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UID:4708@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230328T110000
DTEND;TZID=Europe/Paris:20230328T120000
DTSTAMP:20230321T160041Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-julian-hennicker/
SUMMARY:Julian Hennicker (University of Geneva): Modeling and Analysis of t
 he Coupling in Discrete Fracture Matrix models
DESCRIPTION:Julian Hennicker: Models that contain thin heterogeneous layers
  provide particular challanges for their numerical solution\, as they requ
 ire anisotropic and/or very small mesh cells for a geometrical representat
 ion of the layers. This situation most prominently occurs in subsurface fl
 ow applications\, where the thin heterogeneous layers are called fractures
 \, and they are surrounded by the so-called rock matrix. Such models are u
 npracticable for real life simulations\, and one might consider reduced mo
 dels\, which represent the fractures as hypersurfaces\, embedded in the ma
 trix domain. These reduced models are called in the literature mixed- or h
 ybrid-dimensional models\, or Discrete Fracture Matrix models. In this pre
 sentation\, I will show a new approach to develop and analyze reduced orde
 r models for general linear elliptic problems. The focus lies on the deriv
 ation of coupling conditions\, which have to be satisfied by the traces of
  the solutions for the matrix domain on each side of the matrix-fracture i
 nterfaces. Let it be emphasized that we are not only interested in the der
 ivation of coupling conditions that have to be satisfied in the limit of v
 anishing aperture\, but in particular with the derivation of coupling cond
 itions that have to hold up to a certain order of the aperture\, which in 
 turn occurs as a model parameter in the reduced model. The idea is to firs
 t use a Fourier transform in the fracture tangential direction\, which all
 ows us to eliminate the fracture unknowns and to derive exact coupling con
 ditions between the matrix subdomains\, a technique which can be regarded 
 as a continuous analogue to a Schur complement of the fracture unknowns on
 to the matrix-fracture interfaces\, and which is frequently used in domain
  decomposition to derive coupling conditions for optimal or optimized Schw
 arz methods. Reduced order coupling conditions are then obtained by trunca
 ting the asymptotic expansions of the exact conditions at the desired orde
 r. This approach allows us in a second step to derive error estimates for 
 the reduced order solutions\, in terms of powers of the fracture aperture\
 , a result which was still missing in the literature. Numerical tests will
  illustrate the results.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 023/01/image_seminar_AA-DOI.10.1007978-3-030-69363-3_3-fig.4-Nodal_Discret
 ization_of_Two-Phase_Discrete_Fracture_Matrix_Models-Brenner-Hennicker-Rol
 and-x300.png
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage)\
 , 39 Rue Joliot Curie\, 13013 Marseille\, France\, Campus Château-Gombert
 \, 
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  Marseille\, France\, Campus Château-Gombert\, ;X-APPLE-RADIUS=100;X-TITL
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