Ljulj, Matko ; Schmidt, Kersten ; Semin, Adrien ; Tambača, Josip (2022)
Homogenization of the time-dependent heat equation on planar one-dimensional periodic structures.
In: Applicable Analysis, 101 (12)
doi: 10.1080/00036811.2022.2078713
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction condition is applied at all (inner) vertices. Using the two-scale convergence adapted to homogenization of lower-dimensional problems we obtain the limit homogenized problem defined on a two-dimensional domain that is occupied by the mesh when the mesh period δ tends to 0. The homogenized model is given by the classical heat equation with the conductivity tensor depending on the unit cell graph only through the topology of the graph and lengthes of its edges. We show the well-posedness of the limit problem and give a purely algebraic formula for the computation of the homogenized conductivity tensor. The analysis is completed by numerical experiments showing a convergence to the limit problem where the convergence order in δ depends on the unit cell pattern.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Ljulj, Matko ; Schmidt, Kersten ; Semin, Adrien ; Tambača, Josip |
| Art des Eintrags: | Bibliographie |
| Titel: | Homogenization of the time-dependent heat equation on planar one-dimensional periodic structures |
| Sprache: | Deutsch |
| Publikationsjahr: | 2022 |
| Verlag: | Taylor & Francis |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Applicable Analysis |
| Jahrgang/Volume einer Zeitschrift: | 101 |
| (Heft-)Nummer: | 12 |
| DOI: | 10.1080/00036811.2022.2078713 |
| URL / URN: | https://doi.org/10.1080/00036811.2022.2078713 |
| Kurzbeschreibung (Abstract): | In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction condition is applied at all (inner) vertices. Using the two-scale convergence adapted to homogenization of lower-dimensional problems we obtain the limit homogenized problem defined on a two-dimensional domain that is occupied by the mesh when the mesh period δ tends to 0. The homogenized model is given by the classical heat equation with the conductivity tensor depending on the unit cell graph only through the topology of the graph and lengthes of its edges. We show the well-posedness of the limit problem and give a purely algebraic formula for the computation of the homogenized conductivity tensor. The analysis is completed by numerical experiments showing a convergence to the limit problem where the convergence order in δ depends on the unit cell pattern. |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 07 Okt 2022 11:17 |
| Letzte Änderung: | 07 Okt 2022 11:17 |
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