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## NUMERICAL METHODS

CODE 72443 2019/2020 3 credits during the 1st year of 9270 Mechanical Engineering - Energy and Aeronautics (LM-33) GENOVA MAT/08 Italian GENOVA (Mechanical Engineering - Energy and Aeronautics) 2° Semester This unit is a module of: AULAWEB

## 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

### LEARNING OUTCOMES

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.

### 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 solution of ordinary differential equations.

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

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

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

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

• 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)

ANGELO ALESSANDRI

FRANCO BAMPI

STEFANO VIGNOLO

## LESSONS

### 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.

Second semester.

### Class schedule

NUMERICAL METHODS

## 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

Date Time Location Type Notes
28/02/2020 01:30 GENOVA Esame su appuntamento
18/09/2020 01:30 GENOVA Esame su appuntamento