Teaching: 557 Numerical Modeling of Earth Systems

This class focuses on 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. We briefly review math and continuum mechanics fundamentals, then discuss ordinary differential equations (ODEs), and spend the majority of the class discussing finite difference (FD) and finite element (FE) solutions to partial differential equations (PDEs).

The class targets graduate students from the Earth sciences, and consists of lectures and joint and individual computer lab exercises. Grading is based on home work/programming project assignments, a final project, and class participation.

This class was last taught in 2016 but lecture notes and problem sets may be useful are are provided in individual chunks below

Prerequisites: None. Recommended: Intro Earth Science, Geodynamics.

Example syllabus for Spring 2016 at USC

Online material

• Complete set of lecture notes:
  • Becker, T. W. and Kaus, B. J. P (2020 update): Numerical Modeling of Earth Systems: An introduction to computational methods with focus on solid Earth applications of continuum mechanics, The University of Texas at Austin, v. 1.2.2, 2020.(PDF)
  • Becker, T. W. and Kaus, B. J. P (2015): Numerical Modeling of Earth Systems: An introduction to computational methods with focus on solid Earth applications of continuum mechanics. figshare, doiL10.6084/m9.figshare.1555628, 2015.
• All accompanying Matlab code for exercises (solutions available for instructors upon request).
• Individual handouts and problem sets:
  Please note that individual PDFs will have broken cross-references, use the complete lecture notes for a consistent document.
  • General handouts for background material:
    1. Basic Calculus and Linear Algebra
    2. Continuum Mechanics Primer
    3. Matlab Intro
  • Homework assignments/exercises
    
    1. Scaling analysis: PDF
    2. Ordinary Differential Equations (ODEs): Lorenz equations: PDF, Matlab code, Python code
    3. Finite differences (FD)
       1. Explicit heat: PDF, Matlab code
       2. Implicit heat: PDF
       3. 2D heat: PDF, Matlab code
       4. advection: PDF, Matlab code
       5. Stokes primitive variables: PDF, Matlab code
       6. Stokes stream function: PDF, Matlab code
       7. Wave propagation: PDF, Matlab code
    4. Finite elements (FE)
       1. 1D heat: PDF, Matlab code.
       2. 2D heat: PDF, Matlab code.
       3. 2D elastic: PDF, Matlab code.
       4. 2D Stokes: PDF, Matlab code.