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 25 articles , 2 standard articles )

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  1. Chaudhry, Jehanzeb H.; Collins, J. B.: \textitAposteriori error estimation for the spectral deferred correction method (2021)
  2. Buvoli, Tommaso: A class of exponential integrators based on spectral deferred correction (2020)
  3. Hessenthaler, Andreas; Southworth, Ben S.; Nordsletten, David; Röhrle, Oliver; Falgout, Robert D.; Schroder, Jacob B.: Multilevel convergence analysis of multigrid-reduction-in-time (2020)
  4. Ong, Benjamin W.; Spiteri, Raymond J.: Deferred correction methods for ordinary differential equations (2020)
  5. 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)
  6. Götschel, Sebastian; Minion, Michael L.: An efficient parallel-in-time method for optimization with parabolic PDEs (2019)
  7. Hamon, François P.; Schreiber, Martin; Minion, Michael L.: Multi-level spectral deferred corrections scheme for the shallow water equations on the rotating sphere (2019)
  8. 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)
  9. Speck, Robert: Algorithm 997(\mathrm_) pySDC -- prototyping spectral deferred corrections (2019)
  10. Crockatt, Michael M.; Christlieb, Andrew J.: Low-storage integral deferred correction methods for scientific computing (2018)
  11. Lindvall, Kristoffer; Scheffel, Jan: A time-spectral method for initial-value problems using a novel spatial subdomain scheme (2018)
  12. Minion, M. L.; Saye, R. I.: Higher-order temporal integration for the incompressible Navier-Stokes equations in bounded domains (2018)
  13. Naumann, Andreas; Ruprecht, Daniel; Wensch, Joerg: Toward transient finite element simulation of thermal deformation of machine tools in real-time (2018)
  14. Zhou, Lingling; Xu, Yan: Stability analysis and error estimates of semi-implicit spectral deferred correction coupled with local discontinuous Galerkin method for linear convection-diffusion equations (2018)
  15. Crockatt, Michael M.; Christlieb, Andrew J.; Garrett, C. Kristopher; Hauck, Cory D.: An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction (2017)
  16. Hesch, C.; Schuß, S.; Dittmann, M.; Eugster, S. R.; Favino, M.; Krause, R.: Variational space-time elements for large-scale systems (2017)
  17. Gander, Martin J.; Neumüller, Martin: Analysis of a new space-time parallel multigrid algorithm for parabolic problems (2016)
  18. Hu, Zhicheng; Li, Ruo; Qiao, Zhonghua: Acceleration for microflow simulations of high-order moment models by using lower-order model correction (2016)
  19. Quaife, Bryan; Biros, George: Adaptive time stepping for vesicle suspensions (2016)
  20. Ruprecht, Daniel; Speck, Robert: Spectral deferred corrections with fast-wave slow-wave splitting (2016)

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