A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation usin...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-02, Vol.43 (3), p.1035-1052
Main Authors: Lukáš, Dalibor, Of, Günther, Zapletal, Jan, Bouchala, Jiří
Format: Article
Language:English
Subjects:
Boundary element method
Boundary integral method
homogenization
Integral equations
Nonlinear programming
Operators (mathematics)
Partial differential equations
Periodic structures
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Summary:Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super‐linearly with the mesh size, and we support the theory with examples in two and three dimensions.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5882