A boundary element method for homogenization of periodic structures

Dalibor Lukáš, Günther Of, Jan Zapletal, Jiří Bouchala

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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.
Originalspracheenglisch
Seiten (von - bis)1035-1052
FachzeitschriftMathematical methods in the applied sciences
Jahrgang43
Ausgabenummer3
DOIs
PublikationsstatusVeröffentlicht - 8 Feb 2020

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Boundary integral equations
Periodic structures
Periodic Structures
Boundary element method
Homogenization
Boundary Elements
Partial differential equations
Mathematical operators
Cell
Finite Element Discretization
Coefficient
Boundary Integral Equations
Three-dimension
Two Dimensions
Partial differential equation
Numerical Solution
Mesh
Converge
Operator

ASJC Scopus subject areas

  • !!Computational Mathematics

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

Dies zitieren

A boundary element method for homogenization of periodic structures. / Lukáš, Dalibor; Of, Günther; Zapletal, Jan; Bouchala, Jiří.

in: Mathematical methods in the applied sciences, Jahrgang 43, Nr. 3, 08.02.2020, S. 1035-1052.

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Lukáš, Dalibor ; Of, Günther ; Zapletal, Jan ; Bouchala, Jiří. / A boundary element method for homogenization of periodic structures. in: Mathematical methods in the applied sciences. 2020 ; Jahrgang 43, Nr. 3. S. 1035-1052.
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