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Domain decomposition methods in a geometrical multiscale domain using finite volume schemes
Author(s) -
Viallon MarieClaude
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4788
Subject(s) - domain decomposition methods , mathematics , discretization , diagonal , node (physics) , uniqueness , domain (mathematical analysis) , finite volume method , interface (matter) , dirichlet distribution , finite element method , mathematical analysis , boundary value problem , geometry , computer science , physics , structural engineering , bubble , maximum bubble pressure method , parallel computing , mechanics , engineering , thermodynamics
Summary The heat equation is solved by using a finite volume discretization in a domain that consists of a two‐dimensional central node and several one‐dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.