Workshop on Domain Decomposition


Speech 1

  • Title: Seven Things I would have liked to know when starting to work on Domain Decomposition
  • Speaker: Martin J. Gander (University of Geneva)
  • Time: 15:10-16:00, Monday, June 10, 2019
  • Venue: MB341

It is not easy to start working in a new field of research. I will give a personal overview over seven things I would have liked to know when I started working on domain decomposition (DD) methods:
1) Seminal contributions to DD not easy to start with
2) Seminal contributions to DD ideal to start with
3) DD solvers are obtained by discretizing
4) There are better transmission conditions than Dirichlet or Neumann
5) "Optimal" in classical DD means scalable, not fast
6) Coarse space components can do more than provide scalability
7) DD methods should always be used as preconditioners

Speech 2

  • Title: Analysis of double sweep optimized Schwarz method
  • Speaker: Hui Zhang (Ocean University of Zhejiang)
  • Time: 16:10-16:50, Monday, June 10, 2019
  • Venue: MB341

We analyze a double sweep optimized Schwarz method for solving the Helmholtz equation in semi-infinite wave guides. The domain is decomposed into nonoverlapped layered subdomains along the axis of the wave guide and local wave propagation problems equipped with complete radiation conditions for high-order absorbing boundary conditions are solved forward and backward sequentially. For communication between subdomains, Neumann data of local solutions in one domain are transferred to the neighboring subdomain in the forward direction and Dirichlet data are exploited in the backward direction. The complete radiation boundary conditions enable us to not only minimize reflection coefficients for most important modes in an optimal way but also find Neumann data without introducing errors that would be produced if finite difference formulas were used for computing Neumann data. The convergence of the double sweep Schwarz method is proved and numerical experiments using it as a preconditioner are presented to confirm the convergence theory.