69721 - Laboratory of Numerical Geophysics

Learning outcomes

At the end of the course, students will possess basic knowledge of the numerical techniques used in Geophysics. Particularly, students will be able:

• to apply explicit methods to solve ordinary differential equations and partial differential equations;
• to compute the propagation of waves through simple numerical models developed in the MATLAB environment.

Course contents

Teaching Unit 1 (Theory, Prof. Tinti)

Discretization methods of ordinary differential equations based on finite-difference schemes. Implicit and explicit multi-step methods. Runge-Kutta methods. Accuracy.

Partial differential equations. Parabolic and hyperbolic systems. Transport equation. Method of characteristics. Discrete differential operators. Stability analysis. Equation of heat transfer. Equation of waves propagation. Application to propagation of long ocean waves. Staggered grids technique.

Teaching Unit 2 (Laboratory, Dott. Zaniboni)

Application of numerical methods described in Teaching Unit 1 to cases of ordinary and partial differential equations.

The students will learn to develop on their own PC (or on one available in laboratory) the numerical codes for the implementation of such methods and the representation of the results. Such activity will be carried out by means of MatLab software (alternatively Octave).

Readings/Bibliography

Teaching Unit 1 (Theory, Prof. Tinti)

Lecture notes.

Teaching Unit 2 (Laboratory, Dott. Zaniboni)

Outline of the exercises performed in laboratory.

Teaching methods

Teaching Unit 1 (Theory, Prof. Tinti)

Classroom lectures

Teaching Unit 2 (Laboratory, Dott. Zaniboni)

Laboratory exercises carried out on own computer.

Assessment methods

The final test is joint for the two teaching units, exclusively oral, which duration ranges between one hour and one hour and half.

It consists of examination concerning theory as well as the numerical tests carried out in the laboratory.

The numerical codes for the resolution of the differential equations developed in laboratory will be shown, commented and run.

Teaching tools

Projector; PC and MATLAB (or Octave).

Office hours

See the website of Filippo Zaniboni

See the website of Stefano Tinti