Belos provides next-generation iterative linear solvers and a powerful linear solver developer framework. This framework includes the following abstract interfaces and implementations: Abstract interfaces to linear algebra using traits mechanisms. This allows the user to leverage any existing investment in their description of matrices and vectors. The provided concrete linear algebra adapters enable Belos to be used anywhere Epetra and Thyra are employed for linear algebra services. Abstract interfaces to orthogonalization; implementations of iterated classical Gram-Schmidt (ICGS), classical Gram-Schmidt with a DGKS correction step, and iterated modified Gram-Schmidt (IMGS) are included. Abstract interfaces to iteration kernels; implementations of conjugate gradient (CG), block CG, block GMRES, pseudo-block GMRES, block flexible GMRES, and GCRO-DR iterations are included. Powerful solver managers are provided for solving a linear system using CG or block CG, GMRES or block GMRES with restarting, pseudo-block GMRES for performing single-vector GMRES simultaneously on multiple right-hand sides, and a single-vector recycled Krylov method (GCRO-DR). Basic linear problem class is provided for the user to define a unpreconditioned or preconditioned (left, right, two-sided) linear system for Belos to solve.

References in zbMATH (referenced in 19 articles )

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  1. Ghosh, Supriyo; Newman, Christopher K.; Francois, Marianne M.: \textttTusas: a fully implicit parallel approach for coupled phase-field equations (2022)
  2. Gross, B. J.; Kuberry, P.; Atzberger, P. J.: First-passage time statistics on surfaces of general shape: surface PDE solvers using generalized moving least squares (GMLS) (2022)
  3. Heinlein, Alexander; Perego, Mauro; Rajamanickam, Sivasankaran: FROSch preconditioners for land ice simulations of Greenland and Antarctica (2022)
  4. Bettencourt, Matthew T.; Brown, Dominic A. S.; Cartwright, Keith L.; Cyr, Eric C.; Glusa, Christian A.; Lin, Paul T.; Moore, Stan G.; Mcgregor, Duncan A. O.; Pawlowski, Roger P.; Phillips, Edward G.; Roberts, Nathan V.; Wright, Steven A.; Maheswaran, Satheesh; Jones, John P.; Jarvis, Stephen A.: EMPIRE-PIC: a performance portable unstructured particle-in-cell code (2021)
  5. Jolivet, Pierre; Roman, Jose E.; Zampini, Stefano: KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners (2021)
  6. D’Elia, M.; Phipps, E.; Rushdi, A.; Ebeida, M. S.: Surrogate-based ensemble grouping strategies for embedded sampling-based uncertainty quantification (2020)
  7. Fang, Rui; Kronbichler, Martin; Wurzer, Maximilian; Wall, Wolfgang A.: Parallel, physics-oriented, monolithic solvers for three-dimensional, coupled finite element models of Lithium-ion cells (2019)
  8. Thomas, S. J.; Ananthan, S.; Yellapantula, S.; Hu, J. J.; Lawson, M.; Sprague, M. A.: A comparison of classical and aggregation-based algebraic multigrid preconditioners for high-fidelity simulation of wind turbine incompressible flows (2019)
  9. D’Elia, M.; Edwards, H. C.; Hu, J.; Phipps, E.; Rajamanickam, S.: Ensemble grouping strategies for embedded stochastic collocation methods applied to anisotropic diffusion problems (2018)
  10. Esmaily, M.; Jofre, L.; Mani, A.; Iaccarino, G.: A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows (2018)
  11. Lin, P. T.; Shadid, J. N.; Hu, J. J.; Pawlowski, R. P.; Cyr, E. C.: Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD (2018)
  12. Ke, Guoyi; Aulisa, Eugenio; Bornia, Giorgio; Howle, Victoria: Block triangular preconditioners for linearization schemes of the Rayleigh-Bénard convection problem. (2017)
  13. Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre M.; Parks, Michael L.: Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics (2017)
  14. Phipps, E.; D’Elia, M.; Edwards, H. C.; Hoemmen, M.; Hu, J.; Rajamanickam, S.: Embedded ensemble propagation for improving performance, portability, and scalability of uncertainty quantification on emerging computational architectures (2017)
  15. Deparis, Simone; Forti, Davide; Grandperrin, Gwenol; Quarteroni, Alfio: Facsi: a block parallel preconditioner for fluid-structure interaction in hemodynamics (2016)
  16. Hupp, Daniel; Arbenz, Peter; Obrist, Dominik: A parallel Navier-Stokes solver using spectral discretisation in time (2016)
  17. Hamilton, Steven P.; Evans, Thomas M.: Efficient solution of the simplified (P_N) equations (2015)
  18. Trask, Nathaniel; Maxey, Martin; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Yang, Kai; Xu, Jinchao: A scalable consistent second-order SPH solver for unsteady low Reynolds number flows (2015)
  19. Howle, Victoria E.; Kirby, Robert C.; Dillon, Geoffrey: Block preconditioners for coupled physics problems (2013)