Schwarz Method in a Geometrical Multi-Scale Domain with Continuous or Discontinuous Junctions

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.