A boundary element method for homogenization of periodic structures

Dalibor Lukáš*, Günther Of, Jan Zapletal, Jiří Bouchala

*Corresponding author for this work

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)1035-1052
Number of pages18
JournalMathematical methods in the applied sciences
Volume43
Issue number3
DOIs
Publication statusPublished - 8 Feb 2020

Keywords

  • boundary element method
  • homogenization

ASJC Scopus subject areas

  • Computational Mathematics
  • Engineering(all)
  • Mathematics(all)

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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