Introduction to Numerical Modeling in the Earth and Planetary Sciences

Christian Huber, Professor of Geophysics, Department of Earth, Environmental and Planetary Sciences,, Brown University

Chistian Huber grew up in Geneva, Switzerland, where he studied earth sciences and physics. He then moved to the University of California Berkeley where he gained his PhD in earth and planetary sciences, before joining the faculty at the Georgia Institute of Technology and then moving to Brown University in 2016. His main interests are in magmatic processes and planetary geodynamics.

Part I - Mathematical concepts1. Introduction to real valued calculus2. Introduction to multivariate calculus3. Elements of complex calculus4. Elements of linear algebra5. Treating functions as vectors6. Ordinary Differential Equations (ODEs)7. Partial Differential Equations (PDEs)Part II - Numerical Modeling, Ordinary Differential Equations (ODEs)8. First order ODE (time integration): The nuclear decay equation as a starting point9. What controls convergence? What relates convergence and stability?10. Box Models: from single to multiple coupled ODEs11. Higher order ODEs12. Higher order discretization methodsPart III - Numerical Modeling, Partial Differential Equations (PDEs)13. Important mathematical notions when working with PDEs14. Von Neumann stability analysis: concepts15. 1-D advection equation16. Diffusion equation17. 1-D advection-diffusion equation18. 1-D wave equation19. The shallow water equationPart IV - Overview of other numerical methods20. Top-down approaches21. Bottom-up approaches