2022/2023

2022/2023

DM270

MAT/08 (NUMERICAL ANALYSIS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

2nd semester (01/03/2023 - 09/06/2023)

6

48 lesson hours

Italian

ORAL TEST

MOIOLA ANDREA (titolare) - 3 ECTS
MARCATI CARLO - 3 ECTS

Basic knowledge of numerical analysis, mathematical analysis, partial differential equations. A basic knowledge of Matlab, python or similar languages is advisable.
It is preferable to have attended, or to attend during the same term, the Finite Elements class.

The course aims at studying in detail some modern methods for the numerical approximation of partial differential equation that are relevant for applications.
The methods under consideration will be analysed theoretically and implemented numerically.

The course will focus on some advanced techniques for the solution of partial differential equations (PDEs) that complement and extend the programme of the Finite Element course.
Some examples are: boundary element method (BEM), neural and operator network approximations for PDEs, tensor compression methods, isogeometric analysis (IGA), virtual element method (VEM), discontinuous Galerkin (DG) method, immersed boundary method (IBM), domain decomposition (DD), eigenvalue problems, space-time Galerkin methods, preconditioning techniques.

Classroom lectures, tutorials in the computer lab, study of research papers, seminars.
The topics presented may vary according to the students' preferences.

Notes prepared by the lecturer.
Scientific papers provided by the lecturer.

Oral exam and report.
Every student will be able to implement the numerical methods presented during the course, focusing on some extensions or applications, or studying in details some theoretical aspects, also using the most recent scientific literature suggested by the lecturers.