Strategies with algebraic multigrid method for coupled systems (Q6544411)

The authors investigate strategies for algebraic multigrid-based solution of coupled systems arising from the anisotropic diffusion problem, the two-phase filtration problem, the Stokes and Navier-Stokes equations for incompressible fluids. The following specific strategies are adopted for each problem: the direct application of the algebraic multigrid (AMG), the constrained pressure residual method with AMG preconditioner for the pressure block, the Bramble-Pasciak conjugate-gradient and biconjugate gradient stabilized methods with AMG preconditioner for the elliptic part of the (linearized) discrete operator. These strategies are shown to reveal an elliptic part of each system, which in turn, is efficiently addressed by the AMG method. Consequently, the proposed methods demonstrate linear complexity with respect to the size of the coupled problems.