References

This list of publications closely related to parallel-in-time integration is probably not complete. Please feel free to add any missing publications through a pull request on GitHub .

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2024

  1. I. Bossuyt, S. Vandewalle, and G. Samaey, “Micro-macro Parareal, from ODEs to SDEs and back again,” arXiv:2401.01798v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2401.01798v1
  2. R. Cao, S. Hou, and L. Ma, “A Pipeline-Based ODE Solving Framework,” IEEE Access, vol. 12, pp. 37995–38004, 2024, doi: 10.1109/ACCESS.2024.3375305.
  3. P. Freese, S. Götschel, T. Lunet, D. Ruprecht, and M. Schreiber, “Parallel performance of shared memory parallel spectral deferred corrections,” arXiv:2403.20135v1 [cs.CE], 2024 [Online]. Available at: http://arxiv.org/abs/2403.20135v1
  4. P. Y. Fung and S. Hon, “Block ω-circulant preconditioners for parabolic optimal control problems,” arXiv:2406.00952v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2406.00952v1
  5. G. Gattiglio, L. Grigoryeva, and M. Tamborrino, “Nearest Neighbors GParareal: Improving Scalability of Gaussian Processes for Parallel-in-Time Solvers,” arXiv:2405.12182v1 [stat.CO], 2024 [Online]. Available at: http://arxiv.org/abs/2405.12182v1
  6. X.-M. Gu, J. Liu, and C. W. Oosterlee, “Parallel-in-Time Iterative Methods for Pricing American Options,” arXiv:2405.08280v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2405.08280v1
  7. B. Heinzelreiter and J. W. Pearson, “Diagonalization-Based Parallel-in-Time Preconditioners for Instationary Fluid Flow Control Problems,” arXiv:2405.18964v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2405.18964v1
  8. J. Huang, L. Ju, and Y. Xu, “A parareal exponential integrator finite element method for semilinear parabolic equations,” Numerical Methods for Partial Differential Equations, May 2024, doi: 10.1002/num.23116. [Online]. Available at: http://dx.doi.org/10.1002/num.23116
  9. A. Q. Ibrahim, S. Götschel, and D. Ruprecht, “Space-time parallel scaling of Parareal with a Fourier Neural Operator as coarse propagator,” arXiv:2404.02521v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2404.02521v1
  10. N. Janssens and J. Meyers, “Parallel-in-time multiple shooting for optimal control problems governed by the Navier–Stokes equations,” Computer Physics Communications, vol. 296, p. 109019, Mar. 2024, doi: 10.1016/j.cpc.2023.109019. [Online]. Available at: http://dx.doi.org/10.1016/j.cpc.2023.109019
  11. L. Kaiser, R. Tsai, and C. Klingenberg, “Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model,” arXiv:2402.02304v4 [math.AP], 2024 [Online]. Available at: http://arxiv.org/abs/2402.02304v4
  12. A. Kumar, “Investigation of Second Order Taylor Series in the Coarse Operator of Parareal Algorithm for Power System Simulation,” IEEE Transactions on Circuits and Systems II: Express Briefs, pp. 1–1, 2024, doi: 10.1109/tcsii.2024.3381372. [Online]. Available at: http://dx.doi.org/10.1109/TCSII.2024.3381372
  13. F. Kwok and D. N. Tognon, “A parallel in time algorithm based ParaExp for optimal control problems,” arXiv:2406.11478v1 [cs.DC], 2024 [Online]. Available at: http://arxiv.org/abs/2406.11478v1
  14. F. Li and Y. Xu, “A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation,” East Asian Journal on Applied Mathematics, vol. 14, no. 1, pp. 47–78, Jun. 2024, doi: 10.4208/eajam.2022-304.070323. [Online]. Available at: http://dx.doi.org/10.4208/eajam.2022-304.070323
  15. Z. Miao, B. W. null, and Y. Jiang, “Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems,” Numerical Mathematics: Theory, Methods and Applications, vol. 17, no. 1, pp. 121–144, Jun. 2024, doi: 10.4208/nmtma.oa-2023-0081. [Online]. Available at: http://dx.doi.org/10.4208/nmtma.oa-2023-0081
  16. Z. Miao, R.-H. Zhang, W.-W. Han, and Y.-L. Jiang, “Analysis of a fractional-step parareal algorithm for the incompressible Navier-Stokes equations,” Computers & Mathematics with Applications, vol. 161, pp. 78–89, May 2024, doi: 10.1016/j.camwa.2024.02.035. [Online]. Available at: http://dx.doi.org/10.1016/j.camwa.2024.02.035
  17. S. J. P. Pamela et al., “Neural-Parareal: Dynamically Training Neural Operators as Coarse Solvers for Time-Parallelisation of Fusion MHD Simulations,” arXiv:2405.01355v1 [physics.plasm-ph], 2024 [Online]. Available at: http://arxiv.org/abs/2405.01355v1
  18. B. Park, “Stochastic Power System Dynamic Simulation Using Parallel-in-Time Algorithm,” IEEE Access, vol. 12, pp. 28500–28510, 2024, doi: 10.1109/access.2024.3367358. [Online]. Available at: http://dx.doi.org/10.1109/ACCESS.2024.3367358
  19. J. Sarpe, A. Klaedtke, and H. D. Gersem, “Periodic Adjoint Sensitivity Analysis,” arXiv:2405.19048v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2405.19048v1
  20. E. Scheiber, “A Convergence Theorem for the Parareal Algorithm Revisited,” arXiv:2405.06954v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2405.06954v1
  21. E. Schnaubelt, M. Wozniak, J. Dular, I. C. Garcia, A. Verweij, and S. Schöps, “Parallel-in-Time Integration of Transient Phenomena in No-Insulation Superconducting Coils Using Parareal,” arXiv:2404.13333v1 [cs.CE], 2024 [Online]. Available at: http://arxiv.org/abs/2404.13333v1
  22. G. R. de Souza, S. Pezzuto, and R. Krause, “High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology,” arXiv:2405.19994v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2405.19994v1
  23. H. D. Sterck, R. D. Falgout, O. A. Krzysik, and J. B. Schroder, “Parallel-in-time solution of scalar nonlinear conservation laws,” arXiv:2401.04936v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2401.04936v1
  24. N. K. Yamaleev and S. Paudel, “A New Parallel-in-time Direct Inverse Method for Nonlinear Differential Equations,” arXiv:2406.00878v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2406.00878v1
  25. R. Yoda, M. Bolten, K. Nakajima, and A. Fujii, “Coarse-grid operator optimization in multigrid reduction in time for time-dependent Stokes and Oseen problems,” Japan Journal of Industrial and Applied Mathematics, Apr. 2024, doi: 10.1007/s13160-024-00652-8. [Online]. Available at: http://dx.doi.org/10.1007/s13160-024-00652-8
  26. Y.-L. Zhao, X.-M. Gu, and C. W. Oosterlee, “A parallel preconditioner for the all-at-once linear system from evolutionary PDEs with Crank-Nicolson discretization,” arXiv:2401.16113v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2401.16113v1
  27. M. Zhen, X. Liu, X. Ding, and J. Cai, “High-order space–time parallel computing of the Navier–Stokes equations,” Computer Methods in Applied Mechanics and Engineering, vol. 423, p. 116880, Apr. 2024, doi: 10.1016/j.cma.2024.116880. [Online]. Available at: http://dx.doi.org/10.1016/j.cma.2024.116880
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2023

