Algebraic multigrid for the finite pointset method

Abstract

We investigate algebraic multigrid (AMG) methods for the linear systems arising from the discretization of Navier-Stokes equations via the finite pointset method. In the segregated approach, three pressure systems and one velocity system need to be solved. In the coupled approach, one of the pressure systems is coupled with the velocity system, leading to a coupled velocity-pressure saddle point system. The discretization of the differential operators used in FPM leads to non-symmetric matrices that do not have the M-matrix property. Even though the theoretical framework for many AMG methods requires these properties, our AMG methods can be successfully applied to these matrices and show a robust and scalable convergence when compared to a BiCGStab(2) solver. Keywords Algebraic multigrid • Finite pointset method • Meshfree method • Saddle point problem Communicated by Gabriel Wittum.