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.
Prerequisites: None. Recommended: GEOL425, GEOL534, GEOL540.
Online material
 Complete set of lecture notes:
 Becker, T. W. and Kaus, B. J. P (2016): Numerical Modeling of
Earth Systems: An introduction to computational methods with focus
on solid Earth applications of continuum mechanics, University of
Southern California, v. 1.2,
2016.(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,
http://dx.doi.org/10.6084/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
crossreferences, use the complete
lecture notes for a consistent document.
 General handouts for background material:
 Basic
Calculus and Linear Algebra
 Continuum
Mechanics Primer
 Matlab Intro
 Homework assignments/exercises
 Scaling analysis:
PDF
 Ordinary Differential Equations (ODEs): Lorenz
equations:
PDF,
Matlab code,
Python code
 Finite differences (FD)
 Explicit heat: PDF,
Matlab code
 Implicit heat:
PDF
 2D heat:
PDF,
Matlab code
 advection:
PDF,
Matlab code
 Stokes primitive variables:
PDF,
Matlab code
 Stokes stream function:
PDF,
Matlab code
 Wave propagation:
PDF,
Matlab code
 Finite elements (FE)
 1D heat:
PDF,
Matlab code.
 2D heat:
PDF,
Matlab code.
 2D elastic:
PDF,
Matlab code.
 2D Stokes:
PDF,
Matlab code.
Updated: October 15, 2019
(c) JSG Geodynamics, 2019.
