A Discrete Sine-Cosine Transforms Galerkin Method for the Conductivity of Heterogeneous Materials With Mixed Dirichlet/Neumann Boundary Conditions

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Joseph Paux, Léo Morin, Lionel Gélébart
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Abstract

This work aims at developing a numerical method for conductivity problems in heterogeneous media subjected to mixed Dirichlet/Neumann boundary conditions. The method relies on a fixed-point iterative solution of an auxiliary problem obtained by a Galerkin discretization using an approximation space spanned by mixed cosine-sine series. The solution field is written as a known term verifying the boundary conditions and an unknown term described by cosine-sine series, having no contribution on the boundary. Discrete sine-cosine transforms, of Type I and III depending on the boundary conditions, are used to approximate the elementary integrals involved in the Galerkin formulation, which makes the method relying on the numerical complexity of fast Fourier transforms. The method is finally assessed in a problem of a composite material.

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来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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