Introduction to Partial Differential Equations
People
Course director
Assistant
Description
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).
Objectives
Knowledge and understanding of the foundations of partial differential equations and finite element methods for their numerical solution in HPC.
Teaching mode
In presence
Learning methods
Direct instruction plus hands-on exercises.
Examination information
Project exam (with report and oral presentation)
Bibliography
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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.
Education
- Master of Science in Artificial Intelligence, Lecture, Elective, 1st year
- Master of Science in Computational Science, Lecture, Elective, 1st year
- Master of Science in Computational Science, Lecture, Elective, 2nd year
- PhD programme of the Faculty of Informatics, Lecture, Elective, 1st year (2 ECTS)
