Partial homogenization of the diffusion equation with a dirac-like potential

The paper is devoted to the diffusion equation, with the Dirac-like periodic potential having different structure in two parts of the domain. The problem can be homogenized in one part of the domain while the standard homogenization does not work in the other. We introduce and test numerically the method of partial homogenization, combining in one multiscale model the homogenized and discrete description. © 2020 by Begell House,.

Authors
Mahiout L.A.1 , Panasenko G.2, 3, 4 , Volpert V. 5, 6, 7
Journal
International Journal for Multiscale Computational Engineering
Publisher
Begell House Inc.
Number of issue
5
Language
English
Pages
507-518
Status
Published
Link
External link
DOI
10.1615/INTJMULTCOMPENG.2020035521
Volume
18
Year
2020
Organizations
  • 1 Laboratoire d’équations aux dérivées partielles non linéaires et histoire des mathématiques, École Normale Supérieure, B.P. 92, Vieux Kouba, Algiers, 16050, Algeria
  • 2 University of Lyon, UJM-Saint-Etienne, CNRS, Institute Camille Jordan, UMR 5208 SFR MODMAD FED 4169, Saint-Etienne, 42023, France
  • 3 National Research University Moscow Power Engineering Institute, Krasnoznamennaya 14, Moscow, 111250, Russian Federation
  • 4 Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, Vilnius, 03225, Lithuania
  • 5 Institut Camille Jordan, UMR 5585, CNRS, University Lyon 1, Villeurbanne, 69622, France
  • 6 INRIA, Université de Lyon, Université Lyon 1, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, Villeurbanne Cedex, 69200, France
  • 7 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str, Moscow, 117198, Russian Federation
Keywords
Diffusion equation; Dirac-like periodic potential; Partial homogenization
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