  1. A. Barman and A. Sharma, “A Space-Time framework for compressible flow simulations using Finite Volume Method,” in AIAA AVIATION 2023 Forum, 2023, doi: 10.2514/6.2023-3431 [Online]. Available at: https://doi.org/10.2514/6.2023-3431
  2. M. Bolten, S. Friedhoff, and J. Hahne, “Task graph-based performance analysis of parallel-in-time methods,” Parallel Computing, vol. 118, p. 103050, Nov. 2023, doi: 10.1016/j.parco.2023.103050. [Online]. Available at: https://doi.org/10.1016/j.parco.2023.103050
  3. N. Bosch, A. Corenflos, F. Yaghoobi, F. Tronarp, P. Hennig, and S. Särkkä, “Parallel-in-Time Probabilistic Numerical ODE Solvers,” arXiv:2310.01145v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2310.01145v1
  4. I. Bossuyt, S. Vandewalle, and G. Samaey, “Monte-Carlo/Moments micro-macro Parareal method for unimodal and bimodal scalar McKean-Vlasov SDEs,” arXiv:2310.11365v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2310.11365v1
  5. A. Bouillon, G. Samaey, and K. Meerbergen, “On generalized preconditioners for time-parallel parabolic optimal control,” arXiv:2302.06406v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2302.06406v1
  6. A. Bouillon, G. Samaey, and K. Meerbergen, “Diagonalization-based preconditioners and generalized convergence bounds for ParaOpt,” arXiv:2304.09235v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2304.09235v1
  7. L. D’Amore and R. Cacciapuoti, “Space-Time Decomposition of Kalman Filter,” Numerical Mathematics: Theory, Methods and Applications, vol. 0, no. 0, pp. 0–0, Sep. 2023, doi: 10.4208/nmtma.oa-2022-0203. [Online]. Available at: https://doi.org/10.4208/nmtma.oa-2022-0203
  8. R. Cacciapuoti and L. D’Amore, “Scalability analysis of a two level domain decomposition approach in space and time solving data assimilation models,” Concurrency and Computation: Practice and Experience, Nov. 2023, doi: 10.1002/cpe.7937. [Online]. Available at: https://doi.org/10.1002/cpe.7937
  9. J. G. Caldas Steinstraesser, P. da Silva Peixoto, and M. Schreiber, “Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT,” arXiv:2306.09497v1 [math.NA], 2023 [Online]. Available at: https://arxiv.org/abs/2306.09497v1
  10. B. Carrel, M. J. Gander, and B. Vandereycken, “Low-rank Parareal: a low-rank parallel-in-time integrator,” BIT Numerical Mathematics, vol. 63, no. 1, Feb. 2023, doi: 10.1007/s10543-023-00953-3. [Online]. Available at: https://doi.org/10.1007%2Fs10543-023-00953-3
  11. Z. Chen and Y. Liu, “Efficient and Parallel Solution of High-order Continuous Time Galerkin for Dissipative and Wave Propagation Problems,” arXiv:2303.05008v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2303.05008v1
  12. T. Cheng, H. Yang, J. Huang, and C. Yang, “Nonlinear parallel-in-time simulations of multiphase flow in porous media,” Journal of Computational Physics, p. 112515, Sep. 2023, doi: 10.1016/j.jcp.2023.112515. [Online]. Available at: https://doi.org/10.1016/j.jcp.2023.112515
  13. E. C. Cyr, “A 2-Level Domain Decomposition Preconditioner for KKT Systems with Heat-Equation Constraints,” arXiv:2305.04421v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2305.04421v1
  14. C. Dajana, C. Eduardo, and V. Carmine, “Non-stationary wave relaxation methods for general linear systems of Volterra equations: convergence and parallel GPU implementation,” Numerical Algorithms, Jun. 2023, doi: 10.1007/s11075-023-01567-0. [Online]. Available at: https://doi.org/10.1007/s11075-023-01567-0
  15. F. Danieli, B. S. Southworth, and J. B. Schroder, “Space-Time Block Preconditioning for Incompressible Resistive Magnetohydrodynamics,” arXiv:2309.00768v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2309.00768v1
  16. Y. A. Erlangga, “Parallel-in-time Multilevel Krylov Methods: A Prototype,” arXiv:2401.00228v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2401.00228v1
  17. L. Fang, S. Vandewalle, and J. Meyers, “An SQP-based multiple shooting algorithm for large-scale PDE-constrained optimal control problems,” Journal of Computational Physics, vol. 477, p. 111927, Mar. 2023, doi: 10.1016/j.jcp.2023.111927. [Online]. Available at: https://doi.org/10.1016/j.jcp.2023.111927
  18. R. Fang and R. Tsai, “Stabilization of parareal algorithms for long time computation of a class of highly oscillatory Hamiltonian flows using data,” arXiv:2309.01225v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2309.01225v1
  19. S. Frei and A. Heinlein, “Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth,” Journal of Computational Physics, vol. 491, p. 112347, Oct. 2023, doi: 10.1016/j.jcp.2023.112347. [Online]. Available at: https://doi.org/10.1016%2Fj.jcp.2023.112347
  20. M. J. Gander and D. Palitta, “A new ParaDiag time-parallel time integration method,” arXiv:2304.12597v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2304.12597v1
  21. M. J. Gander, T. Lunet, D. Ruprecht, and R. Speck, “A Unified Analysis Framework for Iterative Parallel-in-Time Algorithms,” SIAM Journal on Scientific Computing, vol. 45, no. 5, pp. A2275–A2303, 2023, doi: 10.1137/22M1487163. [Online]. Available at: https://doi.org/10.1137/22M1487163
  22. P. Gangl, M. Gobrial, and O. Steinbach, “A space-time finite element method for the eddy current approximation of rotating electric machines,” arXiv:2307.00278v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2307.00278v1
  23. G. Garai and B. C. Mandal, “Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation,” arXiv:2304.14074v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2304.14074v1
  24. G. Garai and B. C. Mandal, “Diagonalization based Parallel-in-Time method for a class of fourth order time dependent PDEs,” Mathematics and Computers in Simulation, Aug. 2023, doi: 10.1016/j.matcom.2023.07.028. [Online]. Available at: https://doi.org/10.1016%2Fj.matcom.2023.07.028
  25. J. Hahne, B. Polenz, I. Kulchytska-Ruchka, S. Friedhoff, S. Ulbrich, and S. Schöps, “Parallel-in-time optimization of induction motors,” Journal of Mathematics in Industry, vol. 13, no. 1, Jun. 2023, doi: 10.1186/s13362-023-00134-5. [Online]. Available at: https://doi.org/10.1186/s13362-023-00134-5
  26. S. Hon and S. Serra-Capizzano, “A block Toeplitz preconditioner for all-at-once systems from linear wave equations,” ETNA - Electronic Transactions on Numerical Analysis, vol. 58, pp. 177–195, 2023, doi: 10.1553/etna_vol58s177. [Online]. Available at: https://doi.org/10.1553/etna_vol58s177
  27. S. Hon, J. Dong, and S. Serra-Capizzano, “A preconditioned MINRES method for optimal control of wave equations and its asymptotic spectral distribution theory,” arXiv:2307.12850v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2307.12850v1
  28. A. Q. Ibrahim, S. Götschel, and D. Ruprecht, “Parareal with a Physics-Informed Neural Network as Coarse Propagator,” in Euro-Par 2023: Parallel Processing, Springer Nature Switzerland, 2023, pp. 649–663 [Online]. Available at: https://doi.org/10.1007/978-3-031-39698-4_44
