Algorithm 997 pySDC prototyping spectral deferred corrections. pySDC: The fast-wave-slow-wave release, v2. This release contains all the code to create the results and plots for the paper ”Spectral deferred corrections with fast-wave slow-wave splitting” by Daniel Ruprecht and Robert Speck. Spectral deferred corrections with fast-wave slow-wave splitting. The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves (“fast-wave slow-wave problem”). We show that for a scalar test problem with two imaginary eigenvalues iλ f , iλ s , having Δt(|λ f |+|λ s |)<1 is sufficient for the fast-wave slow-wave SDC (fwsw-SDC) iteration to converge and that in the limit of infinitely fast waves the convergence rate of the nonsplit version is retained. Stability function and discrete dispersion relation are derived and show that the method is stable for essentially arbitrary fast-wave CFL numbers as long as the slow dynamics are resolved. The method causes little numerical diffusion and its semidiscrete phase speed is accurate also for large wave number modes. Performance is studied for an acoustic-advection problem and for the linearised Boussinesq equations, describing compressible, stratified flow. fwsw-SDC is compared to diagonally implicit Runge-Kutta (DIRK) and implicit-explicit (IMEX) Runge-Kutta methods and found to be competitive in terms of both accuracy and cost

References in zbMATH (referenced in 33 articles , 2 standard articles )

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  1. Benedusi, Pietro; Minion, Michael L.; Krause, Rolf: An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem (2021)
  2. Chaudhry, Jehanzeb H.; Collins, J. B.: \textitAposteriori error estimation for the spectral deferred correction method (2021)
  3. Hahne, Jens; Friedhoff, Stephanie; Bolten, Matthias: Algorithm 1016. PyMGRIT: a python package for the parallel-in-time method MGRIT (2021)
  4. Buvoli, Tommaso: A class of exponential integrators based on spectral deferred correction (2020)
  5. Hamon, François P.; Schreiber, Martin; Minion, Michael L.: Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere (2020)
  6. Hessenthaler, Andreas; Southworth, Ben S.; Nordsletten, David; Röhrle, Oliver; Falgout, Robert D.; Schroder, Jacob B.: Multilevel convergence analysis of multigrid-reduction-in-time (2020)
  7. Ong, Benjamin W.; Spiteri, Raymond J.: Deferred correction methods for ordinary differential equations (2020)
  8. Stiller, Jörg: A spectral deferred correction method for incompressible flow with variable viscosity (2020)
  9. Crockatt, Michael M.; Christlieb, Andrew J.; Garrett, C. Kristopher; Hauck, Cory D.: Hybrid methods for radiation transport using diagonally implicit Runge-Kutta and space-time discontinuous Galerkin time integration (2019)
  10. Emmett, Matthew; Motheau, Emmanuel; Zhang, Weiqun; Minion, Michael; Bell, John B.: A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier-Stokes equations (2019)
  11. Götschel, Sebastian; Minion, Michael L.: An efficient parallel-in-time method for optimization with parabolic PDEs (2019)
  12. Hamon, François P.; Day, Marcus S.; Minion, Michael L.: Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry (2019)
  13. Hamon, François P.; Schreiber, Martin; Minion, Michael L.: Multi-level spectral deferred corrections scheme for the shallow water equations on the rotating sphere (2019)
  14. Liu, Jun; Guo, Hui; Jiang, Yao-Lin; Wang, Yan: High order numerical algorithms based on biquadratic spline collocation for two-dimensional parabolic partial differential equations (2019)
  15. Shi, Rengang; Ge, Ju; Tian, Lulu; Guo, Hui: An arbitrary high order series-based time-marching method with discontinuous Galerkin method for 2D convection problem (2019)
  16. Speck, Robert: Algorithm 997: pySDC -- prototyping spectral deferred corrections (2019)
  17. Crockatt, Michael M.; Christlieb, Andrew J.: Low-storage integral deferred correction methods for scientific computing (2018)
  18. Lindvall, Kristoffer; Scheffel, Jan: A time-spectral method for initial-value problems using a novel spatial subdomain scheme (2018)
  19. Minion, M. L.; Saye, R. I.: Higher-order temporal integration for the incompressible Navier-Stokes equations in bounded domains (2018)
  20. Naumann, Andreas; Ruprecht, Daniel; Wensch, Joerg: Toward transient finite element simulation of thermal deformation of machine tools in real-time (2018)

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