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Detalji o izabranom predavanju:
| Seminar: | Seminar za numeričku matematiku i znan. računanje |
| Naziv predavanja: | Insights into PDE eigenvalue problems and their approximation using adaptive FEMs |
| Predavač: | Stefano Giani, Durham University, Velika Britanija |
| Vrijeme: |
01.06.2023 13:15 |
| Predavaonica: | 105 |
| Tip: |
Gost seminara |
| Opis: | Even the most simple eigenvalue problem is not trivial to solve due to the non-linear nature of the problem. This is true even if the differential operator is linear. The point of view for this lecture is of someone that wants to approximate numerically eigenvalue problem using FEMs or adaptive FEMs. We present some of the theory of eigenvalue problem but we will not indulge in that. Instead, we are going to describe plenty of algorithms to be used in numerical simulations. We aim to make this lecture suitable to anyone with experience with FEMs who would like to tackle eigenvalue problems next. This lecture starts describing some of the characteristics of eigenvalue problems that set
them apart from other non-linear problems. We explore the difficulties of approximating multiple eigenvalues and how we can measure the approximation error that in the case of multiple eigenvalues behaves like a moving target. In the second part, of the lecture, we focus on adaptivity for FEMs and error estimators. A few error estimators are presented with examples of their applications. In this part we cover continuous and discontinuous Galerkin methods. In the last part of the lecture, we explore more advanced techniques and extensions of standard FEMs for eigenvalue problems. We discuss methods for complicated domains and polygonal meshes. Finally, we present a multimesh approach with adaptivity to eigenvalue problems capable of approximate different eigenfunctions on different meshes. The results presented in this lecture are computed using AptoFEM and Hermes (http://www.hpfem.org/). |
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