2021/2022

2021/2022

DM270

MAT/08 (NUMERICAL ANALYSIS)

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

BIOENGINEERING

Cellule, tessuti e dispositivi

1°

1st semester (27/09/2021 - 21/01/2022)

3

24 lesson hours

Italian

ORAL TEST

ZANOTTI PIETRO - 3 ECTS

- Linear algebra
- Calculus for multivariate functions
- C programming language

The course aims at providing an introduction to the design and the implementation of finite element methods to approximate the solution of partial differential equations. The students are expected to develop the following skills
- understanding the principles and the basic properties of the finite element methods,
- knowing the general structure of a code implementing a finite element method, navigating it and being able to modify it according to specific requirements, and
- being able to represent, analyze and interpret the numerical results.

1. Partial differential equations
2. Galerkin method
3. The ALBERTA toolbox
4. Meshes
5. Finite elements
6. Finite element spaces
7. Implementation
8. Assembling
9. Boundary conditions and numerical quadrature
10. Linear solvers
11. Errors
12. A posteriori estimates and adaptivity

- Lectures (20 hours) and practical classes (4 hours)
- Individual or group solution of exercises

Main references
- Lecture notes provided by the lecturer
- ALBERTA user guide (available on Kiro)

Advanced references
- A. Ern, J.-L. Guermond, Theory and Practice of Finite Elements, 2004
- A. Quarteroni, Modellistica Numerica per Problemi Differenziali, 2012
- A. Schmidt, K. G. Siebert, Design of adaptive finite element software. The finite element toolbox ALBERTA, 2005

Carrying out of a project and oral examination