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. 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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
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- 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
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- 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
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- 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
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- 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
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- 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
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2021
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2020
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2019
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- 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.
- 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
- 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
- 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
- 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
- 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
2018
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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