3D-1D coupling on non conforming meshes via three-field optimization based domain decomposition
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Publication:6360468
DOI10.1016/J.JCP.2021.110738arXiv2102.06601MaRDI QIDQ6360468
Denise Grappein, Stefano Scialò, Stefano Berrone
Publication date: 12 February 2021
Abstract: A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high robustness and flexibility in handling geometrical complexities. This is achieved by means of a three-field approach to split the 1D problems from the bulk 3D problem, and then resorting to the minimization of a properly designed functional to impose matching conditions at the interfaces. Thanks to the structure of the functional, the method allows the use of independent meshes for the various subdomains.
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Higher-order elliptic equations (35J30)
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