Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

Study Plan

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
6
B
MAT/07
6
B
MAT/06
6
B
MAT/03
12
B
MAT/05
6
B
MAT/05

2° Year   activated in the A.Y. 2024/2025

ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
activated in the A.Y. 2024/2025
ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
1 module among the following
6
C
MAT/08
6
C
MAT/08
Between the years: 1°- 2°
1 module between the following (a.a. 2023/24 Homological Algebra not activated - a.a. 2024/25 Computational Algebra not activated)
6
B
MAT/02
6
B
MAT/02
Between the years: 1°- 2°
3 modules among the following
6
C
MAT/03
6
C
MAT/02 ,MAT/03
6
C
MAT/02
6
C
MAT/08
6
C
MAT/08
6
C
MAT/02
6
C
MAT/06
6
C
INF/01
6
C
MAT/05
6
C
MAT/09
6
C
MAT/02
6
C
MAT/08
6
C
MAT/08
6
C
MAT/07
6
C
INF/01 ,MAT/06
Between the years: 1°- 2°
12
D
-
Between the years: 1°- 2°
Further activities
4
F
-

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Numerical methods for partial differential equations  (2023/2024)

Teaching code

4S008270

Academic staff

Marco Caliari, Giacomo Albi

Coordinator

Marco Caliari

Credits

6

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/08 - NUMERICAL ANALYSIS

Period

Semester 2 dal Mar 4, 2024 al Jun 14, 2024.

Courses Single

Authorized

Lessons timetable MoodleMoodle Seminars 2

Learning objectives

The course will discuss the theory and practice of Finite Element and Volume Methods. The theoretical part will follow course notes provided by the Instructor, advanced textbooks on Differential Equations, Iterative Methods for Sparse Linear Systems and numerical methods of Optimization. A part of the course will be held in a Laboratory setting where the methods discussed will be implemented in Matlab, using either the commercial version provided by Mathworks or else the open source version GNU Octave. In addition, high level scientific languages such as FreeFem++ and Clawpack for the numerical solution of elliptic, parabolic and hyperbolic equations will be introduced. At the end of the course the student is expected to have an excellent knowledge of the scientific and computational aspects of the techniques used to solve Partial Differential Equations by means of Finite Elements and Volumes.

Prerequisites and basic notions

Functional analysis, main numerical methods for differential equations.

Program

The course will discuss the following topics:
* Minimum Principle and the weak form, existence, uniqueness and regularity
* The Rayleigh-Ritz and Galerkin methods, finite element method, optimization methods, methods for the solution of sparse linear systems
* Transport and Diffusion equations, artificial diffusion, the generalized Galerkin method, discontinuous elements
* Hyperbolic and parabolic equations, finite volume method, semi and completely discretized problems

Bibliography

Vai alla bibliografia
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.

Didactic methods

The course will last 52 hours, 20 of which in the computer laboratory.The rights of students will be preserved in situations of travel limitation or confinement due to national provisions to combat COVID or in particular situations of fragile health. In these cases, you are invited to contact the teacher directly to organize the most appropriate remedial strategies.

Learning assessment procedures

The purpose of the exam is to see if the student is able to recall and reproduce the theory and practice of Finite Elements. The exam will be oral. Alternatively, the student may choose to be examined on the basis of a specific software programming language. In this case, part of the evaluation will be replaced by a small project using the package FreeFem++ or Clawpack.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE

Evaluation criteria

To pass the exam you will have to demonstrate:
* knowing and understanding the fundamentals of the finite element method
* knowing and understanding the fundamentals of the finite volume method
* having an adequate capacity for analysis and synthesis and abstraction
* knowledge apply this knowledge to solve problems and exercises, knowing how to argue their arguments with mathematical rigor.

Criteria for the composition of the final grade

The grade is given by the oral exam.

Exam language

English

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