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-St”uben 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.

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  4. Leveque, Santolo; Pearson, John W.: Fast iterative solver for the optimal control of time-dependent PDEs with Crank-Nicolson discretization in time. (2022)
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  7. Cao, Shan-Mou; Wang, Zeng-Qi: PMHSS iteration method and preconditioners for Stokes control PDE-constrained optimization problems (2021)
  8. Manzoni, Andrea; Quarteroni, Alfio; Salsa, Sandro: Optimal control of partial differential equations. Analysis, approximation, and applications (2021)
  9. Alrehaili, A. H.; Walkley, M. A.; Jimack, P. K.; Hubbard, Matthew E.: An efficient numerical algorithm for a multiphase tumour model (2019)
  10. Benner, Peter; Onwunta, Akwum; Stoll, Martin: A low-rank inexact Newton-Krylov method for stochastic eigenvalue problems (2019)
  11. Bootland, Niall; Bentley, Alistair; Kees, Christopher; Wathen, Andrew: Preconditioners for two-phase incompressible Navier-Stokes flow (2019)
  12. Bosch, Jessica; Kahle, Christian; Stoll, Martin: Preconditioning of a coupled Cahn-Hilliard Navier-Stokes system (2018)
  13. Porcelli, Margherita; Simoncini, Valeria; Stoll, Martin: Preconditioning PDE-constrained optimization with (L^1)-sparsity and control constraints (2017)
  14. Robbe, Pieterjan; Nuyens, Dirk; Vandewalle, Stefan: A multi-index quasi-Monte Carlo algorithm for lognormal diffusion problems (2017)
  15. Benner, Peter; Dolgov, Sergey; Onwunta, Akwum; Stoll, Martin: Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data (2016)
  16. Benner, Peter; Onwunta, Akwum; Stoll, Martin: Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs (2016)
  17. McDonald, Eleanor; Wathen, Andy: A simple proposal for parallel computation over time of an evolutionary process with implicit time stepping (2016)
  18. Palitta, Davide; Simoncini, Valeria: Matrix-equation-based strategies for convection-diffusion equations (2016)
  19. Pearson, John W.: Fast iterative solvers for large matrix systems arising from time-dependent Stokes control problems (2016)
  20. Wu, Yirong; Wang, Heyu: An AMG preconditioner for solving the Navier-Stokes equations with a moving mesh finite element method (2016)

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