OVERVIEW

The course aims to provide the student knowledge about numerical methods for mechanical engineering problems, particularly with regard to the solution of ordinary and partial differential equations.

AIMS AND CONTENT

TEACHING METHODS

The time-schedule of the course is four hours per week in the second semester. The module consists of a theoretical part complemented by laboratory exercises carried out in Matlab.

SYLLABUS/CONTENT

The module aims to provide the basic elements of numerical analysis. The main part concerns numerical methods for solving ordinary differential equations (ODE) and partial differential equations (PDE). The purpose is to acquire a knowledge of numerical methods and their implementation, with a focus on stability analysis, accuracy and convergence of the methods. The lectures are complemented by laboratory exercises carried out using Matlab, one of the most used programming languages ​​for scientific computing.

1. Numerical methods for solving systems of nonlinear equations. Polynomial interpolation, data fitting and least squares method.

2. Numerical solution of ordinary differential equations.

3. Numerical methods for partial differential equation: elliptic, parabolic and hyperbolic. Choice of the most suitable type of method depending on the type of PDE.

4. Finite Difference Method for problems in smooth domains: Poisson and diffusion equation.

5. Finite Element Method for elliptic and parabolic equations. Advection-diffusion equation and stabilization techniques.

6. Finite Volume Method for elliptic, parabolic and first-order hyperbolic (nonlinear conservation laws). The Riemann problem: characteristics, shock waves, rarefaction, contact discontinuities.

RECOMMENDED READING/BIBLIOGRAPHY

• Lecture notes of the course are available in aulaweb;

• Quarteroni, F. Saleri, Introduzione al Calcolo Scientifico, Sprinter-Verlag 2006;

• Quarteroni, Modellistica Numerica per Problemi Differenziali, Springer-Verlag 2008;

• S. Chapra, R.Canale, Metodi numerici per l’Ingegneria, McGraw-Hill 1988;

• S. Chapra, R. Canale, Numerical methods for Engineers, McGraw-Hill 2009 (edizione più recente);

• R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press 2002.

TEACHERS AND EXAM BOARD

Exam Board

PATRIZIA BAGNERINI (President)

ROBERTO CIANCI (President)

LESSONS

LESSONS START

Second semester.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The examination mode consists of an oral test to ensure learning of the course content.

ASSESSMENT METHODS

The oral exam focuses on the learning of one or two subjects from those discussed in class.

Exam schedule

FURTHER INFORMATION

See the aulaweb page for more information and details.