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math.NA2026
The diffuse interface approximation to fluid-structure interaction
Francis R. A. Aznaran, Martina BukaÄ, Boris Muha
We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressibl…
math.NA2025
Reduced Order Modeling of Partial Differential Equations on Parameter-Dependent Domains Using Deep Neural Networks
Martina BukaÄ, Iva ManojloviÄ, Boris Muha +1
Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identifi…
math.NA2024
Analysis and finite element approximation of a diffuse interface approach to the Stokes--Biot coupling
Francis R. A. Aznaran, Martina BukaÄ, Boris Muha +1
We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressibl…