ADVANCED NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Stampa
Enrollment year
2022/2023
Academic year
2022/2023
Regulations
DM270
Academic discipline
MAT/08 (NUMERICAL ANALYSIS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
Period
2nd semester (01/03/2023 - 09/06/2023)
ECTS
6
Lesson hours
48 lesson hours
Language
Italian
Activity type
ORAL TEST
Teacher
MOIOLA ANDREA (titolare) - 3 ECTS
MARCATI CARLO - 3 ECTS
Prerequisites
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.
Learning outcomes
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.
Course contents
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.
Teaching methods
Classroom lectures, tutorials in the computer lab, study of research papers, seminars.
The topics presented may vary according to the students' preferences.
Reccomended or required readings
Notes prepared by the lecturer.
Scientific papers provided by the lecturer.
Assessment methods
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.
Further information
Sustainable development goals - Agenda 2030