Parallel Coarse-Grid Treatment in AMG for Coupled Systems

We present a parallel implementation of an agglomeration scheme for the coarse-grid treatment in algebraic multigrid algorithms for coupled systems. The association of the components of the solution vector with different physical unknowns bearing particular difficulties to parallel agglomeration techniques is considered through an appropriate re-ordering of the components of the solution vector. A benchmark of a system of mixed elliptic-hyperbolic character shows that the proposed scheme allows to apply an agglomeration technique which is significantly faster than conventional approaches based on a parallel direct solution of the coarse-grid system.