Adaptive domain decomposition preconditioners for time-dependent flow problems

Abstract: We deal with the numerical solution of the time/dependent compressible Navier-Stokes equations by the space-time adaptive discontinuous Galerkin method (DGM). It involves adaptive choice of the time steps and anisotropic hp-mesh adaptation. The discretization leads to a sequence of large algebraic systems which are solved by GMRES method with domain decomposition based preconditioners. Particularly, we focus on two-level additive and hybrid Schwarz techniques which can be easily treated in the context of DGM. We study the convergence of the linear solver in dependence on the number of subdomains and the number of element of the coarse grid. We propose a simplified cost model measuring the computational costs in terms of floating-point operations, the speed of computation, and the wall-clock time for communications among computer cores. Moreover, the cost model serves as a base of the presented adaptive domain decomposition method which choose the number of subdomains and the number of element of the coarse grid in order to minimize the computational costs. The efficiency of the proposed technique is demonstrated by two benchmarks of compressible flow simulation.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)