HSL_MI20: An efficient AMG preconditioner for finite element problems in 3D

Algebraic multigrid (AMG) is one of the most effective iterative methods for the solution of large, sparse linear systems obtained from the discretization of second‐order scalar elliptic self‐adjoint partial differential equations. It can also be used as a preconditioner for Krylov subspace methods. In this communication, we report on the design and development of a robust, effective and portable Fortran 95 implementation of the classical Ruge–Stüben AMG, which is available as package HSL _ MI20 within the HSL mathematical software library. The routine can be used as a ‘black‐box’ preconditioner, but it also offers the user a range of options and parameters. Proper tuning of these parameters for a particular application can significantly enhance the performance of an AMG‐preconditioned Krylov solver. This is illustrated using a number of examples arising in the unstructured finite element discretization of the diffusion, the convection–diffusion, and the Stokes equations, as well as transient thermal convection problems associated with the Boussinesq approximation of the Navier–Stokes equations in 3D.