Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers

Published on Feb 23, 2021in SIAM Journal on Numerical Analysis2.712
路 DOI :10.1137/20M1329664
Miroslav Kuchta8
Estimated H-index: 8
,
Federica Laurino2
Estimated H-index: 2
+ 1 AuthorsPaolo Zunino28
Estimated H-index: 28
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Abstract
Coupled partial differential equations (PDEs) defined on domains with different dimensionality are usually called mixed-dimensional PDEs. We address mixed-dimensional PDEs on three-dimensional (3D)...
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#1Nora Hagmeyer (Bundeswehr University Munich)H-Index: 1
#2Matthias MayrH-Index: 5
Last. Alexander PoppH-Index: 63
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This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-d...
#1Miroslav Kuchta (Simula Research Laboratory)H-Index: 8
In numerous applications the mathematical model consists of different processes coupled across a lower dimensional manifold. Due to the multiscale coupling, finite element discretization of such models presents a challenge. Assuming that only singlescale finite element forms can be assembled we present here a simple algorithm for representing multiscale models as linear operators suitable for Krylov methods. Flexibility of the approach is demonstrated by numerical examples with coupling across d...
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