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
- M. Appel and J. Alexandersen, “One-shot Parareal Approach for Topology Optimisation of Transient Heat Flow,” arXiv:2411.19030v1 [cs.CE], 2024 [Online]. Available at: http://arxiv.org/abs/2411.19030v1
- M. M. Betcke, L. M. Kreusser, and D. Murari, “Parallel-in-Time Solutions with Random Projection Neural Networks,” arXiv:2408.09756v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2408.09756v1
- 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
- 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.
- 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
- 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
- P. Y. Fung and S. Hon, “Block \(\boldsymbolω\)-Circulant Preconditioners for Parabolic Optimal Control Problems,” SIAM Journal on Matrix Analysis and Applications, vol. 45, no. 4, pp. 2263–2286, Dec. 2024, doi: 10.1137/23m1601432. [Online]. Available at: http://dx.doi.org/10.1137/23M1601432
- M. J. Gander, M. Ohlberger, and S. Rave, “A Parareal algorithm without Coarse Propagator?,” arXiv:2409.02673v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2409.02673v1
- 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
- G. Gattiglio, L. Grigoryeva, and M. Tamborrino, “RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks,” arXiv:2411.06225v1 [stat.CO], 2024 [Online]. Available at: http://arxiv.org/abs/2411.06225v1
- 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
- H. Gu, M. Cai, and J. Li, “Crank-Nicolson-type iterative decoupled algorithms for Biot’s consolidation model using total pressure,” arXiv:2409.18391v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2409.18391v1
- T. He, J. Lu, and M. Li, “The parareal algorithm for Caputo-Hadamard fractional differential equations,” Communications on Analysis and Computation, vol. 0, no. 0, pp. 0–0, 2024, doi: 10.3934/cac.2024021. [Online]. Available at: http://dx.doi.org/10.3934/cac.2024021
- M. Heinkenschloss and N. J. Kroeger, “A new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problems,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 30, p. 62, 2024, doi: 10.1051/cocv/2024051. [Online]. Available at: http://dx.doi.org/10.1051/cocv/2024051
- 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
- S. Y. Hon, P. Y. Fung, and X.-lei Lin, “An optimal parallel-in-time preconditioner for parabolic optimal control problems,” arXiv:2410.22686v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2410.22686v1
- J. Hope-Collins, A. Hamdan, W. Bauer, L. Mitchell, and C. Cotter, “asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond,” arXiv:2409.18792v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2409.18792v1
- 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
- Y.-Y. Huang, P. Y. Fung, S. Y. Hon, and X.-L. Lin, “An efficient preconditioner for evolutionary partial differential equations with θ-method in time discretization,” arXiv:2408.03535v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2408.03535v1
- Y.-Y. Huang, S. Y. Hon, L.-K. Chou, and S.-L. Lei, “Optimal preconditioners for nonsymmetric multilevel Toeplitz systems with application to solving non-local evolutionary partial differential equations,” arXiv:2409.15770v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2409.15770v1
- C. Iacob, H. Abdulsamad, and S. Särkkä, “A Parallel-in-Time Newton’s Method for Nonlinear Model Predictive Control,” arXiv:2409.20027v2 [math.OC], 2024 [Online]. Available at: http://arxiv.org/abs/2409.20027v2
- 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
- S. Iqbal, H. Abdulsamad, T. Cator, U. Braga-Neto, and S. Särkkä, “Parallel-in-Time Probabilistic Solutions for Time-Dependent Nonlinear Partial Differential Equations,” in 2024 IEEE 34th International Workshop on Machine Learning for Signal Processing (MLSP), 2024, pp. 1–6, doi: 10.1109/mlsp58920.2024.10734739 [Online]. Available at: http://dx.doi.org/10.1109/MLSP58920.2024.10734739
