Applications 270 12.5 Conclusions 273 References 273 13. Iterative Coupled–Cluster Methods on Graphics Processing Units 279 A. Eugene DePrince III, Jeff R. Hammond and C. David Sherrill 13.1 Introduction 279 13.2 Related Work 280 13.3 Theory 281 13.4 Algorithm Details 284 13.5 Computational Details 287 13.6 Results 290 13.7 Conclusions 295 Acknowledgments 296 References 296 14. Perturbative Coupled–Cluster Methods on Graphics Processing Units: Single– and Multi–Reference Formulations 301 Wenjing Ma, Kiran Bhaskaran–Nair, Oreste Villa, Edoardo Aprà, Antonino Tumeo, Sriram Krishnamoorthy and Karol Kowalski 14.1 Introduction 302 14.2 Overview of Electronic Structure Methods 303 14.3 NWChem Software Architecture 308 14.4 GPU Implementation 309 14.5 Performance 315 14.6 Outlook 319 Acknowledgments 320 References 320 Index 327