Introduction to Partial Differential Equations
Persone
Docente titolare del corso
Assistente
Descrizione
Many phenomena in real life applications are modeled by partial differential equations (PDEs). These mathematical models are sets of equations, which describe the essential behavior of a natural or artificial system, in order to forecast and control its evolution. We will give an overview on the derivation of PDEs from physical applications and discuss their mathematical background. The theoretical investigations will be accompanied by the introduction and implementation of numerical schemes for their actual solution with FEniCSX (https://numfocus.org/project/fenics-project), an open-source Finite Element Platform sponsored by NUMFocus (Google).
Obiettivi
Knowledge and understanding of the foundations of partial differential equations and finite element methods for their numerical solution in HPC.
Modalità di insegnamento
In presenza
Impostazione pedagogico-didattica
Direct instruction plus hands-on exercises.
Modalità d’esame
Project exam (with report and oral presentation)
Bibliografia
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Langtangen, Hans Petter, Mardal, Kent-Andre. "Quick Overview of the Finite Element Method" Texts in Computational Science and Engineering: 1-6.
10.1007/978-3-030-23788-2_1 - Quarteroni, Alfio. Numerical Models for Differential Problems: Numerical Models for Differential Problems. Springer Milan, 2014.
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Aravas, N.. "Finite elements: theory, fast solvers, and applications in solid mechanics [Book and Web reviews]" Computing in Science & Engineering, 1, 2 (1999): 81-81.
10.1109/mcise.1999.753051 - Brenner, Susanne C., Scott, L. Ridgway. The Mathematical Theory of Finite Element Methods: The Mathematical Theory of Finite Element Methods. Springer New York, 2008.
Offerta formativa
- Master of Science in Artificial Intelligence, Lezione, A scelta, 1° anno
- Master of Science in Computational Science, Lezione, A scelta, 1° anno
- Master of Science in Computational Science, Lezione, A scelta, 2° anno
- Dottorato in Scienze informatiche, Lezione, A scelta, 1° anno (2.0 ECTS)
