Abstract:
In this talk we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the Finite Element Immersed Boundary Method (FE-IBM) to the actual Finite Element Distributed Lagrange Multiplier method (FE-DLM) (see [1]). We recall the well-posedness of our formulation at the continuous and discrete level in a simplified setting (see [2, 3]). An extension to the case of compressible solid can be found in [4]. Finally, we discuss some computational aspects related with the computatiion of the coupling terms and with a parallel solver (see [5, 6]).
The results presented in this talk have been obtained in collaboartion with Daniele Boffi, Nicola Cavallini, Luca Heltai, Fabio Credali and Simone Scacchi.
References：
[1] Boffi, D., Cavallini, N. and Gastaldi L. The Finite Element Immersed Boundary Method with Distributed Lagrange multiplier SIAM J. of Numerical Analysis (2015) 53:2584–2604.
[2] Boffi, D. and Gastaldi, L. On the existence and the uniqueness of the solution to a fluidstructure interaction problem J. Differential Equations (2021) 279:136–161.
[3] Boffi, D. and Gastaldi, L. A fictitious domain approach with Lagrange multiplier for fluidstructure interactions. Numer. Math. (2017) 135:711–732.
[4] Boffi, D., Gastaldi, L. and Heltai, L. A distributed Lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids Mathematical and numerical modeling of the cardiovascular system and applications SEMA SIMAI Springer Ser. Vol. 16, (2018) 1–21.
[5] Boffi, D., Credali F. and Gastaldi, L. On the interface matrix for fluid-structure interaction problems with fictitious domain approach Comput. Methods Appl. Mech. Engrg. (2022) 401:Paper No.115650.
[6] Boffi, D., Credali F., Gastaldi, L. and Scacchi S. A parallel solver for fluid-structure interaction problems with Lagrange multiplier Math. Comput. Simulation (2024) 220:406–424.
Bio:
Lucia-Gastaldi_CV
DICATAM, Universita di Brescia, Italy `
Email address: lucia.gastaldi@unibs.it
URL: http://lucia-gastaldi.unibs.it
