Szczegóły publikacji
Opis bibliograficzny
Reutilization of partial LU factorizations for self-adaptive hp Finite Element Method solver / Maciej PASZYŃSKI, Robert SCHAEFER // W: Computational Science – ICCS 2008 : 8th International Conference : Kraków, Poland, June 23–25, 2008 : proceedings , Pt. 1 / eds. Marian Bubak, Geert Dick van Albada, Jack Dongarra, Peter M. A. Sloot. — Berlin ; Heidelberg : Springer-Verlag, cop. 2008 + CD-ROM. — ( Lecture Notes in Computer Science ; ISSN 0302-9743 ; LNCS 5101. Theoretical Computer Science and General Issues ; ISSN 0302-9743 ). — Dołączony CD-ROM zawiera pełne teksty referatów z pt. 1, pt. 2, pt. 3. — ISBN: 978-3-540-69383-3; ISBN: 3-540-69383-1; e-ISBN: 978-3-540-69384-0. — S. 965–974. — Bibliogr. s. 974, Abstr.
Autorzy (2)
Dane bibliometryczne
| ID BaDAP | 40266 |
|---|---|
| Data dodania do BaDAP | 2008-09-25 |
| DOI | 10.1007/978-3-540-69384-0_101 |
| Rok publikacji | 2008 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Czasopisma/serie | Lecture Notes in Computer Science, Theoretical Computer Science and General Issues |
Abstract
The paper presents theoretical analysis of the extension of the new direct solver dedicated for the fully automatic hp adaptive Finite Element Method. The self-adaptive hp-FEM generates in a fully automatic mode (without any user interaction) a sequence of meshes delivering exponential convergence of the numerical error with respect to the mesh size. The consecutive meshes are obtained by performing h, p or hp refinements. The proposed solver constructs an initial elimination tree based on the nested dissection algorithm executed over the initial mesh. The constructed elimination tree is updated each time the mesh is refined, by adding the elimination sub-tree related to the executed refinement. We propose a new strategy for reutilization of partial LU factorizations computed by the direct solver on the previous mesh, when solving a consecutive mesh from the sequence. We show that the number of LU factorizations that must be recomputed is linearly proportional to the number of singularities in the problem.
