Becker T.W., Kaus B.J.P. Numerical Modeling of Earth Systems. An introduction to computational methods with focus on solid Earth applications of continuum mechanics

Lecture notes for USC GEOL557, 2006. — 222 p.The course discusses the numerical solution of problems arising in the quantitative modeling of Earth systems. The focus is on continuum mechanics problems as applied to geological processes in the solid Earth, but the numerical methods have broad applications including in geochemistry or climate modeling. The quantitative skills which are to be learned are therefore useful for all Earth scientists, but the focus of the class is on mantle convection and seismology type problems.
After an introduction with few details on numerical analysis and programming, we briefly discuss ordinary differential equations (ODEs). Thereafter, the class spends the majority of the time discussing finite difference (FD) and finite element (FE) solutions to partial differential equations (PDEs). An example syllabus for how to use these notes is given in sec. 9. 1 A brief review of basic math and continuum mechanics fundamentals is provided in secs. 6 and 7, respectively.
We chose MatLAB as a programming language because of its ease in developing and debugging, as well as the built-in visualization capabilities. The fact that the language is interpreted, and not compiled, does somewhat limit the direct applications of the implementations that are discussed, pretty much to 2D problems, yet potentially at high efficiencies. Moreover, MatLAB code does easily translate to F90/95 compiled languare code, which can be done to improve efficiency. Solutions for the MatLAB exercises are available for instructors upon request, and a brief introduction to MatLAB exercise is provided in sec. 8.