- J. Jackaman and S. MacLachlan, “Space-time waveform relaxation multigrid for Navier-Stokes,” arXiv:2407.13997v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2407.13997v1
- 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
- F. C. Joseph and G. Gurrala, “Adaptive Homotopy Based Coarse Solver for Parareal-in-Time Transient Stability Simulations,” IEEE Transactions on Power Systems, pp. 1–12, 2024, doi: 10.1109/tpwrs.2024.3424555. [Online]. Available at: http://dx.doi.org/10.1109/TPWRS.2024.3424555
- 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
- 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
- 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
- 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
- K.-A. Mardal, J. Sogn, and S. Takacs, “A robust and time-parallel preconditioner for parabolic reconstruction problems using Isogeometric Analysis,” arXiv:2407.17964v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2407.17964v1
- N. Margenberg and P. Munch, “A Space-Time Multigrid Method for Space-Time Finite Element Discretizations of Parabolic and Hyperbolic PDEs,” arXiv:2408.04372v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2408.04372v1
- 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
- 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
- S. Muralikrishnan and R. Speck, “ParaPIF: A Parareal Approach for Parallel-in-Time Integration of Particle-in-Fourier schemes,” arXiv:2407.00485v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2407.00485v1
- 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
- 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
- N. A. Petersson, S. Günther, and S. W. Chung, “A time-parallel multiple-shooting method for large-scale quantum optimal control,” arXiv:2407.13950v1 [quant-ph], 2024 [Online]. Available at: http://arxiv.org/abs/2407.13950v1
- Y. Poirier, J. Salomon, A. Babarit, P. Ferrant, and G. Ducrozet, “Acceleration of a wave-structure interaction solver by the Parareal method,” Engineering Analysis with Boundary Elements, vol. 167, p. 105870, Oct. 2024, doi: 10.1016/j.enganabound.2024.105870. [Online]. Available at: http://dx.doi.org/10.1016/j.enganabound.2024.105870
- 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
- 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
- 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
- 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
- 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
- H. D. Sterck, R. D. Falgout, O. A. Krzysik, and J. B. Schroder, “Parallel-in-time solution of hyperbolic PDE systems via characteristic-variable block preconditioning,” arXiv:2407.03873v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2407.03873v1
- S.-L. Wu and T. Zhou, “Convergence Analysis of the Parareal Algorithm with Nonuniform Fine Time Grid,” SIAM Journal on Numerical Analysis, vol. 62, no. 5, pp. 2308–2330, Oct. 2024, doi: 10.1137/23m1592481. [Online]. Available at: http://dx.doi.org/10.1137/23M1592481
- 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
- Z. Yang, Y. Wang, and W. T. Leung, “Parallel in time partially explicit splitting scheme for high contrast multiscale problems,” arXiv:2411.09244v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2411.09244v1
- 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
- L. Zhang and Q. Zhang, “Convergence analysis of the parareal algorithms for stochastic Maxwell equations driven by additive noise,” arXiv:2407.10907v1 [math.NA], 2024 [Online]. Available at: http://arxiv.org/abs/2407.10907v1
- 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
- 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
- M. Zhen, X. Ding, K. Qu, J. Cai, and S. Pan, “Enhancing the Convergence of the Multigrid-Reduction-in-Time Method for the Euler and Navier–Stokes Equations,” Journal of Scientific Computing, vol. 100, no. 2, Jun. 2024, doi: 10.1007/s10915-024-02596-0. [Online]. Available at: http://dx.doi.org/10.1007/s10915-024-02596-0
- T. Baumann, S. Götschel, T. Lunet, D. Ruprecht, and R. Speck, “Adaptive time step selection for spectral deferred correction,” Numerical Algorithms, Oct. 2024, doi: 10.1007/s11075-024-01964-z. [Online]. Available at: https://doi.org/10.1007/s11075-024-01964-z
- T. Baumann, S. Götschel, T. Lunet, D. Ruprecht, and R. Speck, “Resilience Against Soft Faults through Adaptivity in Spectral Deferred Correction.” 2024 [Online]. Available at: https://arxiv.org/abs/2412.00529
2023
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- K. Trotti, “A domain splitting strategy for solving PDEs,” arXiv:2303.01163v1 [math.NA], 2023 [Online]. Available at: http://arxiv.org/abs/2303.01163v1
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
2022
- 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
- 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
- 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
- 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
- S. Costanzo, T. Sayadi, M. F. de Pando, P. J. Schmid, and P. Frey, “Parallel-in-time adjoint-based optimization – application to unsteady incompressible flows,” Journal of Computational Physics, p. 111664, Oct. 2022, doi: 10.1016/j.jcp.2022.111664. [Online]. Available at: https://doi.org/10.1016/j.jcp.2022.111664
- L. D’Amore, E. Constantinescu, and L. Carracciuolo, “A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation,” Journal of Scientific Computing, vol. 91, no. 2, Apr. 2022, doi: 10.1007/s10915-022-01826-7. [Online]. Available at: https://doi.org/10.1007/s10915-022-01826-7
- F. Danieli, B. S. Southworth, and A. J. Wathen, “Space-Time Block Preconditioning for Incompressible Flow,” SIAM Journal on Scientific Computing, vol. 44, no. 1, pp. A337–A363, Feb. 2022, doi: 10.1137/21m1390773. [Online]. Available at: https://doi.org/10.1137%2F21m1390773
- F. Danieli and S. MacLachlan, “Multigrid reduction in time for non-linear hyperbolic equations,” ETNA - Electronic Transactions on Numerical Analysis, vol. 58, pp. 43–65, 2022, doi: 10.1553/etna_vol58s43. [Online]. Available at: https://doi.org/10.1553%2Fetna_vol58s43
- S. Frei and A. Heinlein, “Efficient coarse correction for parallel time-stepping in plaque growth simulations,” arXiv:2207.02081v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2207.02081v1
- I. C. Garcia, I. Kulchytska-Ruchka, and S. Schöps, “Parareal for index two differential algebraic equations,” Numerical Algorithms, Mar. 2022, doi: 10.1007/s11075-022-01267-1. [Online]. Available at: https://doi.org/10.1007%2Fs11075-022-01267-1
- O. Gorynina, F. Legoll, T. Lelievre, and D. Perez, “Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects,” arXiv:2212.10508v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2212.10508v1
- J. Hahne, B. S. Southworth, and S. Friedhoff, “Asynchronous Truncated Multigrid-Reduction-in-Time,” SIAM Journal on Scientific Computing, pp. S281–S306, Nov. 2022, doi: 10.1137/21m1433149. [Online]. Available at: https://doi.org/10.1137/21m1433149
- G. He, “Time Parallel Denoising Algorithm Based on P-M Equation for Real Image,” Wireless Communications and Mobile Computing, vol. 2022, pp. 1–9, Aug. 2022, doi: 10.1155/2022/8008912. [Online]. Available at: https://doi.org/10.1155/2022/8008912
- Y. He and J. Liu, “A Vanka-type multigrid solver for complex-shifted Laplacian systems from diagonalization-based parallel-in-time algorithms,” Applied Mathematics Letters, vol. 132, p. 108125, Oct. 2022, doi: 10.1016/j.aml.2022.108125. [Online]. Available at: https://doi.org/10.1016/j.aml.2022.108125
- K. Herb and P. Welter, “Parallel time integration using Batched BLAS (Basic Linear Algebra Subprograms) routines,” Computer Physics Communications, vol. 270, p. 108181, Jan. 2022, doi: 10.1016/j.cpc.2021.108181. [Online]. Available at: https://doi.org/10.1016/j.cpc.2021.108181
