Algebraic multigrid (AMG) for saddle point systems from meshfree discretizations

Meshfree discretizations construct approximate solutions to partial differential equation based on particles, not on meshes, so that it is well suited to solve the problems on irregular domains. Since the nodal basis property is not satisfied in meshfree discretizations, it is difficult to handle essential boundary conditions. In this paper, we employ the Lagrange multiplier approach to solve this problem, but this will result in an indefinite linear system of a saddle point type. We adapt a variation of the smoothed aggregation AMG method of Vaněk et al. to this saddle point system. We give numerical results showing that this method is practical and competitive with other methods with convergence rates that are ∼c/logN. Copyright © 2004 John Wiley & Sons, Ltd.