Szczegóły publikacji
Opis bibliograficzny
Computational costs of multi-frontal direct solvers with analysis-suitable T-splines / Anna Paszyńska, Maciej PASZYŃSKI // Symmetry [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 2073-8994. — 2020 — vol. 12 iss. 12 art. no. 2070, s. 1–26. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 24–26, Abstr. — Publikacja dostępna online od: 2020-12-13
Autorzy (2)
- Paszyńska Anna
- AGHPaszyński Maciej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 131628 |
|---|---|
| Data dodania do BaDAP | 2020-12-17 |
| Tekst źródłowy | URL |
| DOI | 10.3390/sym12122070 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Symmetry |
Abstract
In this paper, we consider the computational cost of a multi-frontal direct solver used for the factorization of matrices resulting from a discretization of isogeometric analysis with T-splines, and analysis-suitable T-splines. We start from model projection or model heat transfer problems discretized over two-dimensional meshes, either uniformly refined or refined towards a point or an edge. These grids preserve several symmetries and they are the building blocks of more complicated grids constructed during adaptive isotropic refinement procedures. A large class of computational problems construct meshes refined towards point or edge singularities. We propose an ordering that permutes the matrix in a way that the computational cost of a multi-frontal solver executed on adaptive grids is linear. We show that analysis-suitable T-splines with our ordering, besides having other well-known advantages, also significantly reduce the computational cost of factorization with the multi-frontal direct solver. Namely, the factorization with N T-splines of order p over meshes refined to a point has a linear O(Np4) cost, and the factorization with T-splines on meshes refined to an edge has O(N2pp2) cost. We compare the execution time of the multi-frontal solver with our ordering to the Approximate Minimum Degree (AMD) and Cuthill–McKee orderings available in Octave.