- Y. Jiang and J. Liu, “Fast Parallel-in-Time Quasi-Boundary Value Methods for Backward Heat Conduction Problems,” Applied Numerical Mathematics, Oct. 2022, doi: 10.1016/j.apnum.2022.10.006. [Online]. Available at: https://doi.org/10.1016/j.apnum.2022.10.006
- E. Kazakov, D. Efremenko, V. Zemlyakov, and J. Gao, “A Time-Parallel Ordinary Differential Equation Solver with an Adaptive Step Size: Performance Assessment,” in Lecture Notes in Computer Science, Springer International Publishing, 2022, pp. 3–17 [Online]. Available at: https://doi.org/10.1007/978-3-031-22941-1_1
- D. Kressner, S. Massei, and J. Zhu, “Improved parallel-in-time integration via low-rank updates and interpolation,” arXiv:2204.03073v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2204.03073v1
- Y. Lee, J. Park, and C.-O. Lee, “Parareal Neural Networks Emulating a Parallel-in-Time Algorithm,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–12, 2022, doi: 10.1109/tnnls.2022.3206797. [Online]. Available at: https://doi.org/10.1109/tnnls.2022.3206797
- C.-O. Lee, Y. Lee, and J. Park, “A Parareal Architecture for Very Deep Convolutional Neural Networks,” in Lecture Notes in Computational Science and Engineering, Springer International Publishing, 2022, pp. 407–415 [Online]. Available at: http://dx.doi.org/10.1007/978-3-030-95025-5_43
- F. Legoll, T. Lelièvre, and U. Sharma, “An Adaptive Parareal Algorithm: Application to the Simulation of Molecular Dynamics Trajectories,” SIAM Journal on Scientific Computing, vol. 44, no. 1, pp. B146–B176, Jan. 2022, doi: 10.1137/21m1412979. [Online]. Available at: https://doi.org/10.1137/21m1412979
- S. Li, L. Xie, and L. Zhou, “Convergence analysis of space-time domain decomposition method for parabolic equations,” Computers &\mathsemicolon Mathematics with Applications, Aug. 2022, doi: 10.1016/j.camwa.2022.08.012. [Online]. Available at: https://doi.org/10.1016/j.camwa.2022.08.012
- J. Liu and Z. Wang, “A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems in unsteady convection-diffusion PDEs,” vol. 416, p. 126750, Mar. 2022, doi: 10.1016/j.amc.2021.126750. [Online]. Available at: https://doi.org/10.1016/j.amc.2021.126750
- J. Liu, X.-S. Wang, S.-L. Wu, and T. Zhou, “A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations,” Advances in Computational Mathematics, vol. 48, no. 3, Apr. 2022, doi: 10.1007/s10444-022-09928-4. [Online]. Available at: https://doi.org/10.1007%2Fs10444-022-09928-4
- C. Lohmann, J. Dünnebacke, and S. Turek, “Fourier analysis of a time-simultaneous two-grid algorithm using a damped Jacobi waveform relaxation smoother for the one-dimensional heat equation,” Journal of Numerical Mathematics, vol. 0, no. 0, Jun. 2022, doi: 10.1515/jnma-2021-0045. [Online]. Available at: https://doi.org/10.1515/jnma-2021-0045
- G. E. Moon and E. C. Cyr, “Parallel Training of GRU Networks with a Multi-Grid Solver for Long Sequences,” arXiv:2203.04738v1 [cs.CV], 2022 [Online]. Available at: http://arxiv.org/abs/2203.04738v1
- K. Pentland, M. Tamborrino, D. Samaddar, and L. C. Appel, “Stochastic Parareal: An Application of Probabilistic Methods to Time-Parallelization,” SIAM Journal on Scientific Computing, pp. S82–S102, Jul. 2022, doi: 10.1137/21m1414231. [Online]. Available at: https://doi.org/10.1137%2F21m1414231
- K. Pentland, M. Tamborrino, and T. J. Sullivan, “Error bound analysis of the stochastic parareal algorithm,” arXiv:2211.05496v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2211.05496v1
- K. Pentland, M. Tamborrino, T. J. Sullivan, J. Buchanan, and L. C. Appel, “GParareal: a time-parallel ODE solver using Gaussian process emulation,” Statistics and Computing, vol. 33, no. 1, Dec. 2022, doi: 10.1007/s11222-022-10195-y. [Online]. Available at: https://doi.org/10.1007%2Fs11222-022-10195-y
