Compatible Coarse Nodal and Edge Elements Through Energy Functionals

We propose new algorithms for the setup phase of algebraic multigrid (AMG) solvers for linear systems coming from edge element discretization. The construction of coarse levels is performed by solving an optimization problem with a Lagrange multiplier method: we minimize the energy of coarse bases under a constraint linking coarse nodal and edge element bases. On structured meshes, the resulting AMG method and the geometric multigrid method behave similarly as preconditioner. On unstructured meshes, the convergence rate of our method compares favorably with the AMG method of Reitzinger and Schöberl.