Practical Finite Element Modeling in Earth Science using Matlab

1. Auflage 2017
ISBN: 978-1-119-24862-0
Verlag: John Wiley & Sons

Buch, Englisch, 272 Seiten, Format (B × H): 185 mm x 249 mm, Gewicht: 739 g

Mathematical models have become a crucial way for the Earth scientist to understand and predict how our planet functions and evolves through time and space. The finite element method (FEM) is a remarkably flexible and powerful tool with enormous potential in the Earth Sciences. This pragmatic guide explores how a variety of different Earth science problems can be translated and solved with FEM, assuming only basic programming experience.

This book begins with a general introduction to numerical modeling and includes multiple sample Matlab codes to illustrate how FEM is implemented in practice. Textboxes have been included to provide additional detail, such as specialized Matlab usage or advanced topics. Covering all the key aspects, this is essential reading for those looking to master the technique, as well as those simply seeking to increase their basic level of understanding and appreciation of FEM.

Autoren/Hrsg.

Simpson, Guy

Fachgebiete

• Geowissenschaften Geologie Geophysik
• Geowissenschaften Geologie Tektonik, Strukturgeologie
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Geowissenschaften Geologie Geologie
• Geowissenschaften Geologie GIS, Geoinformatik

Inhaltsverzeichnis

Preface xiii

Symbols xv

About the Companion Website xvii

Part I The Finite Element Method with Matlab 1

1 Preliminaries 3

2 Beginning with the Finite Element Method 13

3 Programming the Finite Element Method in Matlab 25

4 Numerical Integration and Local Coordinates 35

5 The Finite Element Method in Two Dimensions 49

6 The Finite Element Method in Three Dimensions 67

7 Generalization of Finite Element Concepts 81

Part II Applications of the Finite Element Method in Earth Science 119

8 Heat Transfer 121

9 Landscape Evolution 137

10 Fluid Flow in Porous Media 151

11 Lithospheric Flexure 167

12 Deformation of Earth’s Crust 183

13 Going Further 207

Appendix A Derivation of the Diffusion Equation 217

Appendix B Basics of Linear Algebra with Matlab 221

Appendix c Comparison between Different Numerical Methods 227

Appendix d Integration by Parts 237

Appendix E Time Discretization 239

References 241

Index 245

Über Autor(innen)

Guy Simpson obtained his PhD in Geology from ETH Zurich. He is currently within the Department of Earth Science at the University of Geneva. Over the past decade, he has taught numerous courses at the Universities of Geneva, École Normale Supérieure in Paris, and ETH Zurich on numerical modeling in Earth science using Matlab. He also uses this method in his own research that includes investigation of earthquakes, tectonics and erosion of active mountain ranges, fluid flow, magmatism, and tsunamis.