Loosely coupled, non-iterative time-splitting scheme based on Robin–Robin coupling: Unified analysis for parabolic/parabolic and parabolic/hyperbolic problems

References

[1] M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells, The FEniCS Project Version 1.5, Archive of Numerical Software 3 (2015).Search in Google Scholar

[2] S. Badia, F. Nobile, and C. Vergara, Fluid–structure partitioned procedures based on Robin transmission conditions, J. Comput. Phys. 227 (2008), No. 14, 7027–7051.10.1016/j.jcp.2008.04.006Search in Google Scholar

[3] F. Ballarin, Multiphenics: Mathlab Innovating with Mathematics. https://mathlab.sissa.it/multiphenicsSearch in Google Scholar

[4] J.W. Banks, W. D. Henshaw, and D.W. Schwendeman, An analysis of a new stable partitioned algorithm for FSI problems. Part I: Incompressible flow and elastic solids, J. Comput. Phys. 269 (2014), 108–137.10.1016/j.jcp.2014.03.006Search in Google Scholar

[5] M. Benes, Convergence and stability analysis of heterogeneous time step coupling schemes for parabolic problems, Appl. Math. Comput. 121 (2017), 198–222.10.1016/j.apnum.2017.07.003Search in Google Scholar

[6] M. Benes, A. Nekvinda, and M. K. Yadav, Multi-time-step domain decomposition method with non-matching grids for parabolic problems, Appl. Math. Comput. 267 (2015), 571–582.10.1016/j.amc.2015.01.055Search in Google Scholar

[7] M. Bukač, A. Seboldt, and C. Trenchea, Refactorization of Cauchy’s method: A second-order partitioned method for fluid–thick structure interaction problems, J. Math. Fluid Mechanics 23 (2021), No. 3, 1–25.10.1007/s00021-021-00593-zSearch in Google Scholar

[8] E. Burman, R. Durst, M. Fernandez, and J. Guzman, Fully discrete loosely coupled Robin–Robin scheme for incompressible fluid– structure interaction: stability and error analysis, Numerische Mathematik 151 (2022), No. 4, 807–840.10.1007/s00211-022-01295-ySearch in Google Scholar

[9] E. Burman and M. A. Fernández, Stabilization of explicit coupling in fluid–structure interaction involving fluid incompressibility, Comp. Methods Appl. Mech. Engrg. 198 (2009), No. 5, 766–784.10.1016/j.cma.2008.10.012Search in Google Scholar

[10] E. Burman, R. Durst, and J. Guzman, Stability and error analysis of a splitting method using Robin–Robin coupling applied to a fluid–structure interaction problem, Numer. Methods Part. Diff. Equ. (2021).10.1002/num.22840Search in Google Scholar

[11] E. Burman and M. A. Fernández, Explicit strategies for incompressible fluid–structure interaction problems: Nitsche type mortaring versus Robin–Robin coupling, Int. J. Numer. Methods Engrg. 97 (2014), No. 10, 739–758.10.1002/nme.4607Search in Google Scholar

[12] C. Canuto and A. Lo Giudice, A multi-timestep Robin–Robin domain decomposition method for time dependent advection– diffusion problems, Appl. Math. Comp. 363 (2019), 124596.10.1016/j.amc.2019.124596Search in Google Scholar

[13] Y. Cao, M. Gunzburger, X. He, and X.Wang, Parallel, non-iterative, multiphysics domain decomposition methods for time-dependent Stokes–Darcy systems, Math. Comput. 83 (2014), No. 288, 1617–1644.10.1090/S0025-5718-2014-02779-8Search in Google Scholar

[14] P. Causin, J.-F. Gerbeau, and F. Nobile, Added-mass effect in the design of partitioned algorithms for fluid–structure problems, Comp. Methods Appl. Mech. Engrg 194 (2005), No. 42-44, 4506–4527.10.1016/j.cma.2004.12.005Search in Google Scholar

[15] C. Förster, W. A. Wall, and E. Ramm, Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows, Comput. Methods Appl. Mech. Engrg. 196 (2007), No. 7, 1278–1293.10.1016/j.cma.2006.09.002Search in Google Scholar

[16] L. Gerardo-Giorda, F. Nobile, and C. Vergara, Analysis and optimization of Robin–Robin partitioned procedures in fluid–structure interaction problems, SIAM J. Numer. Anal. 48 (2010), No. 6, 2091–2116.10.1137/09076605XSearch in Google Scholar

[17] P. Le Tallec and J. Mouro, Fluid structure interaction with large structural displacements, Comput. Meth. Appl. Mech. Engrg. 190 (2001), 3039–3067.10.1016/S0045-7825(00)00381-9Search in Google Scholar

[18] P.-L. Lions, On the Schwarz alternating method. III: a variant for nonoverlapping subdomains, In: Third Int. Symposium on Domain Decomposition Methods for Partial Differential Equations, Vol. 6, SIAM, Philadelphia, PA, 1990, pp. 202–223.Search in Google Scholar

[19] A. Logg, K.-A. Mardal, and G. Wells (Eds.), Automated Solution of Differential Equations by the Finite Element Method, Springer, 2012.10.1007/978-3-642-23099-8Search in Google Scholar

[20] F. Nobile and C. Vergara, An effective fluid–structure interaction formulation for vascular dynamics by generalized Robin conditions, SIAM J. Sci. Comput. 30 (2008), No. 2, 731–763.10.1137/060678439Search in Google Scholar

[21] A. Seboldt and M. Bukač, A non-iterative domain decomposition method for the interaction between a fluid and a thick structure, Numer. Methods Part. Diff. Equ. 37 (2021), No. 4, 2803–2832.10.1002/num.22771Search in Google Scholar