Numerical simulation is a technique of major importance in various technical and scientific fields. Used to understand diverse physical phenomena or to design everyday objects, it plays a major role in innovation in the industrial sector. Whilst engineering curricula now include training courses dedicated to it, numerical simulation is still not well-known in some economic sectors, and even less so among the general public. Simulation involves the mathematical modeling of the real world, coupled with the computing power offered by modern technology. Designed to perform virtual experiments, digital simulation can be considered as an "art of prediction". Embellished with a rich iconography and based on the testimony of researchers and engineers, this book shines a light on this little-known art. It is the first of two volumes and focuses on the principles, methods and industrial practice of numerical modeling.
Jean-Francois Sigrist is a doctor of engineering sciences who has worked for almost 20 years in the industry, leading a team of research engineers in numerical simulation. He is now an independent expert.
Foreword vii
Preface ix
Acknowledgements xiii
Chapter 1. The World in Equations1
1.1. Numerical modeling 3
1.1.1. Modeling 3
1.1.2. Understanding, designing, forecasting, optimizing 4
1.2. Putting the world into equations: example of mechanics 5
1.2.1. Construction of classical mechanical models 5
1.2.2. Emergence of quantum mechanics 23
1.3. Solving an equation 34
1.3.1. Finding a mathematical formula 34
1.3.2. Calculating using a computer 38
Chapter 2. Simulation Practice49
2.1. Validating a simulation 50
2.1.1. Demonstrating a theorem 50
2.1.2. Confronting points of view 51
2.1.3. Relying on experience 54
2.1.4. Changing point of view 57
2.2. Maturity of a technique 61
2.3. Practice, practice, practice... 63
2.3.1. The engineers palette 63
2.3.2. Complementary philosophies 68
2.3.3. Users with different needs 70
Chapter 3. A Global Technique77
3.1. A very generalized technique 78
3.2. A strategic technique 80
3.3. Hercules of the calculation 85
3.3.1. High-performance computing 85
3.3.2. Stroke to computing power 88
Chapter 4. The Data World101
4.1. Big data 102
4.2. Data and networks 104
4.3. Learning from data 115
4.4. Biological and digital brains 121
4.4.1. Biological neurons 123
4.4.2. Digital neural networks 129
4.5. Are humans overwhelmed by machines? 137
4.5.1. All-round machine victories 137
4.5.2. A war of intelligence? 139
4.5.3. Science fiction 140
4.5.4. Science without fiction 142
4.5.5. Complementarity of intelligence 145
4.5.6. Complexity and robustness 150
4.5.7. Imitation game 151
4.5.8. Priority to the law! 153
4.5.9. More human than human? 155
Conclusion 159
Glossary of Terms 171
References 201
Index 237
