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Peer-Reviewed Publications

  1. H. De Sterck, R. D. Falgout, O. A. Krzysik, and J. B. Schroder, Parallel-in-time solution of scalar nonlinear conservation laws, Arxiv preprint, (submitted) (2024).

  2. E. C. Cyr, J. Hahne, N. S. Moore, J. B. Schroder, B. S. Southworth, D. A. Vargas, TorchBraid: High-Performance Layer-Parallel Training of Deep Neural Networks with MPI and GPU Acceleration. (submitted) 2023.

  3. H. De Sterck, R. D. Falgout, O. A. Krzysik, and J. B. Schroder, Efficient multigrid reduction-in-time for method-of-lines discretizations of linear advection, Journal of Scientific Computing, pp. 1-31. 96 (2023).

  4. H. De Sterck, R. D. Falgout, and O. A. Krzysik, Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators, SIAM Journal on Scientific Computing, A1890-A1916 45 (2023).

  5. S. M. Guzik, J. Christopher, S. Walters, X. Gao, J. B. Schroder, and R. D. Falgout, On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulent simulations, Computers and Fluids, pp.1-16 261 (2023).

  6. M Sugiyama, J. B. Schroder, B. S. Southworth, and S. Friedhoff, Weighted Relaxation for Multigrid Reduction in Time, Numer. Linear Algebra Appl., e2465 30 (2023).

  7. 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, A2019-A2042 45 (2023).

  8. H. De Sterck, S. Friedhoff, O. A. Krzysik, and S. P. MacLachlan, Multigrid reduction-in-time convergence for advection problems: A Fourier analysis perspective, Arxiv preprint, (submitted) (2022).

  9. J. Hahne, B. Southworth, and S. Friedhoff, Asynchronous Truncated Multigrid-reduction-in-time, AT-MGRIT, SIAM Journal on Scientific Computing, S281-S306, 2022.

  10. A. Hessenthaler, R. D. Falgout, J. B. Schroder, Adelaide de Vecchi, D. Nordsletten, and O. Rohrle, Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time, Computer Methods in Applied Mechanics and Engineering, pp. 1-27. 389 (2022).

  11. G. E. Moon, E. C. Cyr, Parallel Training of GRU Networks with a Multi-Grid Solver for Long Sequences, ICLR (2022).

  12. D. A. Vargas, R. D. Falgout, S. Guenther, and J. B. Schroder, Toward Parallel in Time for Chaotic Dynamical Systems, Arxiv preprint, Copper Mountain Conference Student Paper Winner, (2022)

  13. E. C. Cyr, S. Guenther, and J. B. Schroder, Multilevel Initialization for Layer-Parallel Deep Neural Network Training, International Journal of Computing and Visualization in Science and Engineering, pp. 1-9. 1 (2021).

  14. F. Danieli and S. MacLachlan, Multigrid Reduction in Time for non-linear hyperbolic equations, Arxiv preprint, (submitted) (2021).

  15. H. De Sterck, R. D. Falgout, S. Friedhoff, O. A. Krzysik, and S. P. MacLachlan, Optimizing Multigrid Reduction-in-Time and Parareal Coarse-grid Operators for Linear Advection, Numer. Linear Algebra Appl., e2367 28 (2021).

  16. R.D. Falgout, T. A. Manteuffel, B. O'Neill, and J.B. Schroder, Multigrid Reduction in Time with Richardson Extrapolation. ETNA, pp. 210-233. 54 (2021).

  17. S. Friedhoff, and B. S. Southworth, On "Optimal" h-Independent Convergence of Parareal and MGRIT using Runge-Kutta Time Integration, Numer. Linear Algebra Appl., e2301. 28 (2021).

  18. J. Hahne, S. Friedhoff, M. Bolten, PyMGRIT: A Python Package for the Parallel-in-Time Method MGRIT, ACM TOMS, 47 (2021).

  19. B. S. Southworth, W. Mitchell, A. Hessenthaler, F. Danieli, Tight two-level convergence of Linear Parareal and MGRIT: Extensions and implications in practice, Springer Proceedings in Mathematics and Statistics, 356 (2021).

