Szczegóły publikacji
Opis bibliograficzny
Deep learning driven self-adaptive hp finite element method / Maciej PASZYŃSKI, Rafał GRZESZCZUK, David Pardo, Leszek Demkowicz // W: Computational Science – ICCS 2021 : 21st international conference : Krakow, Poland, June 16–18, 2021 : proceedings, Pt. 1 / eds. Maciej Paszyński, [et al.]. — Cham : Springer Nature Switzerland, cop. 2021. — (Lecture Notes in Computer Science ; ISSN 0302-9743 ; LNCS 12742. Theoretical Computer Science and General Issues ; ISSN 0302-9743). — ISBN: 978-3-030-77960-3; e-ISBN: 978-3-030-77961-0. — S. 114–121. — Bibliogr. s. 120–121, Abstr. — Publikacja dostępna online od: 2021-06-09
Autorzy (4)
- AGHPaszyński Maciej
- AGHGrzeszczuk Rafał
- Pardo David
- Demkowicz Leszek
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 134698 |
|---|---|
| Data dodania do BaDAP | 2021-07-08 |
| Tekst źródłowy | URL |
| DOI | 10.1007/978-3-030-77961-0_11 |
| Rok publikacji | 2021 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Creative Commons | |
| Wydawca | Springer |
| Konferencja | 21st International Conference on Computational Science |
| Czasopisma/serie | Lecture Notes in Computer Science, Theoretical Computer Science and General Issues |
Abstract
Rafał Grzeszczuk 1 David Pardo 234 Leszek Demkowicz 5 1.AGH University of Science and TechnologyKrakówPoland 2.The University of the Basque CountryBilbaoSpain 3.Basque Center for Applied MathematicsBilbaoSpain 4.IKERBASQUEBilbaoSpain 5.Oden Institute, The University of Texas at AustinAustinUSA Open Access Conference paper First Online: 09 June 2021 28 Downloads Part of the Lecture Notes in Computer Science book series (LNCS, volume 12742) Abstract The finite element method (FEM) is a popular tool for solving engineering problems governed by Partial Differential Equations (PDEs). The accuracy of the numerical solution depends on the quality of the computational mesh. We consider the self-adaptive hp-FEM, which generates optimal mesh refinements and delivers exponential convergence of the numerical error with respect to the mesh size. Thus, it enables solving difficult engineering problems with the highest possible numerical accuracy. We replace the computationally expensive kernel of the refinement algorithm with a deep neural network in this work. The network learns how to optimally refine the elements and modify the orders of the polynomials. In this way, the deterministic algorithm is replaced by a neural network that selects similar quality refinements in a fraction of the time needed by the original algorithm.