TY - JOUR
T1 - Schwarz Method in a Geometrical Multi-Scale Domain with Continuous or Discontinuous Junctions 
AU - Viallon , Marie-Claude
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 534
EP - 555
PY - 2025
DA - 2025/04
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1023
UR - https://global-sci.org/intro/article_detail/ijnam/24039.html
KW - Finite volume scheme, parabolic problem, multi-scale domain, domain decomposition, stability and convergence of numerical methods, Schwarz methods, Robin interface condition.
AB - <p style="text-align: justify;">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.</p>