Szczegóły publikacji
Opis bibliograficzny
Least-squares space-time formulation for advection-diffusion problem with efficient adaptive solver based on matrix compression / Marcin ŁOŚ, Paulina Sepúlveda, Mateusz Dobija, Anna Paszyńska // W: Computational Science – ICCS 2023 : 23rd international conference : Prague, Czech Republic, July 3–5, 2023 : proceedings, Pt. 2 / eds. Jiří Mikyška [et al.]. — Cham, Switzerland : Springer, cop. 2023. — (Lecture Notes in Computer Science ; ISSN 0302-9743 ; LNCS 14074). — ISBN: 978-3-031-36020-6; e-ISBN: 978-3-031-36021-3. — S. 547–560. — Bibliogr. s. 559–560, Abstr. — Publikacja dostępna online od: 2023-06-26
Autorzy (4)
- AGHŁoś Marcin Mateusz
- Sepúlveda Paulina
- Dobija Mateusz
- Paszyńska Anna
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 147658 |
|---|---|
| Data dodania do BaDAP | 2023-07-20 |
| DOI | 10.1007/978-3-031-36021-3_54 |
| Rok publikacji | 2023 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Konferencja | 23rd International Conference on Computational Science |
| Czasopismo/seria | Lecture Notes in Computer Science |
Abstract
We present the hierarchical matrix compression algorithms to speed up the computations to solve unstable space-time finite element method. Namely, we focus on the non-stationary time-dependent advection dominated diffusion problem solved by using space-time finite element method. We formulate the problem on the space-time mesh, where two axes of coordinates system denote the spatial dimension, and the third axis denotes the temporal dimension. By employing the space-time mesh, we avoid time iterations, and we solve the problem “at once” by calling a solver once for the entire mesh. This problem, however, is challenging, and it requires the application of special stabilization methods. We propose the stabilization method based on least-squares. We derive the space-time formulation, and solve it using adaptive finite element method. To speed up the solution process, we compress the matrix of the space-time formulation using the low-rank compression algorithm. We show that the compressed matrix allows for quasi-linear computational cost matrix-vector multiplication. Thus, we apply the GMRES solver with hierarchical matrix-vector multiplications. Summing up, we propose a quasi-linear computational cost solver for stabilized space-time formulations of advection dominated diffusion problem.