- B. Philippi and T. Slawig, “The Parareal Algorithm Applied to the FESOM 2 Ocean Circulation Model,” arXiv:2208.07598v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2208.07598v1
- M. K. Riahi, “PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm,” Applied Numerical Mathematics, vol. 181, pp. 225–233, Nov. 2022, doi: 10.1016/j.apnum.2022.06.004. [Online]. Available at: https://doi.org/10.1016%2Fj.apnum.2022.06.004
- S. Riffo, F. Kwok, and J. Salomon, “Time-parallelization of sequential data assimilation problems,” arXiv:2212.02377v1 [math.OC], 2022 [Online]. Available at: http://arxiv.org/abs/2212.02377v1
- J. Rosemeier, T. Haut, and B. Wingate, “Multi-level Parareal algorithm with Averaging,” arXiv:2211.17239v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2211.17239v1
- S. Särkkä and Á. F. García-Fernández, “Temporal Parallelisation of the HJB Equation and Continuous-Time Linear Quadratic Control,” arXiv:2212.11744v1 [math.OC], 2022 [Online]. Available at: http://arxiv.org/abs/2212.11744v1
- H. D. Sterck, R. D. Falgout, and O. A. Krzysik, “Fast multigrid reduction-in-time for advection via modified semi-Lagrangian coarse-grid operators,” arXiv:2203.13382v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2203.13382v1
- H. D. Sterck, S. Friedhoff, O. A. Krzysik, and S. P. MacLachlan, “Multigrid reduction-in-time convergence for advection problems: A Fourier analysis perspective,” arXiv:2208.01526v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2208.01526v1
- H. D. Sterck, R. D. Falgout, O. A. Krzysik, and J. B. Schroder, “Efficient multigrid reduction-in-time for method-of-lines discretizations of linear advection,” arXiv:2209.06916v1 [math.NA], 2022 [Online]. Available at: http://arxiv.org/abs/2209.06916v1
- J. Strake, D. Döhring, and A. Benigni, “MGRIT-Based Multi-Level Parallel-in-Time Electromagnetic Transient Simulation,” Energies, vol. 15, no. 21, p. 7874, Oct. 2022, doi: 10.3390/en15217874. [Online]. Available at: https://doi.org/10.3390/en15217874
- M. Sugiyama, J. B. Schroder, B. S. Southworth, and S. Friedhoff, “Weighted relaxation for multigrid reduction in time,” Numerical Linear Algebra with Applications, Sep. 2022, doi: 10.1002/nla.2465. [Online]. Available at: https://doi.org/10.1002%2Fnla.2465
- M. A. Sultanov, V. E. Misilov, and Y. Nurlanuly, “Efficient Parareal algorithm for solving time-fractional diffusion equation,” Dal nevostochnyi Matematicheskii Zhurnal, vol. 22, no. 2, pp. 245–251, 2022, doi: 10.47910/femj202233. [Online]. Available at: https://doi.org/10.47910/femj202233
- Y. Takahashi, K. Fujiwara, and T. Iwashita, “Parallel-in-space-and-time finite-element analysis of electric machines using time step overlapping in a massively parallel computing environment,” COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Jul. 2022, doi: 10.1108/compel-04-2022-0161. [Online]. Available at: https://doi.org/10.1108/compel-04-2022-0161
- R. Tielen, M. Möller, and C. Vuik, “Combining p-multigrid and Multigrid Reduction in Time methods to obtain a scalable solver for Isogeometric Analysis,” SN Applied Sciences, vol. 4, no. 6, May 2022, doi: 10.1007/s42452-022-05043-7. [Online]. Available at: https://doi.org/10.1007%2Fs42452-022-05043-7
- Utkarsh, C. Elrod, Y. Ma, K. Althaus, and C. Rackauckas, “Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations,” in 2022 IEEE High Performance Extreme Computing Conference (HPEC), 2022, doi: 10.1109/hpec55821.2022.9926357 [Online]. Available at: https://doi.org/10.1109%2Fhpec55821.2022.9926357
- C.-Y. Wang, Y.-L. Jiang, and Z. Miao, “Time domain decomposition of parabolic control problems based on discontinuous Galerkin semi-discretization,” Applied Numerical Mathematics, Feb. 2022, doi: 10.1016/j.apnum.2022.02.016. [Online]. Available at: https://doi.org/10.1016/j.apnum.2022.02.016