  29. Y. Jiang and J. Liu, “Fast parallel-in-time quasi-boundary value methods for backward heat conduction problems,” Applied Numerical Mathematics, vol. 184, pp. 325–339, Feb. 2023, doi: 10.1016/j.apnum.2022.10.006. [Online]. Available at: https://doi.org/10.1016%2Fj.apnum.2022.10.006
  30. Y. Jiang, J. Liu, and X.-S. Wang, “A direct parallel-in-time quasi-boundary value method for inverse space-dependent source problems,” Journal of Computational and Applied Mathematics, vol. 423, p. 114958, May 2023, doi: 10.1016/j.cam.2022.114958. [Online]. Available at: https://doi.org/10.1016%2Fj.cam.2022.114958
  31. B. Jin, Q. Lin, and Z. Zhou, “Learning Coarse Propagators in Parareal Algorithm,” arXiv:2311.15320v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2311.15320v1
  32. R. Kraft, S. Koraltan, M. Gattringer, F. Bruckner, D. Suess, and C. Abert, “Parallel-in-Time Integration of the Landau-Lifshitz-Gilbert Equation with the Parallel Full Approximation Scheme in Space and Time,” arXiv:2310.11819v1 [physics.comp-ph], 2023 [Online]. Available at: http://arxiv.org/abs/2310.11819v1
  33. S. Leveque, L. Bergamaschi, Á. Martínez, and J. W. Pearson, “Fast Iterative Solver for the All-at-Once Runge–Kutta Discretization,” arXiv:2303.02090v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2303.02090v1
  34. G. Li, “Wavelet-based Edge Multiscale Parareal Algorithm for subdiffusion equations with heterogeneous coefficients in a large time domain,” arXiv:2307.06529v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2307.06529v1
  35. J. Li and Y. Jiang, “Analysis of a New Accelerated Waveform Relaxation Method Based on the Time-Parallel Algorithm,” Journal of Scientific Computing, vol. 96, no. 3, Jul. 2023, doi: 10.1007/s10915-023-02285-4. [Online]. Available at: https://doi.org/10.1007/s10915-023-02285-4
  36. X.-lei Lin and S. Hon, “A block α-circulant based preconditioned MINRES method for wave equations,” arXiv:2306.03574v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2306.03574v1
  37. Z. Miao and Y.-L. Jiang, “A Fast Simulation Approach to Switched Systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, pp. 1–1, 2023, doi: 10.1109/tcsii.2023.3332694. [Online]. Available at: http://dx.doi.org/10.1109/TCSII.2023.3332694
  38. P. Munch, I. Dravins, M. Kronbichler, and M. Neytcheva, “Stage-Parallel Fully Implicit Runge–Kutta Implementations with Optimal Multilevel Preconditioners at the Scaling Limit,” SIAM Journal on Scientific Computing, pp. S71–S96, Jul. 2023, doi: 10.1137/22m1503270. [Online]. Available at: https://doi.org/10.1137%2F22m1503270
  39. V.-T. Nguyen and L. Grigori, “Interpretation of parareal as a two-level additive Schwarz in time preconditioner and its acceleration with GMRES,” Numerical Algorithms, Mar. 2023, doi: 10.1007/s11075-022-01492-8. [Online]. Available at: https://doi.org/10.1007/s11075-022-01492-8
  40. H. Nguyen and R. Tsai, “Numerical wave propagation aided by deep learning,” Journal of Computational Physics, vol. 475, p. 111828, Feb. 2023, doi: 10.1016/j.jcp.2022.111828. [Online]. Available at: https://doi.org/10.1016%2Fj.jcp.2022.111828
  41. B. Philippi and T. Slawig, “A Micro-Macro Parareal Implementation for the Ocean-Circulation Model FESOM2,” arXiv:2306.17269v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2306.17269v1
  42. B. Philippi, M. S. Miraz, and T. Slawig, “A Micor-Macro parallel-in-time Implementation for the 2D Navier-Stokes Equations,” arXiv:2309.03037v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2309.03037v1
  43. J. Sarpe, A. Klaedtke, and H. D. Gersem, “A Parallel-In-Time Adjoint Sensitivity Analysis for a B6 Bridge-Motor Supply Circuit,” arXiv:2307.00802v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2307.00802v1
  44. J. Schleuß, K. Smetana, and L. ter Maat, “Randomized Quasi-Optimal Local Approximation Spaces in Time,” SIAM Journal on Scientific Computing, vol. 45, no. 3, pp. A1066–A1096, May 2023, doi: 10.1137/22m1481002. [Online]. Available at: https://doi.org/10.1137%2F22m1481002
  45. X. Shan and M. B. van Gijzen, “Parareal Method for Anisotropic Diffusion Denoising,” in Parallel Processing and Applied Mathematics, Springer International Publishing, 2023, pp. 313–322 [Online]. Available at: https://doi.org/10.1007/978-3-031-30445-3_26
  46. B. Song, J.-Y. Wang, and Y.-L. Jiang, “Analysis of a New Krylov subspace enhanced parareal algorithm for time-periodic problems,” Numerical Algorithms, Nov. 2023, doi: 10.1007/s11075-023-01704-9. [Online]. Available at: http://dx.doi.org/10.1007/s11075-023-01704-9
  47. Y. Takahashi, K. Fujiwara, and T. Iwashita, “Parallel-in-Space-and-Time Finite-Element Method for Time-Periodic Magnetic Field Problems with Hysteresis,” IEEE Transactions on Magnetics, pp. 1–1, 2023, doi: 10.1109/tmag.2023.3307498. [Online]. Available at: https://doi.org/10.1109/tmag.2023.3307498
  48. K. Trotti, “A domain splitting strategy for solving PDEs,” arXiv:2303.01163v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2303.01163v1
  49. D. A. Vargas, R. D. Falgout, S. Günther, and J. B. Schroder, “Multigrid Reduction in Time for Chaotic Dynamical Systems,” SIAM Journal on Scientific Computing, vol. 45, no. 4, pp. A2019–A2042, Aug. 2023, doi: 10.1137/22m1518335. [Online]. Available at: https://doi.org/10.1137%2F22m1518335
  50. Y. Wang, “Parallel Numerical Picard Iteration Methods,” Journal of Scientific Computing, vol. 95, no. 1, Mar. 2023, doi: 10.1007/s10915-023-02156-y. [Online]. Available at: https://doi.org/10.1007/s10915-023-02156-y
  51. M. Wang and S. Zhang, “A Preconditioner for Galerkin–Legendre Spectral All-at-Once System from Time-Space Fractional Diffusion Equation,” Symmetry, vol. 15, no. 12, p. 2144, Dec. 2023, doi: 10.3390/sym15122144. [Online]. Available at: http://dx.doi.org/10.3390/sym15122144
  52. S.-L. Wu, Z. Wang, and T. Zhou, “PinT Preconditioner for Forward-Backward Evolutionary Equations,” SIAM Journal on Matrix Analysis and Applications, vol. 44, no. 4, pp. 1771–1798, Nov. 2023, doi: 10.1137/22m1516476. [Online]. Available at: http://dx.doi.org/10.1137/22M1516476
  53. H. Yamazaki, C. J. Cotter, and B. A. Wingate, “Time-parallel integration and phase averaging for the nonlinear shallow-water equations on the sphere,” Quarterly Journal of the Royal Meteorological Society, Jul. 2023, doi: 10.1002/qj.4517. [Online]. Available at: https://doi.org/10.1002%2Fqj.4517
  54. X. Yue, Z. Wang, and S.-L. Wu, “Convergence Analysis of a Mixed Precision Parareal Algorithm,” SIAM Journal on Scientific Computing, vol. 45, no. 5, pp. A2483–A2510, Sep. 2023, doi: 10.1137/22m1510169. [Online]. Available at: https://doi.org/10.1137/22m1510169
  55. J. Zeifang, A. T. Manikantan, and J. Schütz, “Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method,” Applied Mathematics and Computation, vol. 457, p. 128198, Nov. 2023, doi: 10.1016/j.amc.2023.128198. [Online]. Available at: https://doi.org/10.1016/j.amc.2023.128198
