Abstract: Nowadays standard processors are becoming multi-cores and there is a strong incentive to make use of all these parallel resources while avoiding conflict in memory access. We have also an overwhelming abundance of parallel computers available with the grid. Modern numerical solver such as Krylov methods or Multigrid technique are sensitive to memory cache, high latency network and low bandwidth. The computation of a scalar product or the solution process on the coarse grid introduces a strong bottleneck in the execution time. We will present in this talk a new family of domain decomposition solver that works efficiency in grid computing and is competitive with today fast solvers. Our method is based on the acceleration of the traces generated by any blockwise relaxation scheme such as the additive Schwarz method. This postprocessing algorithm can be added easily to an existing code. We will illustrate our method on elliptic and parabolic solver for CFD problems.