Multigrid and M-matrices in the Finite Pointset Method for incompressible flows

Abstract

The Finite Pointset Method (FPM) is a meshfree Lagrangian particle method for flow problems. We focus on incompressible, viscous flow equations, which are solved using the Chorin projection method. In the classical FPM second order 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, and investigate conditions on the particle geometry. This approach yields an M-matrix structure, which is of interest for various linear solvers, for instance multigrid. We solve the arising linear systems using algebraic multigrid.