Szczegóły publikacji
Opis bibliograficzny
Isogeometric Residual Minimization method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems / V. M. Calo, M. ŁOŚ, Q. Deng, I. Muga, M. PASZYŃSKI // Computer Methods in Applied Mechanics and Engineering ; ISSN 0045-7825. — 2021 — vol. 373, art. no. 113214, s. 1–16. — Bibliogr. s. 15–16, Abstr. — Publikacja dostępna online od: 2020-11-21
Autorzy (5)
- Calo Victor Manuel
- AGHŁoś Marcin Mateusz
- Deng Quanling
- Muga Ignacio
- AGHPaszyński Maciej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 131151 |
|---|---|
| Data dodania do BaDAP | 2020-11-25 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.cma.2020.113214 |
| Rok publikacji | 2021 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Computer Methods in Applied Mechanics and Engineering |
Abstract
In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems.We stabilize the method via residual minimization. We discretize the problem using B-spline basis functions. We then seek to minimize the isogeometric residual over a spline space built on a tensor product mesh. We construct the solution over a smooth subspace of the residual. We can specify the solution subspace by reducing the polynomial order, by increasing the continuity, or by a combination of these. The Gramm matrix for the residual minimization method is approximated by a weighted norm, which we can express as Kronecker products, due to the tensor-product structure of the approximations. We use the Gramm matrix as a preconditional which can be applied in a computational cost proportional to the number of degrees of freedom in 2D and 3D. Building on these approximations, we construct an iterative algorithm. We test the residual minimization method on several numerical examples, and we compare it to the Discontinuous Petrov–Galerkin (DPG) and the Streamline Upwind Petrov–Galerkin (SUPG) stabilization methods. The iGRM method delivers similar quality solutions as the DPG method, it uses smaller grids, it does not require breaking of the spaces, but it is limited to tensor-product meshes. The computational cost of the iGRM is higher than for SUPG, but it does not require the determination of problem specific parameters.
