Year: 2025
Author: Marie-Claude Viallon
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 4 : pp. 534–555
Abstract
A model parabolic linear partial differential equation in a geometrical multi-scale domain is studied. The domain consists of a two-dimensional central node, and several one-dimensional outgoing branches. The physical coupling conditions between the node and the branches are either continuity of the solution or continuity of the normal flux. An iterative Schwarz method based on Robin transmission conditions is adjusted to the problem in each case and formulated in substructured form. The convergence of the method is stated. Numerical results when the method is used as preconditioner for a Krylov method (GMRES) are provided.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1023
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 4 : pp. 534–555
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Finite volume scheme parabolic problem multi-scale domain domain decomposition stability and convergence of numerical methods Schwarz methods Robin interface condition.