Ge 263 Webpage

Ge 263. Computational Geophysics

9 units, (3-0-6), second term. Offered alternate years, Offfered 2004-2005 Finite-difference, pseudospectral, finite-element and spectral-element methods will be presented and applied to a number of geophysical problems including heat flow, deformation and wave propagation. Students will program simple versions of the methods. Prerequisites: an introductory class in geophysics, class in partial differential equations, ability to program in some language.
Instructors: Clayton, Gurnis, Tromp
TA: Qinya Liu

Syllabus
Homework

2004-2005 Schedule

Mon, Wed, Fri 9-10am, Rm 162 South Mudd

Syllabus

1) Finite-Difference Methods

a) approximating 1st and 2nd derivatives
b) combining approximations to solve a partial differential eqn. - centering
c) stability analysis
d) initial (source) and boundary conditions
e) application to the heat-flow equation (Crank-Nicholson method)
f) application to the acoustic wave equation
g) staggered-grid 4th order elastic wave equation.
h> application to scalar, vector and multinode computers
i) approximating derivatives with Fourier/Chebychev transforms
j) multidimensional Fourier transforms

2) Finite-Element Methods

a) Weak and strong forms of governing equations, boundary conditions, sources
b) Mesh design
c) Integration over an element
d) Discretization of the weak form
e) Assembly
f) Heat-flow equation
g) Advection-Diffusion equation
h) Incompressible viscous flow equation

3) Spectral-Element Methods

a) Mesh design
b) Interpolation over an element
c) Integration over an element
d) Discretization of the weak form
e) Assembly
f) Time marching
g) Heat-flow equation
h) Acoustic wave equation

Homework

Homework 1	Finite-difference Method: Heat Flow Example	Solution
Homework 2	Finite-difference Method: Tsunami Example	Solution
Homework 3	Finite Difference Method: Tsunami Source	Solution (html files)
Homework 4	Finite Element Method: 1-D Steady-state Diffusion	Solution Code
Homework 5	Finite Element Method: 1-D unsteady-state Diffusion	Solution Code