Element-Free AMGe: General Algorithms for Computing Interpolation Weights in AMG

We propose anew general algorithm for constructing interpolation weights in algebraic multigrid (AMG). It exploits a proper extension mapping outside a neighborhood about a fine degree of freedom (dof) to be interpolated. The extension mapping provides boundary values (based on the coarse dofs used to perform the interpolation) at the boundary of the neighborhood. The interpolation value is then obtained by matrix dependent harmonic extension of the boundary values into the interior of the neighborhood. We describe the method, present examples of useful extension operators, provide a two-grid analysis of model problems, and, by way of numerical experiments, demonstrate the successful application of the method to discretized elliptic problems.