A boundary element method for homogenization of periodic structures

Dalibor Lukáš; Günther Of; Jan Zapletal; Jiří Bouchala

doi:10.1002/mma.5882

A boundary element method for homogenization of periodic structures

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

^*Corresponding author for this work

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1035-1052
Number of pages	18
Journal	Mathematical Methods in the Applied Sciences
Volume	43
Issue number	3
DOIs	https://doi.org/10.1002/mma.5882
Publication status	Published - 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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10.1002/mma.5882

Cite this

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title = "A boundary element method for homogenization of periodic structures",

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–Poincar{\'e} 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.",

keywords = "boundary element method, homogenization",

author = "Dalibor Luk{\'a}{\v s} and G{\"u}nther Of and Jan Zapletal and Ji{\v r}{\'i} Bouchala",

year = "2020",

month = feb,

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doi = "10.1002/mma.5882",

language = "English",

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T1 - A boundary element method for homogenization of periodic structures

AU - Lukáš, Dalibor

AU - Of, Günther

AU - Zapletal, Jan

AU - Bouchala, Jiří

PY - 2020/2/8

Y1 - 2020/2/8

N2 - 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.

AB - 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.

KW - boundary element method

KW - homogenization

UR - https://doi.org/10.1002/mma.5882

UR - http://www.scopus.com/inward/record.url?scp=85076376757&partnerID=8YFLogxK

U2 - 10.1002/mma.5882

DO - 10.1002/mma.5882

M3 - Article

VL - 43

SP - 1035

EP - 1052

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 3

ER -

A boundary element method for homogenization of periodic structures

Abstract

Keywords

ASJC Scopus subject areas

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