Algebraic Multigrid Preconditioner for Statically Condensed Systems Arising from Lowest-Order Hybrid Discretizations

We address the numerical solution of linear systems arising from hybrid discretizations second-order elliptic partial differential equations. Such hinge on a set degrees freedom (DoFs), respectively, defined in cells and faces, which naturally gives rise to global system Assuming that cell unknowns are only locally coupled, they can be efficiently eliminated system, leaving face resulting Schur complement, is also called statically condensed matrix. propose this work an algebraic multigrid (AMG) preconditioner specifically targeting corresponding lowest-order (piecewise constant). Like traditional AMG methods, we retrieve geometric information coupling DoFs data. However, as matrix use uncondensed version reconstruct connectivity graph between elements faces. An aggregation-based coarsening strategy mimicking or semicoarsening then up build coarse levels. Numerical experiments performed diffusion problems discretized by high-order method at lowest order. Our approach uses K-cycle precondition outer flexible Krylov method. The results demonstrate similar performances, most cases, compared standard notable improvement anisotropic with Cartesian meshes.