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 as well as implicit 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

Module 1 – Theory (Prof. Tinti)

Discretization methods for solving ordinary differential equations (ODE) based on finite-difference schemes. Implicit and explicit multi-step methods. Runge-Kutta methods. Accuracy.

Partial differential equations (PDE). 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.

Module 2 – Laboratory (Prof. Zaniboni)

Application of numerical methods described in the Teaching Unit 1 to cases of generic ODEs and PDEs describing specific geophysical problems (transport equation, heat equation, wave equation).

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

Readings/Bibliography

Module 1 – Theory (Prof. Tinti)

Slides presented during the lectures.

Module 2 – Laboratory (Prof. Zaniboni)

Outlines of the exercises performed in the laboratory.

Teaching methods

Module 1 – Theory (Prof. Tinti)

Classroom lectures, projection of slides.

Module 2 – Laboratory (Prof. Zaniboni)

Laboratory exercises carried out on own computer.

Assessment methods

The final test is joint for the two modules, exclusively oral, with duration ranging between an hour and an hour and a half. It will concern the theory as well as the numerical tests carried out in the laboratory.

The examinee will be asked to show, discuss and run the numerical codes solving the differential equations developed in the laboratory.

Teaching tools

Projector; PC and MATLAB (or Octave).

Office hours

See the website of Filippo Zaniboni

See the website of Stefano Tinti