Isogeometric methods for hyperbolic partial differential equations

Asma Gdhami 1
1 Acumes - Analysis and Control of Unsteady Models for Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Isogeometric Analysis (IGA) is a modern strategy for numerical solution of partial differential equations, originally proposed by Thomas Hughes, Austin Cottrell and Yuri Bazilevs in 2005. This discretization technique is a generalization of classical finite element analysis (FEA), designed to integrate Computer Aided Design (CAD) and FEA, to close the gap between the geometrical description and the analysis of engineering problems. This is achieved by using B-splines or non-uniform rational B-splines (NURBS), for the description of geometries as well as for the representation of unknown solution fields.The purpose of this thesis is to study isogeometric methods in the context of hyperbolic problems usingB-splines as basis functions. We also propose a method that combines IGA with the discontinuous Galerkin(DG)method for solving hyperbolic problems. More precisely, DG methodology is adopted across the patchinterfaces, while the traditional IGA is employed within each patch. The proposed method takes advantageof both IGA and the DG method.Numerical results are presented up to polynomial order p= 4 both for a continuous and discontinuousGalerkin method. These numerical results are compared for a range of problems of increasing complexity,in 1D and 2D.
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Asma Gdhami. Isogeometric methods for hyperbolic partial differential equations. Analysis of PDEs [math.AP]. Université Côte d'Azur; Université de Tunis El Manar, 2018. English. ⟨NNT : 2018AZUR4210⟩. ⟨tel-02272817⟩

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