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A FFT-based numerical scheme for the transient conductivity of heterogeneous materials with non-periodic boundary conditions

Article dans une revue avec comité de lecture
Author
AMADOU SANOKO, Abdoul Magid
1002421 Institut de Mécanique et d'Ingénierie [I2M]
ccESSONGUE, Simon
1002421 Institut de Mécanique et d'Ingénierie [I2M]
ccGELEBART, Lionel
1228283 Université Paris Saclay
ccLAPOSTOLLE, Lucas
1002421 Institut de Mécanique et d'Ingénierie [I2M]
ccMORIN, Léo
1002421 Institut de Mécanique et d'Ingénierie [I2M]
ccJOSEPH, Paux
1001048 Laboratoire des Sciences des Procédés et des Matériaux [LSPM]

URI
http://hdl.handle.net/10985/26370
DOI
10.1016/j.euromechsol.2025.105680
Date
2025
Journal
European Journal of Mechanics - A/solids

Abstract

The aim of this work is to develop FFT-based solvers for transient diffusion in heterogeneous materials subjected to non-periodic (Dirichlet/Neumann) boundary conditions. We focus on a problem of thermal conductivity and derive a theta-method which includes an implicit solver for transient thermal conductivity in heterogeneous materials. The method is based on a fixed-point iterative solution of an auxiliary problem obtained by a Galerkin discretization using an approximation space based on mixed sine–cosine series. The solution field is decomposed as a known term verifying the boundary conditions and a fluctuation (unknown) term described by appropriate sine–cosine series. The solution of the auxiliary problem involves discrete sine–cosine transforms, of type I and III, which makes the solver rely on the computational complexity of fast Fourier transforms. The method is applied to the prediction of transient thermal fields in a composite material subjected to non periodic boundary conditions.

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