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
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The 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.
1° Year
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2° Year It will be activated in the A.Y. 2025/2026
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1 module between the following:
- A.A. 2024/2025 Computational algebra not activated;
- A.A. 2025/2026 Homological Algebra not activated.1 module between the following 3 modules among the following
- A.A. 2025/2026 Homological algebra not activated.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.
Data Fitting and Reconstruction (2024/2025)
Teaching code
4S008269
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/08 - NUMERICAL ANALYSIS
Period
Semester 1 dal Oct 1, 2024 al Jan 31, 2025.
Courses Single
Authorized
Learning objectives
The course will discuss the theoretical and practical aspects and the possible applications of the numerical methods for the solution of partial differential equations of hyperbolic type.
We will focus in particular on Finite volume and discontinuous Galerkin methods with emphasis on the high order of accuracy. An integral part of the course will be the laboratory in which the methods presented during the lectures will be implemented in a programming language suitable for scientific computing, also providing elements of parallel computing. At the end of the course, students are expected to have knowledge and skills in numerical analysis concerning hyperbolic equations and the numerical methods for their solution, to be able to evaluate both their limitations and potential, and to show competence with their implementation.
Prerequisites and basic notions
Students must have completed a bachelor's degree in mathematics, computer science or engineering.
In addition, they must possess knowledge and skills in linear algebra, differential calculus in one and several variables, integral calculus, fundaments of differential equations, and the main methods of numerical calculus.
Program
- Introduction and revision of basical concepts
- Linear & nonlinear hyperbolic equations and systems of hyperbolic equations (e.g. LAE, Burgers, Shallow Water, Euler)
- Numerical methods for linear advection equations and their analysis
- Monotone methods and Godunov theorem
- Finite Volume schemes
• The method in 1D
• Godunov method
• Properties
• Exact Riemann solvers
• Approximate Riemann Solvers
• Finite volume schemes on unstructured two-dimensional grids
- High order Finite Volume schemes
• Second order schemes
• TVD reconstruction and limiters
• High order ENO and WENO nonlinear reconstruction procedures
• High order reconstruction in time: the ADER approach
- Discontinuous Galerkin methods
- Arbitrary-Lagrangian-Eulerian methods
- Programming in a compiled language (Fortran)
- Elements of parallel programming: the OpenMP paradigm
- Elements of parallel programming: the MPI paradigm
Depending on time and students preferences some of the following topics may be studied:
- Delaunay triangulations & Voronoi diagrams
- Path-conservative FV schemes
- Semi-implicit schemes for the incompressible Navier-Stokes equations
Bibliography
Didactic methods
Theoretical lectures in the classroom and numerous lectures dedicated to the implementation, motivation and discussion of the numerical methods subject of the course.
A laptop with installed MATLAB and a fortran compiler is required.
Learning assessment procedures
The examination consists of A) a written test of theory and computational exercises and B) an oral examination.
During the oral examination (B) you will be asked to run and comment on some of the methods implemented during the lectures and one of the exercises left as an assignment.
Evaluation criteria
The examination aims to ascertain that the student possesses knowledge and skills in the field of numerical analysis for hyperbolic equations, numerical methods for solving them, and in serial and parallel programming.
Criteria for the composition of the final grade
The grade will be obtained by taking the arithmetic mean of the marks obtained in the written test (A) and the oral test (B).
Exam language
Il testo della prova scritta sarà in inglese. Gli studenti possono rispondere in inglese o in italiano.