  56. Q. Zhou, Y. Liu, and S.-L. Wu, “Parareal algorithm via Chebyshev-Gauss spectral collocation method,” arXiv:2304.10152v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2304.10152v1
  57. Z. Zhou, H. Gu, G. Ju, and W. Xing, “A Parallel-in-time Method Based on Preconditioner for Biot’s Model,” arXiv:2310.10430v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2310.10430v1
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2022

  1. W. C. Agboh, D. Ruprecht, and M. R. Dogar, “Combining Coarse and Fine Physics for Manipulation using Parallel-in-Time Integration,” in Robotics Research, 2022, pp. 725–740, doi: 10.1007/978-3-030-95459-8_44 [Online]. Available at: https://doi.org/10.1007/978-3-030-95459-8_44
  2. A. Arrarás, F. J. Gaspar, L. Portero, and C. Rodrigo, “Space-Time Parallel Methods for Evolutionary Reaction-Diffusion Problems,” in Domain Decomposition Methods in Science and Engineering XXVI, Springer International Publishing, 2022, pp. 643–651 [Online]. Available at: https://doi.org/10.1007/978-3-030-95025-5_70
  3. D. Q. Bui, C. Japhet, Y. Maday, and P. Omnes, “Coupling Parareal with Optimized Schwarz Waveform Relaxation for Parabolic Problems,” SIAM Journal on Numerical Analysis, vol. 60, no. 3, pp. 913–939, May 2022, doi: 10.1137/21m1419428. [Online]. Available at: https://doi.org/10.1137/21m1419428
  4. T. Cheng, N. Lin, and V. Dinavahi, “Hybrid Parallel-in-Time-and-Space Transient Stability Simulation of Large-Scale AC/DC Grids,” IEEE Transactions on Power Systems, pp. 1–1, 2022, doi: 10.1109/tpwrs.2022.3153450. [Online]. Available at: https://doi.org/10.1109/tpwrs.2022.3153450
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top

2021

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  36. B. Park, K. Sun, A. Dimitrovski, Y. Liu, and S. Simunovic, “Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation,” IEEE Transactions on Power Systems, pp. 1–1, 2021, doi: 10.1109/tpwrs.2021.3069136. [Online]. Available at: https://doi.org/10.1109/tpwrs.2021.3069136
  37. M. Patil and A. Datta, “Time-Parallel Scalable Solution of Periodic Rotor Dynamics for Large-Scale 3D Structures,” in AIAA Scitech 2021 Forum, 2021, doi: 10.2514/6.2021-1079 [Online]. Available at: https://doi.org/10.2514/6.2021-1079
  38. A. Pels, I. Kulchytska-Ruchka, and S. Schöps, “Parallel-in-Time Simulation of Power Converters Using Multirate PDEs,” in Scientific Computing in Electrical Engineering, Springer International Publishing, 2021, pp. 33–41 [Online]. Available at: https://doi.org/10.1007%2F978-3-030-84238-3_4
  39. J. Schütz, D. C. Seal, and J. Zeifang, “Parallel-in-Time High-Order Multiderivative IMEX Solvers,” Journal of Scientific Computing, vol. 90, no. 1, Dec. 2021, doi: 10.1007/s10915-021-01733-3. [Online]. Available at: https://doi.org/10.1007%2Fs10915-021-01733-3
  40. A. A. Sivas, B. S. Southworth, and S. Rhebergen, “AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion),” vol. 43, no. 5, pp. A3393–A3416, Jan. 2021, doi: 10.1137/20m1375103. [Online]. Available at: https://doi.org/10.1137%2F20m1375103
  41. C. S. Skene, M. F. Eggl, and P. J. Schmid, “A parallel-in-time approach for accelerating direct-adjoint studies,” Journal of Computational Physics, vol. 429, p. 110033, Mar. 2021, doi: 10.1016/j.jcp.2020.110033. [Online]. Available at: https://doi.org/10.1016/j.jcp.2020.110033
  42. Y. Sun, S.-L. Wu, and Y. Xu, “A Parallel-in-Time Implementation of the Numerov Method For Wave Equations,” Journal of Scientific Computing, vol. 90, no. 1, Nov. 2021, doi: 10.1007/s10915-021-01701-x. [Online]. Available at: https://doi.org/10.1007/s10915-021-01701-x
  43. Y. Takahashi, K. Fujiwara, T. Iwashita, and H. Nakashima, “Comparison of Parallel-in-Space-and-Time Finite-Element Methods for Magnetic Field Analysis of Electric Machines,” IEEE Transactions on Magnetics, pp. 1–1, 2021, doi: 10.1109/tmag.2021.3064320. [Online]. Available at: https://doi.org/10.1109/tmag.2021.3064320
  44. R. van Venetië and J. Westerdiep, “A Parallel Algorithm for Solving Linear Parabolic Evolution Equations,” Springer International Publishing, 2021, pp. 33–50 [Online]. Available at: https://doi.org/10.1007/978-3-030-75933-9_2
  45. A. S. Walker and K. E. Niemeyer, “Applying the Swept Rule for Solving Two-Dimensional Partial Differential Equations on Heterogeneous Architectures,” Mathematical and Computational Applications, vol. 26, no. 3, p. 52, Jul. 2021, doi: 10.3390/mca26030052. [Online]. Available at: https://doi.org/10.3390/mca26030052
  46. S.-L. Wu and T. Zhou, “Parallel implementation for the two-stage SDIRK methods via diagonalization,” Journal of Computational Physics, vol. 428, p. 110076, Mar. 2021, doi: 10.1016/j.jcp.2020.110076. [Online]. Available at: https://doi.org/10.1016/j.jcp.2020.110076
  47. S. Wu, T. Zhou, and Z. Zhou, “Stability implies robust convergence of a class of preconditioned parallel-in-time iterative algorithms,” arXiv:2102.04646v2 [math.NA], 2021 [Online]. Available at: https://arxiv.org/abs/2102.04646v2
  48. S. Wu and Z. Zhou, “A Parallel-in-Time Algorithm for High-Order BDF Methods for Diffusion and Subdiffusion Equations,” vol. 43, no. 6, pp. A3627–A3656, Jan. 2021, doi: 10.1137/20m1355690. [Online]. Available at: https://doi.org/10.1137/20m1355690
  49. D. Xue, Y. Hou, and Y. Li, “Analysis of the local and parallel space-time algorithm for the heat equation,” Computers & Mathematics with Applications, vol. 100, pp. 167–181, Oct. 2021, doi: 10.1016/j.camwa.2021.09.008. [Online]. Available at: https://doi.org/10.1016/j.camwa.2021.09.008
  50. X. Yue, K. Pan, J. Zhou, Z. Weng, S. Shu, and J. Tang, “A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems,” Computers & Mathematics with Applications, vol. 89, pp. 57–67, May 2021, doi: 10.1016/j.camwa.2021.02.020. [Online]. Available at: https://doi.org/10.1016/j.camwa.2021.02.020
  51. Y. Zeng, Y. Duan, and B.-S. Liu, “Solving 2D parabolic equations by using time parareal coupling with meshless collocation RBFs methods,” Engineering Analysis with Boundary Elements, vol. 127, pp. 102–112, Jun. 2021, doi: 10.1016/j.enganabound.2021.03.008. [Online]. Available at: https://doi.org/10.1016/j.enganabound.2021.03.008
  52. Y.-L. Zhao, X.-M. Gu, and A. Ostermann, “A Preconditioning Technique for an All-at-once System from Volterra Subdiffusion Equations with Graded Time Steps,” Journal of Scientific Computing, vol. 88, no. 1, May 2021, doi: 10.1007/s10915-021-01527-7. [Online]. Available at: https://doi.org/10.1007/s10915-021-01527-7
  53. Y.-L. Zhao, J. Wu, and X.-M. Gu, “On the bilateral preconditioning for a L2-type all-at-once system arising from time-space fractional Bloch-Torrey equations,” arXiv:2109.06510v1 [math.NA], 2021 [Online]. Available at: http://arxiv.org/abs/2109.06510v1
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2020

