
A parallel solver for fluid-structure interaction problems with Lagrange multiplier
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We consider a distributed Lagrange multiplier formulation for fluid-structure interaction problems in the spirit of the fictitious domain approach [Boffi, Cavallini, Gastaldi, 2015]. A viscous hyper-elastic solid is immersed in an incompressible Newtonian fluid. The solid evolution is described in Lagrangian framework with a reference domain mapped, at each time instant, into the actual configuration of the body. The fluid dynamics is described in Eulerian framework on a fixed mesh, which is extended to the region occupied by the solid. The kinematic constraints are weakly enforced in the fictitious region employing a Lagrange multiplier. After recalling the main features of our formulation, with a particular focus on assembly techniques for the coupling term and condition number, we present a first prototype of parallel solver [Boffi, Credali, Gastaldi, Scacchi, 2024], highlighting the main challenges that arose during its design and future developments.