pySDC swMATH ID: 16754 Software Authors: Ruprecht, Daniel; Speck, Robert Description: 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 Homepage: https://zenodo.org/record/53849#.V9pAMp6mneQ Keywords: spectral deferred corrections; fast-wave slow-wave splitting; Euler equations; acoustic advection Related Software: RODAS; PFASST; XBraid; PARAEXP; RIDC; Matplotlib; SciPy; PETSc; LibPFASST; RADAU; GitHub; PREMIX; MAESTRO; TRANSPORT; GRI-Mech 3.0; pyParareal; chammp; SHTns; HOLOMAC; NumPy Cited in: 35 Publications Standard Articles 3 Publications describing the Software, including 3 Publications in zbMATH Year Using performance analysis tools for a parallel-in-time integrator. Does my time-parallel code do what I think it does? Zbl 07624850Speck, Robert; Knobloch, Michael; Lührs, Sebastian; Gocht, Andreas 2021 Algorithm 997: pySDC – prototyping spectral deferred corrections. Zbl 1486.65275Speck, Robert 2019 Spectral deferred corrections with fast-wave slow-wave splitting. Zbl 1348.65127Ruprecht, Daniel; Speck, Robert 2016 all top 5 Cited by 65 Authors 11 Minion, Michael L. 7 Speck, Robert 6 Ruprecht, Daniel 4 Emmett, Matthew 4 Krause, Rolf H. 3 Bolten, Matthias 3 Christlieb, Andrew J. 3 Crockatt, Michael M. 3 Hamon, François P. 2 Bell, John B. 2 Day, Marcus S. 2 Gander, Martin Jakob 2 Garrett, C. Kristopher 2 Guo, Hui 2 Hauck, Cory D. 2 Schreiber, Martin 1 Benedusi, Pietro 1 Biros, George 1 Bourgault, Yves 1 Buvoli, Tommaso 1 Chaudhry, Jehanzeb Hameed 1 Collins, Joseph B. 1 Dittmann, M. 1 Eugster, Simon Raphael 1 Falgout, Robert D. 1 Favino, Marco 1 Friedhoff, Stephanie 1 Garon, André 1 Ge, Ju 1 Gocht, Andreas 1 Götschel, Sebastian 1 Hahne, Jens 1 Hesch, Christian 1 Hessenthaler, Andreas 1 Hu, Zhicheng 1 Jiang, Yaolin 1 Knobloch, Michael 1 Li, Ruo 1 Lindvall, Kristoffer 1 Liu, Jun 1 Lührs, Sebastian 1 Motheau, Emmanuel 1 Naumann, Andreas 1 Neumüller, Martin 1 Nordsletten, David A. 1 Ong, Benjamin W. 1 Pazner, Will E. 1 Qiao, Zhonghua 1 Quaife, Bryan D. 1 Röhrle, Oliver 1 Saye, Robert I. 1 Scheffel, Jan 1 Schroder, Jacob B. 1 Schuß, Stefan 1 Shi, Rengang 1 Southworth, Ben S. 1 Spiteri, Raymond J. 1 Stiller, Jörg 1 Tian, Lulu 1 Wang, Yan 1 Wensch, Jörg 1 Winkel, Mathias 1 Xu, Yan 1 Zhang, Weiqun 1 Zhou, Lingling all top 5 Cited in 13 Serials 9 Journal of Computational Physics 7 SIAM Journal on Scientific Computing 3 Combustion Theory and Modelling 2 ACM Transactions on Mathematical Software 2 BIT 2 Journal of Scientific Computing 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational and Applied Mathematics 1 Computational Mechanics 1 International Journal of Computer Mathematics 1 Cogent Mathematics & Statistics 1 Results in Applied Mathematics all top 5 Cited in 10 Fields 30 Numerical analysis (65-XX) 7 Partial differential equations (35-XX) 7 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Geophysics (86-XX) 2 Biology and other natural sciences (92-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year