Bootstrap AMG

We develop an Algebraic Multigrid setup scheme based on the Bootstrap framework for multi-scale scientific computation. Our approach uses a weighted least squares definition of interpolation, based on a set of test vectors that are computed by a Bootstrap setup cycle and then improved by a multigrid eigensolver and a local residual-based adaptive relaxation process. To emphasize the robustness, efficiency, and flexibility of the individual components of the proposed approach, we include extensive numerical results of the method applied to scalar elliptic partial differential equations discretized on structured meshes. As a first test problem, we consider the Laplace equation discretized on a uniform quadrilateral mesh, a problem for which multigrid is well understood. Then, we consider various more challenging variable coefficient systems coming from covariant finite-difference approximations of the two dimensional Gauge Laplacian system, a commonly used model problem in AMG algorithm development for linear systems arising in lattice field theory computations.