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@ARTICLE{Piotrowski:907778,
      author       = {Piotrowski, Zbigniew P. and Smolarkiewicz, Piotr K.},
      title        = {{A} suite of {R}ichardson preconditioners for semi-implicit
                      all-scale atmospheric models},
      journal      = {Journal of computational physics},
      volume       = {463},
      issn         = {0021-9991},
      address      = {Amsterdam},
      publisher    = {Elsevier},
      reportid     = {FZJ-2022-02207},
      pages        = {111296},
      year         = {2022},
      abstract     = {The paper documents a suite of preconditioners for
                      Krylov-subspace solvers of elliptic boundary-value problems
                      (BVPs) that underlie semi-implicit integrations of the
                      nonhydrostatic equations governing the dynamics of all-scale
                      atmospheric flows. Effective preconditioning of the linear
                      operators inherent in the semi-implicit models lies at the
                      heart of the state-of-the-art multiscale-flow simulation.
                      This is especially evident in simulations of global weather
                      and climate—posed on a thin spherical shell—where some
                      form of direct tridiagonal inversion of the operator in the
                      vertical is crucial to relax the often enormous stiffness of
                      the problem. The documented preconditioners stem from the
                      Richardson's (1910) idea of augmenting an elliptic BVP with
                      a transient diffusion equation. Exploiting this idea for
                      mixed explicit-implicit pseudo-time-stepping schemes leads
                      to a broad suite of stationary-iteration solvers, including
                      the many classical algorithms. Here, the high-performance
                      all-scale EULAG model (Smolarkiewicz et al. (2014) [58]),
                      with a flexible three-dimensional decomposition of MPI
                      tasks, is furnished with the preconditioners akin to the
                      classical alternating-direction-implicit (ADI) algorithms,
                      generalized to optional permutations of parallel tridiagonal
                      inversions. The utility of various options is found to be
                      problem dependent, in terms of computational accuracy as
                      well as efficiency. The main thrust of the work is on the
                      long-range forecasts using large anisotropic grids. The
                      relative efficiency and/or accuracy gains attainable with
                      the developed preconditioners are illustrated for idealized
                      scenarios representative of atmospheric flows from planetary
                      to a single-cloud and laboratory scales. The key insight
                      that best encapsulates the significance and novelty of the
                      present work is that there is no single
                      “super-preconditioner” that will perform best in all
                      cases, yet the suite as a whole offers substantial gains in
                      the model performance.},
      cin          = {JSC},
      ddc          = {000},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000828339600005},
      doi          = {10.1016/j.jcp.2022.111296},
      url          = {https://juser.fz-juelich.de/record/907778},
}