- R. Watschinger, M. Merta, G. Of, and J. Zapletal, “A Parallel Fast Multipole Method for a Space-Time Boundary Element Method for the Heat Equation,” SIAM Journal on Scientific Computing, vol. 44, no. 4, pp. C320–C345, Aug. 2022, doi: 10.1137/21m1430157. [Online]. Available at: https://doi.org/10.1137%2F21m1430157
- J. Yang, Z. Yuan, and Z. Zhou, “Robust Convergence of Parareal Algorithms with Arbitrarily High-Order Fine Propagators,” SSRN Electronic Journal, 2022, doi: 10.2139/ssrn.4097528. [Online]. Available at: https://doi.org/10.2139%2Fssrn.4097528
- L. Yang and H. Li, “A hybrid algorithm based on parareal and Schwarz waveform relaxation,” Electronic Research Archive, vol. 30, no. 11, pp. 4086–4107, 2022, doi: 10.3934/era.2022207. [Online]. Available at: https://doi.org/10.3934/era.2022207
- R. Yoda, M. Bolten, K. Nakajima, and A. Fujii, “Assignment of idle processors to spatial redistributed domains on coarse levels in multigrid reduction in time,” in International Conference on High Performance Computing in Asia-Pacific Region, 2022, doi: 10.1145/3492805.3492810 [Online]. Available at: https://doi.org/10.1145/3492805.3492810
- R. Yoda, M. Bolten, K. Nakajima, and A. Fujii, “Acceleration of Optimized Coarse-Grid Operators by Spatial Redistribution for Multigrid Reduction in Time,” in Computational Science – ICCS 2022, Springer International Publishing, 2022, pp. 214–221 [Online]. Available at: https://doi.org/10.1007/978-3-031-08754-7_29
- R.-H. Zhang, Y.-L. Jiang, J. Li, and B. Song, “Analysis of the parareal algorithm for linear parametric differential equations,” International Journal of Computer Mathematics, pp. 1–0, Nov. 2022, doi: 10.1080/00207160.2022.2153225. [Online]. Available at: https://doi.org/10.1080/00207160.2022.2153225
2021
- J. Angel, S. Götschel, and D. Ruprecht, “Impact of spatial coarsening on Parareal convergence,” arXiv:2111.10228v1 [math.NA], 2021 [Online]. Available at: http://arxiv.org/abs/2111.10228v1
- P. Benedusi, M. L. Minion, and R. Krause, “An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem,” Computers & Mathematics with Applications, vol. 99, pp. 162–170, Oct. 2021, doi: 10.1016/j.camwa.2021.07.008. [Online]. Available at: https://doi.org/10.1016%2Fj.camwa.2021.07.008
- S. Blanes, “Novel parallel in time integrators for ODEs,” Applied Mathematics Letters, p. 107542, Jul. 2021, doi: 10.1016/j.aml.2021.107542. [Online]. Available at: https://doi.org/10.1016/j.aml.2021.107542
- A. L. Blumers, M. Yin, H. Nakajima, Y. Hasegawa, Z. Li, and G. E. Karniadakis, “Multiscale parareal algorithm for long-time mesoscopic simulations of microvascular blood flow in zebrafish,” Computational Mechanics, Aug. 2021, doi: 10.1007/s00466-021-02062-w. [Online]. Available at: https://doi.org/10.1007%2Fs00466-021-02062-w
- T. Buvoli and M. Minion, “IMEX Runge-Kutta Parareal for Non-diffusive Equations,” in Springer Proceedings in Mathematics &\mathsemicolon Statistics, Springer International Publishing, 2021, pp. 95–127 [Online]. Available at: https://doi.org/10.1007%2F978-3-030-75933-9_5
- M. Cai, J. Mahseredjian, I. Kocar, X. Fu, and A. Haddadi, “A parallelization-in-time approach for accelerating EMT simulations,” Electric Power Systems Research, vol. 197, p. 107346, Aug. 2021, doi: 10.1016/j.epsr.2021.107346. [Online]. Available at: https://doi.org/10.1016/j.epsr.2021.107346
- J. G. Caldas Steinstraesser, “Coupling large and small scale shallow water models with porosity in the presence of anisotropy,” PhD thesis, Université de Montpellier, 2021 [Online]. Available at: https://www.theses.fr/2021MONTS040
- J. G. Caldas Steinstraesser, V. Guinot, and A. Rousseau, “Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes,” The SMAI journal of computational mathematics, vol. 7, pp. 159–184, 2021, doi: 10.5802/smai-jcm.75. [Online]. Available at: https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.75/
