Communication Dans Un Congrès Année : 2024

Adaptive Mesh Deformation Based on Randomized RBF Solvers

Résumé

Mesh deformation methods have been widely used for the past decades in various fields such as fluid-structure interaction and aerodynamic shape optimization [3,4-9]. Among the existing methods, radial basis functions interpolation (RBF) is particularly suitable for unstructured mesh applications due to its simplicity and the high quality of the resulting mesh. Such approach requires solving dense linear systems, generally symmetric positive definite (SPD), which tends to be computationally expensive and memory demanding, which is a major drawback when dealing with large-scale meshes [1]. In this work, we aim to speed-up RBF mesh deformation procedure using methods coming from probabilistic linear algebra to solve the associated dense linear system. We will explore the adaptive creation of an approximation to the RBF matrix by projecting the initial large-scale operator onto a smaller subspace. This subspace will that exhibits specific properties such as a better sparsity, while taking into account diverse solving strategies. Utilizing the spectral properties of RBF matrices, we will introduce a novel adaptive strategy to determine the projection dimension at each factorization step. Additionally, we will present a new randomized variant of the traditional linear solver for SPD matrices and conduct a comparative analysis with the existing randomized strategy. Our proposed approach will be thoroughly examined through practical applications in both 2D and 3D contexts.

Siam2024_LA_Wael_Abstract.pdf (116.79 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04888416 , version 1 (15-01-2025)

Identifiants

  • HAL Id : hal-04888416 , version 1

Citer

Wael Bader, Augustin Parret-Fréaud, Sébastien da Viga, Youssef Mesri. Adaptive Mesh Deformation Based on Randomized RBF Solvers. 2024 SIAM Conference on Applied Linear Algebra, May 2024, Paris, France. ⟨hal-04888416⟩
56 Consultations
44 Téléchargements

Partager

  • More