Szczegóły publikacji
Opis bibliograficzny
A Kronecker product linear-cost solver for the high-order generalized-$\alpha$ method for multi-dimensional hyperbolic systems / V. M. Calo, P. Behnoudfar, M. ŁOŚ, M. PASZYŃSKI // Computers and Mathematics with Applications ; ISSN 0898-1221. — 2023 — vol. 142, s. 257-267. — Bibliogr. s. 266-267, Abstr. — Publikacja dostępna online od: 2023-05-18
Autorzy (4)
- Calo V. M.
- Behnoudfar Pouria
- AGHŁoś Marcin Mateusz
- AGHPaszyński Maciej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 146816 |
|---|---|
| Data dodania do BaDAP | 2023-06-14 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.camwa.2023.04.043 |
| Rok publikacji | 2023 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Computers & Mathematics with Applications |
Abstract
The main result of the work is the generalization of the concept of the variational splitting from [3] to the higher-order generalized-α schemes proposed in [5] in the context of hyperbolic and elastic wave propagation problems. It is possible to factorize the matrix of the linear system of equations in the linear computational cost. Here M is the mass matrix, and K is the stiffness matrix. We discretize using the isogeometric finite element method. Following the idea proposed in [3], factorizing the matrix , we obtained an additional error of the order of . This paper introduces a technique to couple the possibility of fast factorization of with higher-order generalized-α schemes proposed in [5] for hyperbolic and elastic wave propagation problems. Thus, we introduce a variationally separable splitting technique for the high-order accuracy generalized-α method. We use tensor-product meshes to develop the splitting method, which results in the linear cost for multi-dimensional problems. We consider standard finite elements as well as smoother isogeometric analysis for spatial discretization. The direction splitting method requires the mass and the stiffness matrices to have the Kronecker product structure. For other problems, the corresponding Kronecker product solver can be employed as a preconditioner as long as a Kronecker product can sufficiently well approximate the problem matrix. We also study the spectrum of the amplification matrix to establish the unconditional stability of the method. We use various examples to demonstrate the performance of the method and the optimal approximation accuracy. In numerical tests, we compute the and norms to show the optimal convergence of the discrete method in space and high-order accuracy in time.