  1. W. Agboh, O. Grainger, D. Ruprecht, and M. Dogar, “Parareal with a Learned Coarse Model for Robotic Manipulation,” Computing and Visualization in Science, vol. 23, no. 8, 2020 [Online]. Available at: https://doi.org/10.1007/s00791-020-00327-0
  2. D. Bast, I. Kulchytska-Ruchka, S. Schoeps, and O. Rain, “Accelerated Steady-State Torque Computation for Induction Machines Using Parallel-In-Time Algorithms,” IEEE Transactions on Magnetics, pp. 1–1, 2020, doi: 10.1109/tmag.2019.2945510. [Online]. Available at: https://doi.org/10.1109/tmag.2019.2945510
  3. C.-E. Brehier and X. Wang, “On Parareal Algorithms for Semilinear Parabolic Stochastic PDEs,” SIAM Journal on Numerical Analysis, vol. 58, no. 1, pp. 254–278, Jan. 2020, doi: 10.1137/19m1251011. [Online]. Available at: https://doi.org/10.1137/19m1251011
  4. T. Buvoli, “Exponential Polynomial Time Integrators,” arXiv:2011.00670v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2011.00670v1
  5. T. Buvoli and M. L. Minion, “IMEX Parareal Integrators,” arXiv:2011.01604v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2011.01604v1
  6. T. Cheng, T. Duan, and V. Dinavahi, “Parallel-in-Time Object-Oriented Electromagnetic Transient Simulation of Power Systems,” IEEE Open Access Journal of Power and Energy, pp. 1–1, 2020, doi: 10.1109/oajpe.2020.3012636. [Online]. Available at: https://doi.org/10.1109/oajpe.2020.3012636
  7. C.-K. Cheng, C.-T. Ho, C. Jia, X. Wang, Z. Zen, and X. Zha, “A Parallel-in-Time Circuit Simulator for Power Delivery Networks with Nonlinear Load Models,” in 2020 IEEE 29th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS), 2020, doi: 10.1109/epeps48591.2020.9231406 [Online]. Available at: https://doi.org/10.1109/epeps48591.2020.9231406
  8. J. Christopher, R. D. Falgout, J. B. Schroder, S. M. Guzik, and X. Gao, “A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics,” Computing and Visualization in Science, vol. 23, no. 1-4, Sep. 2020, doi: 10.1007/s00791-020-00334-1. [Online]. Available at: https://doi.org/10.1007/s00791-020-00334-1
  9. A. T. Clarke, C. J. Davies, D. Ruprecht, and S. M. Tobias, “Parallel-in-time integration of Kinematic Dynamos,” Journal of Computational Physics: X, vol. 7, p. 100057, 2020, doi: 10.1016/j.jcpx.2020.100057. [Online]. Available at: https://doi.org/10.1016/j.jcpx.2020.100057
  10. A. Clarke, C. Davies, D. Ruprecht, S. Tobias, and J. S. Oishi, “Performance of parallel-in-time integration for Rayleigh Bénard Convection,” Computing and Visualization in Science, vol. 23, no. 10, 2020 [Online]. Available at: https://doi.org/10.1007/s00791-020-00332-3
  11. L. D’Amore and R. Cacciapuoti, “Model Reduction in Space and Time for the ab initio decomposition of 4D Variational Data Assimilation Problems,” Applied Numerical Mathematics, Oct. 2020, doi: 10.1016/j.apnum.2020.10.003. [Online]. Available at: https://doi.org/10.1016/j.apnum.2020.10.003
  12. C. Flamant, P. Protopapas, and D. Sondak, “Solving Differential Equations Using Neural Network Solution Bundles,” arXiv:2006.14372v1 [cs.LG], 2020 [Online]. Available at: http://arxiv.org/abs/2006.14372v1
  13. M. J. Gander and T. Lunet, “ParaStieltjes: Parallel computation of Gauss quadrature rules using a Parareal-like approach for the Stieltjes procedure,” Numerical Linear Algebra with Applications, Jun. 2020, doi: 10.1002/nla.2314. [Online]. Available at: https://doi.org/10.1002/nla.2314
  14. M. J. Gander, F. Kwok, and J. Salomon, “PARAOPT: A Parareal Algorithm for Optimality Systems,” SIAM Journal on Scientific Computing, vol. 42, no. 5, pp. A2773–A2802, Jan. 2020, doi: 10.1137/19m1292291. [Online]. Available at: https://doi.org/10.1137/19m1292291
  15. M. J. Gander and S.-L. Wu, “A Diagonalization-Based Parareal Algorithm for Dissipative and Wave Propagation Problems,” SIAM Journal on Numerical Analysis, vol. 58, no. 5, pp. 2981–3009, Jan. 2020, doi: 10.1137/19m1271683. [Online]. Available at: https://doi.org/10.1137/19m1271683
  16. M. J. Gander, I. Kulchytska-Ruchka, and S. Schöps, “A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs,” in Lecture Notes in Computational Science and Engineering, Springer International Publishing, 2020, pp. 243–250 [Online]. Available at: https://doi.org/10.1007/978-3-030-56750-7_27
  17. I. C. Garcia, I. Kulchytska-Ruchka, M. Clemens, and S. Schops, “Parallel-in-Time Solution of Eddy Current Problems Using Implicit and Explicit Time-stepping Methods,” in 2020 IEEE 19th Biennial Conference on Electromagnetic Field Computation (CEFC), 2020, doi: 10.1109/cefc46938.2020.9451465 [Online]. Available at: https://doi.org/10.1109%2Fcefc46938.2020.9451465
  18. A. Garmon and D. Perez, “Exploiting Model Uncertainty to Improve the Scalability of Long-Time Simulations using Parallel Trajectory Splicing,” Modelling and Simulation in Materials Science and Engineering, Jul. 2020, doi: 10.1088/1361-651x/aba511. [Online]. Available at: https://doi.org/10.1088/1361-651x/aba511
  19. X.-M. Gu and S.-L. Wu, “A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel,” Journal of Computational Physics, vol. 417, p. 109576, Sep. 2020, doi: 10.1016/j.jcp.2020.109576. [Online]. Available at: https://doi.org/10.1016/j.jcp.2020.109576
  20. S. Günther, L. Ruthotto, J. B. Schroder, E. C. Cyr, and N. R. Gauger, “Layer-Parallel Training of Deep Residual Neural Networks,” SIAM Journal on Mathematics of Data Science, vol. 2, no. 1, pp. 1–23, Jan. 2020, doi: 10.1137/19m1247620. [Online]. Available at: https://doi.org/10.1137/19m1247620
  21. J. Hahne, S. Friedhoff, and M. Bolten, “PyMGRIT: A Python Package for the parallel-in-time method MGRIT,” arXiv:2008.05172v1 [cs.MS], 2020 [Online]. Available at: http://arxiv.org/abs/2008.05172v1
  22. F. P. Hamon, M. Schreiber, and M. L. Minion, “Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere,” Journal of Computational Physics, vol. 407, p. 109210, Apr. 2020, doi: 10.1016/j.jcp.2019.109210. [Online]. Available at: https://doi.org/10.1016/j.jcp.2019.109210
  23. A. Hessenthaler, B. S. Southworth, D. Nordsletten, O. Röhrle, R. D. Falgout, and J. B. Schroder, “Multilevel Convergence Analysis of Multigrid-Reduction-in-Time,” SIAM Journal on Scientific Computing, vol. 42, no. 2, pp. A771–A796, Jan. 2020, doi: 10.1137/19m1238812. [Online]. Available at: https://doi.org/10.1137/19m1238812
  24. N. E. Hodge, “Towards Improved Speed and Accuracy of Laser Powder Bed FusionSimulations via Representation of Multiple Time Scales,” Additive Manufacturing, p. 101600, Oct. 2020, doi: 10.1016/j.addma.2020.101600. [Online]. Available at: https://doi.org/10.1016/j.addma.2020.101600
  25. X. Hu, C. Rodrigo, and F. J. Gaspar, “Using hierarchical matrices in the solution of the time-fractional heat equation by multigrid waveform relaxation,” Journal of Computational Physics, p. 109540, May 2020, doi: 10.1016/j.jcp.2020.109540. [Online]. Available at: https://doi.org/10.1016/j.jcp.2020.109540
