Multigrid and M-Matrices in the Finite Pointset Method

We consider the Finite Pointset Method (FPM) for incompressible flows. In the classical FPM derivatives are approximated by a least squares approximation. In general this approach yields stencils with both positive and negative entries. We present how optimization routines can force the stencils to have only positive weights aside from the central point. This approach yields an M-matrix structure, which is of interest for various linear solvers. We investigate algebraic multigrid to solve the arising linear systems. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)