A boundary element method for homogenization of periodic structures. (8th December 2019)

• Record Type: Journal Article
• Authors: Lukáš, Dalibor; Of, Günther; Zapletal, Jan; Bouchala, Jiří
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 3(2020)
• Page Start: 1035
• Page End: 1052
• Publication Date: 2019-12-08
• Subjects: boundary element method -- homogenization; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5882
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.