  26. K. Jałowiecki, A. Więckowski, P. Gawron, and B. Gardas, “Parallel in time dynamics with quantum annealers,” Scientific Reports, vol. 10, no. 1, Aug. 2020, doi: 10.1038/s41598-020-70017-x. [Online]. Available at: https://doi.org/10.1038/s41598-020-70017-x
  27. A. Kirby, S. Samsi, M. Jones, A. Reuther, J. Kepner, and V. Gadepally, “Layer-Parallel Training with GPU Concurrency of Deep Residual Neural Networks via Nonlinear Multigrid,” in 2020 IEEE High Performance Extreme Computing Conference (HPEC), 2020, doi: 10.1109/hpec43674.2020.9286180 [Online]. Available at: https://doi.org/10.1109/hpec43674.2020.9286180
  28. S. Lakshmiranganatha and S. S. Muknahallipatna, “Graphical Processing Unit Based Time-Parallel Numerical Method for Ordinary Differential Equations,” Journal of Computer and Communications, vol. 08, no. 02, pp. 39–63, 2020, doi: 10.4236/jcc.2020.82004. [Online]. Available at: https://doi.org/10.4236/jcc.2020.82004
  29. F. Legoll, T. Lelièvre, K. Myerscough, and G. Samaey, “Parareal computation of stochastic differential equations with time-scale separation: a numerical convergence study,” Computing and Visualization in Science, vol. 23, no. 1-4, Sep. 2020, doi: 10.1007/s00791-020-00329-y. [Online]. Available at: https://doi.org/10.1007/s00791-020-00329-y
  30. H. Liu, A. Cheng, and H. Wang, “A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations,” Journal of Scientific Computing, vol. 85, no. 1, Oct. 2020, doi: 10.1007/s10915-020-01321-x. [Online]. Available at: https://doi.org/10.1007/s10915-020-01321-x
  31. J. Liu and Z. Wang, “A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems from evolutionary PDEs,” arXiv:2012.09148v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2012.09148v1
  32. J. Liu and S.-L. Wu, “A Fast Block \textdollar}alpha\textdollar-Circulant Preconditoner for All-at-Once Systems From Wave Equations,” SIAM Journal on Matrix Analysis and Applications, vol. 41, no. 4, pp. 1912–1943, Jan. 2020, doi: 10.1137/19m1309869. [Online]. Available at: https://doi.org/10.1137/19m1309869
  33. E. Lorin, “Derivation and analysis of parallel-in-time neural ordinary differential equations,” Annals of Mathematics and Artificial Intelligence, Jul. 2020, doi: 10.1007/s10472-020-09702-6. [Online]. Available at: https://doi.org/10.1007/s10472-020-09702-6
  34. Y. Maday and O. Mula, “An adaptive parareal algorithm,” Journal of Computational and Applied Mathematics, vol. 377, p. 112915, Oct. 2020, doi: 10.1016/j.cam.2020.112915. [Online]. Available at: https://doi.org/10.1016/j.cam.2020.112915
  35. X. Meng, Z. Li, D. Zhang, and G. E. Karniadakis, “PPINN: Parareal physics-informed neural network for time-dependent PDEs,” Computer Methods in Applied Mechanics and Engineering, vol. 370, p. 113250, Oct. 2020, doi: 10.1016/j.cma.2020.113250. [Online]. Available at: https://doi.org/10.1016/j.cma.2020.113250
  36. H. Nguyen and R. Tsai, “A stable parareal-like method for the second order wave equation,” Journal of Computational Physics, vol. 405, p. 109156, 2020, doi: https://doi.org/10.1016/j.jcp.2019.109156. [Online]. Available at: http://www.sciencedirect.com/science/article/pii/S0021999119308617
  37. B. W. Ong and J. B. Schroder, “Applications of time parallelization,” Computing and Visualization in Science, vol. 23, no. 1-4, Sep. 2020, doi: 10.1007/s00791-020-00331-4. [Online]. Available at: https://doi.org/10.1007/s00791-020-00331-4
  38. B. Park et al., “Performance and Feature Improvements in Parareal-based Power System Dynamic Simulation,” in 2020 IEEE International Conference on Power Systems Technology (POWERCON), 2020, doi: 10.1109/powercon48463.2020.9230544 [Online]. Available at: https://doi.org/10.1109/powercon48463.2020.9230544
  39. H. Rittich and R. Speck, “Time-parallel simulation of the Schrödinger Equation,” Computer Physics Communications, vol. 255, p. 107363, Oct. 2020, doi: 10.1016/j.cpc.2020.107363. [Online]. Available at: https://doi.org/10.1016/j.cpc.2020.107363
  40. R. Schöbel and R. Speck, “PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method,” Computing and Visualization in Science, vol. 23, no. 1-4, Sep. 2020, doi: 10.1007/s00791-020-00330-5. [Online]. Available at: https://doi.org/10.1007/s00791-020-00330-5
  41. L. Z. sci, “Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations,” Journal of Computational Mathematics, vol. 38, no. 3, pp. 487–501, Jun. 2020, doi: 10.4208/jcm.1901-m2018-0085. [Online]. Available at: https://doi.org/10.4208/jcm.1901-m2018-0085
  42. B. Song, Y.-L. Jiang, and X. Wang, “Analysis of two new parareal algorithms based on the Dirichlet-Neumann/Neumann-Neumann waveform relaxation method for the heat equation,” Numerical Algorithms, Jun. 2020, doi: 10.1007/s11075-020-00949-y. [Online]. Available at: https://doi.org/10.1007/s11075-020-00949-y
  43. B. Stump and A. Plotkowski, “Spatiotemporal parallelization of an analytical heat conduction model for additive manufacturing via a hybrid OpenMP \mathplus MPI approach,” Computational Materials Science, vol. 184, p. 109861, Nov. 2020, doi: 10.1016/j.commatsci.2020.109861. [Online]. Available at: https://doi.org/10.1016/j.commatsci.2020.109861
  44. S.-L. Wu and J. Liu, “A Parallel-In-Time Block-Circulant Preconditioner for Optimal Control of Wave Equations,” SIAM Journal on Scientific Computing, vol. 42, no. 3, pp. A1510–A1540, Jan. 2020, doi: 10.1137/19m1289613. [Online]. Available at: https://doi.org/10.1137/19m1289613
  45. S. Wu and Z. Zhou, “Parallel-in-time high-order BDF schemes for diffusion and subdiffusion equations,” arXiv:2007.13125v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2007.13125v1
  46. S.-L. Wu and T. Zhou, “Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 26, p. 88, 2020, doi: 10.1051/cocv/2020012. [Online]. Available at: https://doi.org/10.1051/cocv/2020012
  47. Y.-L. Zhao, X.-M. Gu, M. Li, and H.-Y. Jian, “Preconditioners for all-at-once system from the fractional mobile/immobile advection–diffusion model,” Journal of Applied Mathematics and Computing, Jul. 2020, doi: 10.1007/s12190-020-01410-y. [Online]. Available at: https://doi.org/10.1007/s12190-020-01410-y
  48. Y.-L. Zhao, X.-M. Gu, and A. Ostermann, “A parallel preconditioning technique for an all-at-once system from subdiffusion equations with variable time steps,” arXiv:2007.14636v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2007.14636v1
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2019

  1. A. L. Blumers, Z. Li, and G. E. Karniadakis, “Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics,” Journal of Computational Physics, vol. 393, pp. 214–228, 2019, doi: 10.1016/j.jcp.2019.05.016. [Online]. Available at: https://doi.org/10.1016/j.jcp.2019.05.016
  2. K. Carlberg, L. Brencher, B. Haasdonk, and A. Barth, “Data-Driven Time Parallelism via Forecasting,” SIAM Journal on Scientific Computing, vol. 41, no. 3, pp. B466–B496, Jan. 2019, doi: 10.1137/18m1174362. [Online]. Available at: https://doi.org/10.1137/18m1174362
