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A boundary element method for homogenization of periodic structures
Author(s) -
Lukáš Dalibor,
Of Günther,
Zapletal Jan,
Bouchala Jiří
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5882
Subject(s) - homogenization (climate) , mathematics , discretization , mathematical analysis , periodic boundary conditions , boundary value problem , finite element method , boundary element method , partial differential equation , boundary knot method , boundary (topology) , poincaré–steklov operator , mixed boundary condition , robin boundary condition , physics , biodiversity , ecology , biology , thermodynamics
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.