A cheap preconditioner based on fast diagonalization method for matrix-free weighted-quadrature isogeometric analysis applied to nonlinear transient heat transfer problems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2023

A cheap preconditioner based on fast diagonalization method for matrix-free weighted-quadrature isogeometric analysis applied to nonlinear transient heat transfer problems

Résumé

In this paper, IsoGeometric Analysis is applied to a transient nonlinear heat conduction problem using a predictor-corrector scheme. To obtain a better approximation of the solution, we propose the k-refinement method coupled to a Matrix-Free Weighted Quadrature approach which speeds up matrix-vector operations and also reduces memory consumption. The main goal of this work is to introduce a preconditioning strategy to improve the convergence rate of the iterative solver. This method is based on Fast Diagonalization technique which exploits the tensor structure of basis functions. We show that our preconditioner is inexpensive, easy to code and as effective as other more sophisticated methods. It is also robust with respect to polynomial degree, mesh size and time-integration scheme parameters. Numerical experiments for different geometries and materials are presented, which support our theoretical results.
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Dates et versions

hal-04131963 , version 1 (17-06-2023)

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Citer

Joaquín Cornejo Fuentes, Thomas Elguedj, David Dureisseix, Arnaud Duval. A cheap preconditioner based on fast diagonalization method for matrix-free weighted-quadrature isogeometric analysis applied to nonlinear transient heat transfer problems. Computer Methods in Applied Mechanics and Engineering, 2023, 414, pp.116157. ⟨10.1016/j.cma.2023.116157⟩. ⟨hal-04131963⟩
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