Enrollment year
2021/2022
Academic discipline
MAT/08 (NUMERICAL ANALYSIS)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Curriculum
Cellule, tessuti e dispositivi
Period
1st semester (27/09/2021 - 21/01/2022)
Lesson hours
24 lesson hours
Prerequisites
- Linear algebra
- Calculus for multivariate functions
- C programming language
Learning outcomes
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.
Course contents
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
Teaching methods
- Lectures (20 hours) and practical classes (4 hours)
- Individual or group solution of exercises
Reccomended or required readings
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
Assessment methods
Carrying out of a project and oral examination
Sustainable development goals - Agenda 2030