Strategies with Algebraic Multigrid Method for Coupled Systems

We consider 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 fluid. We consider specific strategies 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. The strategies reveal an elliptic part of each system, which is efficiently addressed by the AMG method. As a result, the presented methods demonstrate linear complexity with respect to the size of the coupled problems.