High-order multigrid strategies for hybrid high-order discretizations of elliptic equations

This study compares various multigrid strategies for the fast solution of elliptic equations discretized by the hybrid high-order method. Combinations of h$$ h $$-, p$$ p $$-, and hp$$ hp $$-coarsening strategies are considered, combined with diverse intergrid transfer operators. Comparisons are made experimentally on 2D and 3D test cases, with structured and unstructured meshes, and with nested and non-nested hierarchies. Advantages and drawbacks of each strategy are discussed for each case to establish simplified guidelines for the optimization of the time to solution.