With recent changes in multicore and general-purpose computing on graphics processing units, the way parallel computers are used and programmed has drastically changed. It is important to provide a comprehensive study on how to use such machines written by specialists of the domain. The book provides recent research results in high-performance computing on complex environments, information on how to efficiently exploit heterogeneous and hierarchical architectures and distributed systems, detailed studies on the impact of applying heterogeneous computing practices to real problems, and applications varying from remote sensing to tomography. The content spans topics such as Numerical Analysis for Heterogeneous and Multicore Systems; Optimization of Communication for High Performance Heterogeneous and Hierarchical Platforms; Efficient Exploitation of Heterogeneous Architectures, Hybrid CPU+GPU, and Distributed Systems; Energy Awareness in High-Performance Computing; and Applications of Heterogeneous High-Performance Computing.
• Covers cutting-edge research in HPC on complex environments, following an international collaboration of members of the ComplexHPC
• Explains how to efficiently exploit heterogeneous and hierarchical architectures and distributed systems
• Twenty-three chapters and over 100 illustrations cover domains such as numerical analysis, communication and storage, applications, GPUs and accelerators, and energy efficiency
Preface vii
Notation and conventions xiii
1 Metric spaces and large scale geometry 1 (25)
1.1 Metric spaces 1 (5)
1.2 Groups as metric spaces 6 (3)
1.3 Quasi-isometries 9 (6)
1.4 Coarse equivalences 15 (4)
1.5 Hyperbolic spaces 19 (5)
Exercises 24 (1)
Notes and remarks 25 (1)
2 Asymptotic dimension and decomposition 26 (23)
complexity
2.1 Topological dimension 26 (1)
2.2 Asymptotic dimension 27 (3)
2.3 Dimension of hyperbolic groups 30 (2)
2.4 Upper bounds for asymptotic dimension 32 (4)
2.5 Asymptotic dimension of solvable groups 36 (2)
2.6 Groups with infinite asymptotic dimension 38 (1)
2.7 Decomposition complexity 39 (3)
2.8 Invariance and permanence 42 (3)
2.9 Groups with finite decomposition 45 (2)
complexity
Exercises 47 (1)
Notes and remarks 47 (2)
3 Amenability 49 (14)
3.1 F?lner conditions 49 (6)
3.2 The Hulanicki-Reiter condition 55 (3)
3.3 Invariant means 58 (3)
Exercises 61 (1)
Notes and remarks 61 (2)
4 Property A 63 (20)
4.1 Definition and basic properties 63 (3)
4.2 The Higson-Roe condition 66 (4)
4.3 Finite asymptotic dimension implies 70 (3)
property A
4.4 Property A and residually finite groups 73 (5)
4.5 Locally finite examples 78 (3)
Exercises 81 (1)
Notes and remarks 81 (2)
5 Coarse embeddings 83 (36)
5.1 Coarse embeddings 83 (1)
5.2 Embeddability into Hilbert spaces 84 (5)
5.3 Examples of embeddable spaces without 89 (2)
property A
5.4 Convexity and reflexivity 91 (5)
5.5 Coarse embeddings and finite subsets 96 (2)
5.6 Expanders 98 (3)
5.7 A geometric characterization of 101 (7)
non-embeddability
5.8 Compression of coarse embeddings 108 (2)
5.9 Compression > ｽ implies property A 110 (6)
Exercises 116 (1)
Notes and remarks 117 (2)
6 Group actions on Banach spaces 119 (24)
6.1 Affine isometric actions 119 (2)
6.2 Metrically proper actions and 121 (4)
a-T-menability
6.3 Actions on lp-spaces and reflexive Banach 125 (3)
spaces
6.4 Kazhdan's property (T) 128 (2)
6.5 Fixed points and Kazhdan's property (T) 130 (2)
6.6 Construction of expanders 132 (2)
6.7 Property (T) and spectral conditions 134 (6)
Exercises 140 (1)
Notes and remarks 141 (2)
7 Coarse homology 143 (23)
7.1 Coarse locally finite homology 143 (1)
7.2 Uniformly finite homology 144 (5)
7.3 Eilenberg swindles and Ponzi schemes 149 (5)
7.4 Aperiodic tiles and non-amenable spaces 154 (6)
7.5 Coarsening homology theories 160 (2)
7.6 The coarsening homomorphism 162 (3)
Exercises 165 (1)
Notes and remarks 165 (1)
8 Survey of applications 166 (6)
8.1 Topological rigidity 166 (1)
8.2 Geometric rigidity 167 (2)
8.3 Index theory 169 (3)
References 172 (15)
Index 187
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