- M. Caliari, L. Einkemmer, A. Moriggl, and A. Ostermann, “An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs,” Journal of Computational Physics, vol. 437, p. 110289, Jul. 2021, doi: 10.1016/j.jcp.2021.110289. [Online]. Available at: https://doi.org/10.1016%2Fj.jcp.2021.110289
- J. Chaudhry, D. Estep, and S. Tavener, “A posteriori error analysis for a space-time parallel discretization of parabolic partial differential equations,” arXiv:2111.00606v1 [math.NA], 2021 [Online]. Available at: http://arxiv.org/abs/2111.00606v1
- Y.-C. Chen and K. Nakajima, “Optimized Cascadic Multigrid Parareal Method for Explicit Time-Marching Schemes,” in 2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA), 2021, doi: 10.1109/scala54577.2021.00007 [Online]. Available at: https://doi.org/10.1109/scala54577.2021.00007
- T. Cheng, N. Lin, T. Liang, and V. Dinavahi, “Parallel-in-time-and-space electromagnetic transient simulation of multi-terminal DC grids with device-level switch modelling,” IET Generation, Transmission & Distribution, Sep. 2021, doi: 10.1049/gtd2.12285. [Online]. Available at: https://doi.org/10.1049/gtd2.12285
- F. Danieli and A. J. Wathen, “All-at-once solution of linear wave equations,” Numerical Linear Algebra with Applications, May 2021, doi: 10.1002/nla.2386. [Online]. Available at: https://doi.org/10.1002/nla.2386
- M. Donatelli, R. Krause, M. Mazza, and K. Trotti, “All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations,” vol. 58, no. 4, Oct. 2021, doi: 10.1007/s10092-021-00436-3. [Online]. Available at: https://doi.org/10.1007/s10092-021-00436-3
- A. C. Ellison and B. Fornberg, “A parallel-in-time approach for wave-type PDEs,” Numerische Mathematik, Apr. 2021, doi: 10.1007/s00211-021-01197-5. [Online]. Available at: https://doi.org/10.1007/s00211-021-01197-5
- R. D. Falgout, T. A. Manteuffel, B. O’Neill, and J. B. Schroder, “Multigrid reduction in time with Richardson extrapolation,” ETNA - Electronic Transactions on Numerical Analysis, vol. 54, pp. 210–233, 2021, doi: 10.1553/etna_vol54s210. [Online]. Available at: https://doi.org/10.1553%2Fetna_vol54s210
- L. Fang, S. Vandewalle, and J. Meyers, “A parallel-in-time multiple shooting algorithm for large-scale PDE-constrained optimal control problems,” Journal of Computational Physics, p. 110926, Dec. 2021, doi: 10.1016/j.jcp.2021.110926. [Online]. Available at: https://doi.org/10.1016/j.jcp.2021.110926
- M. J. Gander, J. Liu, S.-L. Wu, X. Yue, and T. Zhou, “ParaDiag: parallel-in-time algorithms based on the diagonalization technique,” arXiv preprint arXiv:2005.09158, 2021 [Online]. Available at: http://arxiv.org/abs/2005.09158
- S. Götschel, M. Minion, D. Ruprecht, and R. Speck, “Twelve Ways to Fool the Masses When Giving Parallel-in-Time Results,” in Springer Proceedings in Mathematics & Statistics, Springer International Publishing, 2021, pp. 81–94 [Online]. Available at: https://doi.org/10.1007/978-3-030-75933-9_4
- L. Grigori, S. A. Hirstoaga, V.-T. Nguyen, and J. Salomon, “Reduced model-based parareal simulations of oscillatory singularly perturbed ordinary differential equations,” Journal of Computational Physics, vol. 436, p. 110282, Jul. 2021, doi: 10.1016/j.jcp.2021.110282. [Online]. Available at: https://doi.org/10.1016/j.jcp.2021.110282
- R. Kumari, S. Prasad, A. Kumari, and A. Kumar, “Parallel in Time Simulation of Automatic Generation Control System for Near Real-Time Transient Stability Analysis,” in 2021 International Conference on Control, Automation, Power and Signal Processing (CAPS), 2021, doi: 10.1109/caps52117.2021.9730716 [Online]. Available at: https://doi.org/10.1109/caps52117.2021.9730716
- S. Lakshmiranganatha and S. S. Muknahallipatna, “Performance Analysis of Accelerator Architectures and Programming Models for Parareal Algorithm Solutions of Ordinary Differential Equations,” Journal of Computer and Communications, vol. 09, no. 02, pp. 29–56, 2021, doi: 10.4236/jcc.2021.92003. [Online]. Available at: https://doi.org/10.4236/jcc.2021.92003