  20. M. Bolten, S. Friedhoff, J. Hahne, S. Schöps, Parallel-in-Time Simulation of an Electrical Machine using MGRIT, Computing and Visualization in Science, pp. 1-14. 23 (2020).

  21. J. Christopher, R. D. Falgout, J. B. Schroder, X. Gao, S. Guzik. A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics. Comput. Visual Sci. 23, 13 (2020).

  22. J. Christopher, X. Gao, S. M. Guzik, R. D. Falgout, and J. B. Schroder, Fully Parallelized Space-Time Adaptive Meshes for the Compressible Navier-Stokes Equations Using Multigrid Reduction in Time, Comput. Vis. Science, Springer, pp. 1-19. 23 (2020).

  23. J. Christopher, X. Gao, S. Guzik, R. D. Falgout, and J. B. Schroder, Parallel In Time for a Fully Space-Time Adaptive Mesh Refinement Algorithm. AIAA SciTech Forum, pp. 1-10. (Jan, 2020).

  24. H. De Sterck, S. Friedhoff, A. J. Howse, and S. P. MacLachlan. Convergence analysis for parallel‐in‐time solution of hyperbolic systems. Numer. Linear Algebra Appl., e2271 27 (2020).

  25. S. Günther, L. Ruthotto, J. B. Schroder, E. C. Cyr, and N. R. Gauger, Layer-Parallel Training of Deep Residual Neural Network, SIAM J. Math Data Science. pp. 1-23. 2 (2020).

  26. A. Hessenthaler, B. S. Southworth, D. Nordsletten, O. Rohrle, R. D. Falgout, and J. B. Schroder, Multilevel convergence analysis of multigrid-reduction-in-time, SIAM J. Sci. Comput, pp. A771-A796. 42 (2020).

  27. O. A. Krzysik, H. De Sterck, S. P. MacLachlan, and S. Friedhoff, On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection, Arxiv preprint, (submitted) (2019).

  28. S. Friedhoff, J. Hahne, S. Schops, Multigrid-reduction-in-time for Eddy Current problems, PAMM, pp. 1-2, 19 (2019).

  29. S. Guenther, R. D. Falgout, P. Top, C. S. Woodward, J. B. Schroder, Parallel-in-Time Solution of Power Systems with Unscheduled Events, 2019 Power and Energy Society General Meeting (PESGM), IEEE, pp. 1-5. (2019).

  30. B. S. Southworth, Necessary conditions and tight two-level convergence bounds for parareal and multigrid reduction in time, SIAM J. Matrix Anal., pp. 564-608. 40 (2019).

  31. R. D. Falgout, M. Lecouvez, and C. S. Woodward, A Parallel-in-Time Algorithm for Variable Step Multistep Methods, Journal of Computational Science, 37 (2019), pp. 101-029. LLNL-JRNL-739759

  32. H. De Sterck, R. D. Falgout, A. J. M Howse, S. P. MacLachlan, and J. B. Schroder, Parallel-in-Time Multigrid with Adaptive Spatial Coarsening for the Linear Advection and Inviscid Burgers Equations, SIAM J. Sci. Comput, 41 (2019), pp. A538-A565. Supplementary Materials. LLNL-JRNL-737050.

  33. S. Gunther, N. R. Gauger, and J. B. Schroder, A Non-Intrusive Parallel-in-Time Approach for Simultaneous Optimization with Unsteady PDEs, Optimization Methods and Software, pp.1-16, (2018). LLNL-JRNL-744565.

  34. J. B. Schroder, M. Lecouvez, R. D. Falgout, C. S. Woodward, P. Top, Parallel-in-Time Solution of Power Systems with Scheduled Events, 2018 Power and Energy Society General Meeting (PESGM), IEEE, (2018). LLNL-CONF-740658.

  35. S. Gunther, N. R. Gauger, and J. B. Schroder, A Non-Intrusive Parallel-in-Time Adjoint Solver with the XBraid Library, Comput. Vis. Science, Springer, (2018). LLNL-JRNL-730159.

  36. A. Hessenthaler, D. Nordsletten, O. Roehrle, J. B. Schroder, R. D. Falgout, Convergence of the Multigrid-Reduction-in-Time Algorithm for the Linear Elasticity Equations, Numer. Linear Algebra Appl., pp. 1-18. 25 (2017). LLNL-JRNL-731168.

