Szczegóły publikacji
Opis bibliograficzny
A three-level linearized time integration scheme for tumor simulations with Cahn-Hilliard equations / Maciej SMOŁKA, Maciej WOŹNIAK, Robert SCHAEFER // W: Computational Science – ICCS 2021 : 21st International Conference : Krakow, Poland, June 16–18, 2021 : proceedings, Pt. 6 / eds. Maciej Paszyński, [et al.]. — Cham : Springer Nature Switzerland, cop. 2021. — (Lecture Notes in Computer Science ; ISSN 0302-9743 ; LNCS 12747. Theoretical Computer Science and General Issues ; ISSN 0302-9743). — ISBN: 978-3-030-77979-5; e-ISBN: 978-3-030-77980-1. — S. 173-185. — Bibliogr., Abstr. — Publikacja dostępna online od: 2021-06-09
Autorzy (3)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 134747 |
|---|---|
| Data dodania do BaDAP | 2021-07-19 |
| DOI | 10.1007/978-3-030-77980-1_14 |
| Rok publikacji | 2021 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Konferencja | International Conference on Computational Science 2021 |
| Czasopisma/serie | Lecture Notes in Computer Science, Theoretical Computer Science and General Issues |
Abstract
The paper contains an analysis of a three-level linearized time integration scheme for Cahn-Hilliard equations. We start with a rigorous mixed strong/variational formulation of the appropriate initial boundary value problem taking into account the existence and uniqueness of its solution. Next we pass to the definition of two time integration schemes: the Crank-Nicolson and a three-level linearized ones. Both schemes are applied to the discrete version of Cahn-Hilliard equation obtained through the Galerkin approximation in space. We prove that the sequence of solutions of the mixed three level finite difference scheme combined with the Galerkin approximation converges when the time step length and the space approximation error decrease. We also recall the verification of the second order of this scheme and its unconditional stability with respect to the time variable. A comparative scalability analysis of parallel implementations of the schemes is also presented.