  3. S. Dohr, J. Zapletal, G. Of, M. Merta, and M. Kravčenko, “A parallel space–time boundary element method for the heat equation,” Computers & Mathematics with Applications, 2019, doi: https://doi.org/10.1016/j.camwa.2018.12.031. [Online]. Available at: http://www.sciencedirect.com/science/article/pii/S0898122118307296
  4. S. Friedhoff, J. Hahne, I. Kulchytska-Ruchka, and S. Schöps, “Exploring Parallel-in-Time Approaches for Eddy Current Problems,” in Progress in Industrial Mathematics at ECMI 2018, Springer International Publishing, 2019, pp. 373–379 [Online]. Available at: https://doi.org/10.1007/978-3-030-27550-1_47
  5. S. Friedhoff, J. Hahne, and S. Schöps, “Multigrid-reduction-in-time for Eddy Current problems,” PAMM, vol. 19, no. 1, Nov. 2019, doi: 10.1002/pamm.201900262. [Online]. Available at: https://doi.org/10.1002/pamm.201900262
  6. S. Friedhoff and B. S. Southworth, “On ‘Optimal’ h-Independent Convergence of Parareal and MGRIT Using Runge-Kutta Time Integration,” arXiv:1906.06672 [math.NA], 2019 [Online]. Available at: https://arxiv.org/abs/1906.06672
  7. M. Gander, L. Halpern, J. Rannou, and J. Ryan, “A Direct Time Parallel Solver by Diagonalization for the Wave Equation,” SIAM Journal on Scientific Computing, vol. 41, no. 1, pp. A220–A245, 2019, doi: 10.1137/17M1148347. [Online]. Available at: https://doi.org/10.1137/17M1148347
  8. M. Gander, Y. Jiang, and B. Song, “A Superlinear Convergence Estimate for the Parareal Schwarz Waveform Relaxation Algorithm,” SIAM Journal on Scientific Computing, vol. 41, no. 2, pp. A1148–A1169, 2019, doi: 10.1137/18M1177226. [Online]. Available at: https://doi.org/10.1137/18M1177226
  9. M. J. Gander, I. Kulchytska-Ruchka, I. Niyonzima, and S. Schöps, “A New Parareal Algorithm for Problems with Discontinuous Sources,” SIAM Journal on Scientific Computing, vol. 41, no. 2, pp. B375–B395, 2019, doi: 10.1137/18M1175653. [Online]. Available at: https://doi.org/10.1137/18M1175653
  10. M. J. Gander and S.-L. Wu, “Convergence analysis of a periodic-like waveform relaxation method for initial-value problems via the diagonalization technique,” Numerische Mathematik, vol. 143, no. 2, pp. 489–527, Jun. 2019, doi: 10.1007/s00211-019-01060-8. [Online]. Available at: https://doi.org/10.1007/s00211-019-01060-8
  11. S. Götschel and M. L. Minion, “An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs,” SIAM Journal on Scientific Computing, vol. 41, no. 6, pp. C603–C626, Jan. 2019, doi: 10.1137/19m1239313. [Online]. Available at: https://doi.org/10.1137/19m1239313
  12. F. Hédin and T. Lelièvre, “gen.parRep: A first implementation of the Generalized Parallel Replica dynamics for the long time simulation of metastable biochemical systems,” Computer Physics Communications, 2019, doi: 10.1016/j.cpc.2019.01.005. [Online]. Available at: https://doi.org/10.1016/j.cpc.2019.01.005
  13. J. Hong, X. Wang, and L. Zhang, “Parareal Exponential \textdollar}theta\textdollar-Scheme for Longtime Simulation of Stochastic Schrödinger Equations with Weak Damping,” SIAM Journal on Scientific Computing, vol. 41, no. 6, pp. B1155–B1177, Jan. 2019, doi: 10.1137/18m1176749. [Online]. Available at: https://doi.org/10.1137/18m1176749
  14. A. Howse, H. Sterck, R. Falgout, S. MacLachlan, and J. Schroder, “Parallel-In-Time Multigrid with Adaptive Spatial Coarsening for The Linear Advection and Inviscid Burgers Equations,” SIAM Journal on Scientific Computing, vol. 41, no. 1, pp. A538–A565, 2019, doi: 10.1137/17M1144982. [Online]. Available at: https://dx.doi.org/10.1137/17M1144982
  15. O. A. Krzysik, H. D. Sterck, S. P. MacLachlan, and S. Friedhoff, “On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection,” arXiv:1902.07757 [math.NA], 2019 [Online]. Available at: https://arxiv.org/abs/1902.07757
  16. F. Kwok and B. Ong, “Schwarz Waveform Relaxation with Adaptive Pipelining,” SIAM Journal on Scientific Computing, vol. 41, no. 1, pp. A339–A364, 2019, doi: 10.1137/17M115311X. [Online]. Available at: https://doi.org/10.1137/17M115311X
  17. S. Li, R. Chen, and X. Shao, “Parallel two-level space–time hybrid Schwarz method for solving linear parabolic equations,” Applied Numerical Mathematics, vol. 139, pp. 120–135, 2019, doi: 10.1016/j.apnum.2019.01.016. [Online]. Available at: https://doi.org/10.1016/j.apnum.2019.01.016
  18. S. Li, X. Shao, and X.-C. Cai, “Highly parallel space-time domain decomposition methods for parabolic problems,” CCF Transactions on High Performance Computing, 2019, doi: 10.1007/s42514-019-00003-x. [Online]. Available at: https://doi.org/10.1007/s42514-019-00003-x
  19. V. Mele, D. Romano, E. M. Constantinescu, L. Carracciuolo, and L. D’Amore, “Performance Evaluation for a PETSc Parallel-in-Time Solver Based on the MGRIT Algorithm,” in Euro-Par 2018: Parallel Processing Workshops, 2019, pp. 716–728, doi: 10.1002/cpe.4928 [Online]. Available at: https://doi.org/10.1002/cpe.4928
  20. M. Neumüller and I. Smears, “Time-Parallel Iterative Solvers for Parabolic Evolution Equations,” SIAM Journal on Scientific Computing, vol. 41, no. 1, pp. C28–C51, 2019, doi: 10.1137/18M1172466. [Online]. Available at: https://doi.org/10.1137/18M1172466
  21. A. G. Peddle, T. Haut, and B. Wingate, “Parareal Convergence for Oscillatory PDEłowercases with Finite Time-Scale Separation,” SIAM Journal on Scientific Computing, vol. 41, no. 6, pp. A3476–A3497, Jan. 2019, doi: 10.1137/17m1131611. [Online]. Available at: https://doi.org/10.1137/17m1131611
  22. Rosa-Raı́ces Jorge L., B. Zhang, and T. F. Miller, “Path-accelerated stochastic molecular dynamics: Parallel-in-time integration using path integrals,” The Journal of Chemical Physics, vol. 151, no. 16, p. 164120, Oct. 2019, doi: 10.1063/1.5125455. [Online]. Available at: https://doi.org/10.1063/1.5125455
  23. D. Samaddar, D. P. Coster, X. Bonnin, L. A. Berry, W. R. Elwasif, and D. B. Batchelor, “Application of the parareal algorithm to simulations of ELMs in ITER plasma,” Computer Physics Communications, vol. 235, pp. 246–257, 2019, doi: 10.1016/j.cpc.2018.08.007. [Online]. Available at: https://doi.org/10.1016/j.cpc.2018.08.007
  24. M. Schreiber, N. Schaeffer, and R. Loft, “Exponential Integrators with Parallel-in-Time Rational Approximations for Shallow-Water Equations on the Rotating Sphere,” Parallel Computing, 2019, doi: 10.1016/j.parco.2019.01.005. [Online]. Available at: https://dx.doi.org/10.1016/j.parco.2019.01.005
  25. M. Schreiber and R. Loft, “A parallel time integrator for solving the linearized shallow water equations on the rotating sphere,” Numerical Linear Algebra with Applications, vol. 26, no. 2, p. e2220, 2019, doi: 10.1002/nla.2220. [Online]. Available at: https://onlinelibrary.wiley.com/doi/abs/10.1002/nla.2220
  26. B. S. Southworth, “Necessary Conditions and Tight Two-level Convergence Bounds for Parareal and Multigrid Reduction in Time,” SIAM J. Matrix Anal. Appl., vol. 40, no. 2, pp. 564–608, 2019, doi: https://doi.org/10.1137/18M1226208.
