Abstract
Independent meshing of subdomains separated by an interface can lead to spatially non-coincident discrete interfaces. We present an optimization-based coupling method for such problems, which does not require a common mesh refinement of the interface, has optimal \(H^1\) convergence rates, and passes a patch test. The method minimizes the mismatch of the state and normal stress extensions on discrete interfaces subject to the subdomain equations, while interface “fluxes” provide virtual Neumann controls.
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References
Farhat, C., Lesoinne, M., Tallec, P.L.: Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Methods Appl. Mech. Engrg. 157(1–2), 95–114 (1998)
de Boer, A., van Zuijlen, A., Bijl, H.: Review of coupling methods for non-matching meshes. Comput. Methods Appl. Mech. Engrg. 196(8), 1515–1525 (2007)
Dohrmann, C.R., Key, S.W., Heinstein, M.W.: A method for connecting dissimilar finite element meshes in two dimensions. Int. J. Numer. Meth. Eng. 48(5), 655–678 (2000)
Dohrmann, C.R., Key, S.W., Heinstein, M.W.: Methods for connecting dissimilar three-dimensional finite element meshes. Int. J. Numer. Meth. Eng. 47(5), 1057–1080 (2000)
Gunzburger, M.D., Peterson, J.S., Kwon, H.: An optimization based domain decomposition method for partial differential equations. Comput. Math. Appl. 37(10), 77–93 (1999)
Gunzburger, M.D., Lee, H.K.: An optimization-based domain decomposition method for the Navier-Stokes equations. SIAM J. Numer. Anal. 37(5), 1455–1480 (2000)
Laursen, T.A., Heinstein, M.W.: Consistent mesh tying methods for topologically distinct discretized surfaces in non-linear solid mechanics. Int. J. Numer. Meth. Eng. 57(9), 1197–1242 (2003)
Parks, M., Romero, L., Bochev, P.: A novel lagrange-multiplier based method for consistent mesh tying. Comput. Methods Appl. Mech. Engrg. 196(35–36), 3335–3347 (2007)
Hecht, F.: New development in FreeFem++. J. Numer. Math. 20(3–4), 251–265 (2012)
Bochev, P., Ridzal, D.: Optimization-based additive decomposition of weakly coercive problems with applications. Comput. Math. with Appl. 71(11), 2140–2154 (2016)
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This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, and the Laboratory Directed Research and Development program at Sandia National Laboratories.
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Bochev, P., Kuberry, P., Peterson, K. (2018). A Virtual Control Coupling Approach for Problems with Non-coincident Discrete Interfaces. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_15
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DOI: https://doi.org/10.1007/978-3-319-73441-5_15
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