Adaptive isogeometric analysis using optimal transport and their fast solvers - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2024

Adaptive isogeometric analysis using optimal transport and their fast solvers

Abstract

The use of adaptive mesh methods is fundamental to the numerical solution of systems of partial differential equations that involve large solution variations or with different scales. Adaptive mesh methods are also a major tool for solving problems with high anisotropy, such those encountered in Computational Plasmas Physics. Grid Adaptation and moving meshes are used in different fields and the litterature is quite rich [11, 34, 27, 35, 31, 23, 22, 30, 29, 28, 39, 9]. They are also used to generate Anisotropic meshes [41, 44, 25, 26, 24]. The proposed methods in this work aim to construct a one-to-one mapping F that maps a logical domain (patch, computational domain) with the physical domain as shown in Fig. 1. The function F is constructed using B-splines or NURBS surfaces which are widely used in the Computer Aided Design (CAD) community. The use of these tools in numerical simulations was made popular thanks to the introdution of the IsoGeometric Analysis paradigm by Hughes [37]. Because of the geometric interpretation of the control points, B-spline curves and surfaces have become very popular in CAD. We are interested in these features as they allow us to construct a set of mappings, where each of them will map the unit square onto a sub-domain of the physical domain. Using the geometric properties of B-splines curves and surfaces, it is easy to stick these mappings together, in order to have a global C1 or even C2 mapping. Local regularity of each mapping is ensured by construction.
Fichier principal
Vignette du fichier
MOC_Bahari.pdf (14.49 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03936627 , version 1 (12-01-2023)

Licence

Identifiers

Cite

Mustapha Bahari, Abderrahmane Habbal, Ahmed Ratnani, Eric Sonnendrücker. Adaptive isogeometric analysis using optimal transport and their fast solvers. Computer Methods in Applied Mechanics and Engineering, 2024, 418, pp.116570. ⟨10.1016/j.cma.2023.116570⟩. ⟨hal-03936627⟩
73 View
146 Download

Altmetric

Share

More