- U. Langer and M. Zank, “Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces,” SIAM Journal on Scientific Computing, vol. 43, no. 4, pp. A2714–A2736, Jan. 2021, doi: 10.1137/20m1358128. [Online]. Available at: https://doi.org/10.1137%2F20m1358128
- S. Li, X. Shao, and R. Chen, “Multilevel space-time multiplicative Schwarz preconditioner for parabolic equations,” Numerical Linear Algebra with Applications, May 2021, doi: 10.1002/nla.2390. [Online]. Available at: https://doi.org/10.1002/nla.2390
- X. Li and Y. Su, “A parallel in time/spectral collocation combined with finite difference method for the time fractional differential equations,” Journal of Algorithms & Computational Technology, vol. 15, p. 174830262110084, Jan. 2021, doi: 10.1177/17483026211008409. [Online]. Available at: https://doi.org/10.1177/17483026211008409
- J. Li, P. Liu, and V. Dinavahi, “Space-Time-Parallel 3-D Finite Element Transformer Model with Adaptive TLM and Parareal Techniques for Electromagnetic Transient Analysis,” IEEE Open Journal of Industry Applications, pp. 1–1, 2021, doi: 10.1109/ojia.2021.3091557. [Online]. Available at: https://doi.org/10.1109/ojia.2021.3091557
- J. Li, Y.-L. Jiang, and Z. Miao, “Analysis of the parareal approach based on discontinuous Galerkin method for time-dependent Stokes equations,” Numerical Methods for Partial Differential Equations, Jul. 2021, doi: 10.1002/num.22782. [Online]. Available at: https://doi.org/10.1002/num.22782
- G. Li and J. Hu, “Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients and Rough Initial Data,” Journal of Computational Physics, p. 110572, Jul. 2021, doi: 10.1016/j.jcp.2021.110572. [Online]. Available at: https://doi.org/10.1016/j.jcp.2021.110572
- J. Li and Y.-L. Jiang, “The study of parareal algorithm for the linear switched systems,” p. 107763, Oct. 2021, doi: 10.1016/j.aml.2021.107763. [Online]. Available at: https://doi.org/10.1016/j.aml.2021.107763
- X.-lei Lin, M. K. Ng, and Y. Zhi, “A parallel-in-time two-sided preconditioning for all-at-once system from a non-local evolutionary equation with weakly singular kernel,” Journal of Computational Physics, vol. 434, p. 110221, Jun. 2021, doi: 10.1016/j.jcp.2021.110221. [Online]. Available at: https://doi.org/10.1016%2Fj.jcp.2021.110221
- X.-L. Lin and Z. Zhang, “A Parallel-in-Time Preconditioner for the Schur Complement of Parabolic Optimal Control Problems,” arXiv:2109.12524v2 [math.NA], 2021 [Online]. Available at: http://arxiv.org/abs/2109.12524v2
- J. Liu and S.-L. Wu, “Parallel-in-time preconditioners for the Sinc-Nyström method,” arXiv:2108.01700v1 [math.NA], 2021 [Online]. Available at: http://arxiv.org/abs/2108.01700v1
- C. Lyu, N. Lin, and V. Dinavahi, “Device-Level Parallel-in-time Simulation of MMC-Based Energy System for Electric Vehicles,” IEEE Transactions on Vehicular Technology, pp. 1–1, 2021, doi: 10.1109/tvt.2021.3081534. [Online]. Available at: https://doi.org/10.1109/tvt.2021.3081534
- N. Margenberg and T. Richter, “Parallel time-stepping for fluid–structure interactions,” Mathematical Modelling of Natural Phenomena, vol. 16, p. 20, 2021, doi: 10.1051/mmnp/2021005. [Online]. Available at: https://doi.org/10.1051/mmnp/2021005
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
2020
- 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
- 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
- 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
- T. Buvoli, “Exponential Polynomial Time Integrators,” arXiv:2011.00670v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2011.00670v1
- T. Buvoli and M. L. Minion, “IMEX Parareal Integrators,” arXiv:2011.01604v1 [math.NA], 2020 [Online]. Available at: http://arxiv.org/abs/2011.01604v1
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
2019
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.