2016/2017

2016/2017

DM270

MAT/08 (NUMERICAL ANALYSIS)

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

BIOENGINEERING

Bioingegneria delle cellule e dei tessuti

1°

1st semester (26/09/2016 - 13/01/2017)

3

30 lesson hours

ITALIAN

WRITTEN AND ORAL TEST

SANGALLI GIANCARLO - 3 ECTS

Calculus for multivariate functions, vectors and matrices. Programming in MATLAB/Octave language

The aim of the course is divided in two parts. DYNAMICAL SYSTEMS: theory and numerical methods (6CFU) and FINITE ELEMENT METHOD AND APPLICATIONS (3CFU).

The second part of the course will be devoted to the introduction of the variation formulation of the stationary problema and to their numerical approximation by the finite element method.

FINITE ELEMENT METHOD AND APPLICATIONS
Basic notions of functional analysis. Sobolev spaces. Variational formulation of elliptic problems (Poisson).

Ritz-Galerkin method
Mesh in one and more dimemsions -- Some finite elements -- Approximation properties -- Error estimates for elliptic problems of second order.

MATLAB solver implementation
Solution of the Poisson problem in one dimension. Solution of the Poisson problem in two dimension: assembling the linear system, numerical quadrature, system solving. Mesh refinement.

METODO DEGLI ELEMENTI FINITI E APPLICAZIONI

Lectures (hours/year in lecture theatre): 12
Practical class (hours/year in lecture theatre): 12
Practicals / Workshops (hours/year in lecture theatre): 0

Quarteroni A.. Modellistica numerica per problemi differenziali. Springer Verlag, 2009.
Braess D.. Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics.. Cambridge University Press..

Oral examination

Oral examination