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Einladung zum Mathematischen Kolloquium
Mittwoch, den 04.02.2026, Seminarraum A (R209), 17 Uhr s.t.
Prof. Dr. Michel Kern, Inria Paris , SERENA Forschungsteam
spricht über das Thema: „Flow in fractured porous media: mathematical analysis, numerical methods and large scale simulations“
Abstract: Subsurface rocks are naturally porous and contain numerous fractures that intersect in complex configurations. Fractures are, in general, permeable pathways and are responsible for most of the flow. They are classically modeled as structures of co-dimension one in the surrounding rock. The 3D flow in the rock is thus coupled to the 2D flow in the fractures. In this talk, we formulate and analyze the mathematical formulation of this coupled system, study its discretization by mixed-hybrid finite element methods and discuss its efficient simulation by means of a domain decomposition preconditioner.
The mathematical analysis rests on a mixed formulation, where the function spaces take into account the mixed-dimensional geometry of the problem. Existence and uniqueness is proved through the Babuska-Brezzi conditions. Next, a finite dimensional approximation by the lowest order Raviart-Thomas-Nédélec finite element is studied, and a first order a priori error estimate is obtained.
The discretization leads to a large linear system that is very poorly conditioned due to the permeability contrasts between rock and fractures, as well as to the low-quality elements present in the mesh.
We show how this system can be solved efficiently by using a domain decomposition preconditioner with a spectral coarse grid, as implemented in the HPDDM library (through PETSc). We show the excellent performance obtained with HPDDM on highly heterogeneous and large-scale fractured porous media, containing up to 700k fractures (242M of unknowns).
Joint work with P. Jolivet , F. Nataf , G. Pichot, R. Zanella , D. Zegarra Vasquez
Bereits ab 16:30 Uhr gibt es für alle Interessierten die Möglichkeit zu einem Gespräch bei Kaffee und Tee im Bibliothekszimmer (R110).
Andreas Potschka
Veranstalter: Institut für Mathematik, Erzstraße 1, 38678 Clausthal-Zellerfeld
Link für die online Teilnahme am Kolloquium:
https://webconf.tu-clausthal.de/rooms/ola-qyv-ml6-ivd/join