  37. A. J. M. Howse (in collaboration with H. De Sterck, R. D. Falgout, S. P. Machlachlan, and J. B. Schroder), Multigrid Reduction in Time with Adaptive Spatial Coarsening for the Linear Advection Equation, Student Paper Winner, 18th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March, 2017. LLNL-PROC-716758

  38. R. D. Falgout, T. A. Manteuffel, B. O’Neill, and J. B. Schroder, Multigrid reduction in time for nonlinear parabolic problems: A Case Study, SIAM J. Sci. Comput., 39 (2017), pp 298-322. LLNL-JRNL-692258.

  39. V. Dobrev, Tz. Kolev, N. A. Petersson, and J. B. Schroder, Two-level convergence theory for Multigrid Reduction in Time (MGRIT), SIAM J. Sci. Comput., 39 (2017), pp. 501-527. LLNL-JRNL-692418.

  40. R.D. Falgout, S. Friedhoff, Tz.V. Kolev, S.P. MacLachlan, J.B. Schroder and S. Vandewalle, Multigrid Methods with Space-Time Concurrency, Comput. Vis. Science, Springer, (2017). LLNL-JRNL-678572.

  41. H. Gahvari, V. A. Dobrev, R. D. Falgout, Tz. V. Kolev, J. B. Schroder, M. Schulz and U. M. Yang, A Performance Model for Allocating the Parallelism in a Multigrid-in-Time Solver, The 7th International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS16), Supercomputing 16. LLNL-CONF-701995.

  42. M. Lecouvez, R. D. Falgout, C. S. Woodward, and P. Top, A parallel multigrid reduction in time method for power systems, in Power and Energy Society General Meeting (PESGM), 2016, IEEE, 2016, pp. 1–5. LNL-CONF-679148

  43. R. D. Falgout, S. Friedhoff, Tz. V. Kolev, S. P. MacLachlan, and J. B. Schroder, Parallel Time Integration with Multigrid, SIAM J. Sci. Comput., 36 (2014), pp.C635-C661. LLNL-JRNL-645325.

  44. S. Friedhoff, R. Falgout, T. Kolev, S. MacLachlan, and J. Schroder, A Multigrid-in-Time Algorithm for Solving Evolution Equations in Parallel, Student paper winner, Sixteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March, 2013. LLNL-CONF-606952.

Technical Reports

  1. R. D. Falgout, J. B. Schroder, Parallel Time Integration – An Approaching Paradigm Shift for Scientific Computing, 2023, LLNL Technical Report, LLNL-TR-851068.

  2. N. Abel, J. Chaudhry, R. D. Falgout, J. B. Schroder, Multigrid-Reduction-in-Time for the Rotating Shallow Water Equations, 2020, LLNL Technical Report, LLNL-TR-813511.

  3. J.B Schroder, On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT), 2018, Technical Report, LLNL-TR-750825.

  4. J. B. Schroder, Parallelizing Over Artificial Neural Network Training Runs with Multigrid, arXiv preprint arXiv:1708.02276, (2017). LLNL-JRNL-736173.

  5. R.D. Falgout, T.A. Manteuffel, J.B. Schroder, B. Southworth, Parallel-in-time for moving meshes, Technical Report, 2016, LLNL-TR-681918.

  6. R. D. Falgout, A. Katz, Tz. V. Kolev, J. B. Schroder, A. Wissink, U. M. Yang, Parallel Time Integration with Multigrid Reduction for a Compressible Fluid Dynamics Application, Technical Report, 2014, LLNL-JRNL-663416.

Tutorials

  1. J. Schroder and R. Falgout, XBraid Tutorial, 18th Copper Mountain Conference on Multigrid Methods, March, 2017, Copper Mountain, Colorado.

  2. J. Schroder and R. Falgout, XBraid Tutorial, 6th Conference on Parallel-in-Time Integration, October, 2017, Ascona, Switzerland.

  3. J. Schroder and R. Falgout, XBraid Tutorial, CBMS Parallel-in-Time Summer School, August, 2022, Houghton, Michigan.

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