  27. R. Speck, “Algorithm 997: pySDC - Prototyping Spectral Deferred Corrections,” ACM Transactions on Mathematical Software, vol. 45, no. 3, pp. 1–23, Aug. 2019, doi: 10.1145/3310410. [Online]. Available at: https://doi.org/10.1145/3310410
  28. R. Speck, M. Knobloch, A. Gocht, and S. Lührs, “Using performance analysis tools for parallel-in-time integrators – Does my time-parallel code do what I think it does?,” arXiv:1911.13027v1 [cs.PF], 2019 [Online]. Available at: http://arxiv.org/abs/1911.13027v1
  29. S. Wang, Y. Shao, and Z. Peng, “A Parallel-in-Space-and-Time Method for Transient Electromagnetic Problems,” IEEE Transactions on Antennas and Propagation, vol. 67, no. 6, pp. 3961–3973, 2019, doi: 10.1109/TAP.2019.2909937. [Online]. Available at: https://doi.org/10.1109/TAP.2019.2909937
  30. S.-L. Wu and T. Zhou, “Acceleration of the Two-Level MGRIT Algorithm via the Diagonalization Technique,” SIAM Journal on Scientific Computing, vol. 41, no. 5, pp. A3421–A3448, Jan. 2019, doi: 10.1137/18m1207697. [Online]. Available at: https://doi.org/10.1137/18m1207697
  31. L. Zhang, W. Zhou, and L. Ji, “Parareal algorithms applied to stochastic differential equations with conserved quantities,” Journal of Computational Mathematics, vol. 37, no. 1, pp. 48–60, 2019, doi: 10.4208/jcm.1708-m2017-0089. [Online]. Available at: https://doi.org/10.4208/jcm.1708-m2017-0089
top

2018

  1. S. Badia and M. Olm, “Nonlinear parallel-in-time Schur complement solvers for ordinary differential equations,” Journal of Computational and Applied Mathematics, vol. 344, pp. 794–806, 2018, doi: 10.1016/j.cam.2017.09.033. [Online]. Available at: https://doi.org/10.1016/j.cam.2017.09.033
  2. P. Benedusi, C. Garoni, R. Krause, X. Li, and S. Serra-Capizzano, “Space-Time FE-DG Discretization of the Anisotropic Diffusion Equation in Any Dimension: The Spectral Symbol,” SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 3, pp. 1383–1420, 2018, doi: 10.1137/17M113527X. [Online]. Available at: https://doi.org/10.1137/17M113527X
  3. M. Bolten, D. Moser, and R. Speck, “Asymptotic convergence of the parallel full approximation scheme in space and time for linear problems,” Numerical Linear Algebra with Applications, vol. 25, no. 6, p. e2208, 2018, doi: 10.1002/nla.2208. [Online]. Available at: https://onlinelibrary.wiley.com/doi/abs/10.1002/nla.2208
  4. Manuel Borregales and Kundan Kumar and Florin Adrian Radu and Carmen Rodrigo and Francisco José Gaspar, “A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model,” Computers & Mathematics with Applications, 2018, doi: 10.1016/j.camwa.2018.09.005. [Online]. Available at: https://doi.org/10.1016/j.camwa.2018.09.005
  5. S. Bu, “Time parallelization scheme with an adaptive time step size for solving stiff initial value problems,” Open Mathematics, vol. 16, no. 1, pp. 210–218, 2018, doi: 10.1515/math-2018-0022. [Online]. Available at: https://doi.org/10.1515/math-2018-0022
  6. L. D’Amore and R. Cacciapuoti, “DD-DA PinT-based model: A Domain Decomposition approach in space and time, based on Parareal, for solving the 4D-Var Data Assimilation model,” arXiv:1807.07107 [math.NA], 2018 [Online]. Available at: https://arxiv.org/abs/1807.07107
  7. N. Duan, S. Simunovic, A. Dimitrovski, and K. Sun, “Improving the Convergence Rate of Parareal-in-time Power System Simulation using the Krylov Subspace,” in 2018 IEEE Power Energy Society General Meeting (PESGM), 2018, pp. 1–5, doi: 10.1109/PESGM.2018.8586354 [Online]. Available at: https://dx.doi.org/10.1109/PESGM.2018.8586354
  8. R. Dyja, B. Ganapathysubramanian, and K. G. van der Zee, “Parallel-In-Space-Time, Adaptive Finite Element Framework for Nonlinear Parabolic Equations,” SIAM Journal on Scientific Computing, vol. 40, no. 3, pp. C283–C304, 2018, doi: 10.1137/16M108985X. [Online]. Available at: https://doi.org/10.1137/16M108985X
  9. L. Fischer, S. Götschel, and M. Weiser, “Lossy data compression reduces communication time in hybrid time-parallel integrators,” Computing and Visualization in Science, vol. 19, no. 1, pp. 19–30, 2018, doi: 10.1007/s00791-018-0293-2. [Online]. Available at: https://doi.org/10.1007/s00791-018-0293-2
  10. S. R. Franco, F. J. Gaspar, M. A. V. Pinto, and C. Rodrigo, “Multigrid method based on a space-time approach with standard coarsening for parabolic problems,” Applied Mathematics and Computation, vol. 317, no. Supplement C, pp. 25–34, 2018, doi: 10.1016/j.amc.2017.08.043. [Online]. Available at: https://doi.org/10.1016/j.amc.2017.08.043
  11. S. R. Franco, C. Rodrigo, F. J. Gaspar, and M. A. V. Pinto, “A multigrid waveform relaxation method for solving the poroelasticity equations,” Computational and Applied Mathematics, pp. 1–16, 2018, doi: 10.1007/s40314-018-0603-9. [Online]. Available at: https://doi.org/10.1007/s40314-018-0603-9
  12. H. Fu and H. Wang, “A Preconditioned Fast Parareal Finite Difference Method for Space-Time Fractional Partial Differential Equation,” Journal of Scientific Computing, 2018, doi: 10.1007/s10915-018-0835-2. [Online]. Available at: https://doi.org/10.1007/s10915-018-0835-2
  13. M. J. Gander, S. Güttel, and M. Petcu, “A Nonlinear ParaExp Algorithm,” in Lecture Notes in Computational Science and Engineering, Springer International Publishing, 2018, pp. 261–270 [Online]. Available at: https://doi.org/10.1007/978-3-319-93873-8_24
  14. M. J. Gander, F. Kwok, and H. Zhang, “Multigrid interpretations of the parareal algorithm leading to an overlapping variant and MGRIT,” Computing and Visualization in Science, 2018, doi: 10.1007/s00791-018-0297-y. [Online]. Available at: https://doi.org/10.1007/s00791-018-0297-y
  15. A. Goddard and A. Wathen, “A note on parallel preconditioning for all-at-once evolutionary PDEs,” pp. 135–150, 2018, doi: 10.1553/etna_vol51s135. [Online]. Available at: https://dx.doi.org/10.1553/etna_vol51s135
  16. S. Götschel and M. L. Minion, “Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST,” in Domain Decomposition Methods in Science and Engineering XXIV, 2018, pp. 363–371, doi: 10.1007/978-3-319-93873-8_34 [Online]. Available at: https://doi.org/10.1007/978-3-319-93873-8_34
  17. S. Günther, N. R. Gauger, and J. B. Schroder, “A Non-Intrusive Parallel-in-Time Adjoint Solver with the XBraid Library,” Computing and Visualization in Science, 2018, doi: 10.1007/s00791-018-0300-7. [Online]. Available at: https://doi.org/10.1007/s00791-018-0300-7
  18. A. Hessenthaler, D. Nordsletten, O. Röhrle, J. B. Schroder, and R. D. Falgout, “Convergence of the multigrid reduction in time algorithm for the linear elasticity equations,” Numerical Linear Algebra with Applications, vol. 25, no. 3, p. e2155, 2018, doi: 10.1002/nla.2155. [Online]. Available at: https://dx.doi.org/10.1002/nla.2155
  19. J. T. Hwang and D. Munster, “Solution of ordinary differential equations in gradient-based multidisciplinary design optimization,” in 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, American Institute of Aeronautics and Astronautics, 2018 [Online]. Available at: https://doi.org/10.2514/6.2018-1646
  20. M. Iizuka and K. Ono, “Influence of the phase accuracy of the coarse solver calculation on the convergence of the parareal method iteration for hyperbolic PDEs,” Computing and Visualization in Science, 2018, doi: 10.1007/s00791-018-0299-9. [Online]. Available at: https://doi.org/10.1007/s00791-018-0299-9
  21. G. L. Kooij, M. A. Botchev, and B. J. Geurts, “An Exponential Time Integrator for the Incompressible Navier–Stokes Equation,” SIAM Journal on Scientific Computing, vol. 40, no. 3, pp. B684–B705, 2018, doi: 10.1137/17M1121950. [Online]. Available at: https://doi.org/10.1137/17M1121950
  22. C. Lederman and D. Bilyeu, “An Approximate Time-Parallel Method for the Fast and Accurate Computation of Particle Trajectories in a Magnetic Field,” Journal of Applied Mathematics and Physics, vol. 6, pp. 498–519, 2018, doi: 10.4236/jamp.2018.63046 . [Online]. Available at: https://doi.org/10.4236/jamp.2018.63046