Stopping criteria for domain decomposition methods

steady

Error components estimates evolution in function of space DD iterations

unsteady

Error components estimates evolution in function of space-time DD iterations

Main results:

  • guaranteed error upper bound on each DD iteration;
  • distinguishes the domain decomposition error, the spatial discretization error, and possibly the temporal discretization error;
  • important savings in terms of the number of domain decomposition iterations;
  • optimized Robin and Ventcell transmission conditions;
  • global-in-time formulation that allows for use of local time stepping (different time grids adapted to different time scales in the subdomains) and parallelization in time.

Details:

  • steady linear setting: paper (preprint) with Sarah Ali Hassan, Caroline Japhet, and Michel Kern
  • unsteady linear setting: paper (preprint) with Sarah Ali Hassan and Caroline Japhet
  • two-phase flow with two different rock types: preprint with Elyes Ahmed, Sarah Ali Hassan, Caroline Japhet, and Michel Kern

Comments are closed.