diff --git a/_bibliography/pint.bib b/_bibliography/pint.bib index a3fc9708..1a489f81 100644 --- a/_bibliography/pint.bib +++ b/_bibliography/pint.bib @@ -6930,6 +6930,28 @@ @unpublished{AppelEtAl2024 year = {2024}, } +@article{BaumannEtAl2024, + abstract = {Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.}, + author = {Baumann, Thomas and G{\"o}tschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Speck, Robert}, + doi = {10.1007/s11075-024-01964-z}, + issn = {1572-9265}, + journal = {Numerical Algorithms}, + month = {October}, + title = {Adaptive time step selection for spectral deferred correction}, + url = {https://doi.org/10.1007/s11075-024-01964-z}, + year = {2024}, +} + +@misc{BaumannEtAl2024b, + archiveprefix = {arXiv}, + author = {Baumann, Thomas and G{\"o}tschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Speck, Robert}, + eprint = {2412.00529}, + primaryclass = {cs.DC}, + title = {Resilience Against Soft Faults through Adaptivity in Spectral Deferred Correction}, + url = {https://arxiv.org/abs/2412.00529}, + year = {2024}, +} + @unpublished{BetckeEtAl2024, abstract = {This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the convergence properties of the proposed algorithm and show its effectiveness for several examples, including Lorenz and Burgers' equations. In our numerical simulations, we further specialize the underpinning neural architecture to Random Projection Neural Networks (RPNNs), a 2-layer neural network where the first layer weights are drawn at random rather than optimized. This restriction substantially increases the efficiency of fitting RPNN's weights in comparison to a standard feedforward network without negatively impacting the accuracy, as demonstrated in the SIR system example.}, author = {Marta M. Betcke and Lisa Maria Kreusser and Davide Murari}, @@ -6939,6 +6961,15 @@ @unpublished{BetckeEtAl2024 year = {2024}, } +@unpublished{BonteEtAl2024, + abstract = {Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The state-of-the-art parallel preconditioner for linear problems leads to a set of independent smaller systems that are currently hard to solve. We generalize the preconditioner to the nonlinear case and propose a new, fast inversion method for these smaller systems, avoiding disadvantages of the current options with adjusted boundary conditions in the subproblems.}, + author = {Corentin Bonte and Arne Bouillon and Giovanni Samaey and Karl Meerbergen}, + howpublished = {arXiv:2412.02425v1 [math.NA]}, + title = {Efficient parallel inversion of ParaOpt preconditioners}, + url = {http://arxiv.org/abs/2412.02425v1}, + year = {2024}, +} + @unpublished{BossuytEtAl2024, abstract = {In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled to the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations (ODEs). Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs.}, author = {Ignace Bossuyt and Stefan Vandewalle and Giovanni Samaey}, @@ -7478,28 +7509,6 @@ @article{ZhenEtAl2024b year = {2024}, } -@article{BaumannEtAl2024, - title = {Adaptive time step selection for spectral deferred correction}, - issn = {1572-9265}, - url = {https://doi.org/10.1007/s11075-024-01964-z}, - doi = {10.1007/s11075-024-01964-z}, - abstract = {Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.}, - journal = {Numerical Algorithms}, - author = {Baumann, Thomas and G{\"o}tschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Speck, Robert}, - month = oct, - year = {2024}, -} - -@misc{BaumannEtAl2024b, - title={Resilience Against Soft Faults through Adaptivity in Spectral Deferred Correction}, - author = {Baumann, Thomas and G{\"o}tschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Speck, Robert}, - year={2024}, - eprint={2412.00529}, - archivePrefix={arXiv}, - primaryClass={cs.DC}, - url={https://arxiv.org/abs/2412.00529}, -} - @article{PamelaEtAl2025, author = {Pamela, S.J.P. and Carey, N. and Brandstetter, J. and Akers, R. and Zanisi, L. and Buchanan, J. and Gopakumar, V. and Hoelzl, M. and Huijsmans, G. and Pentland, K. and James, T. and Antonucci, G.}, doi = {10.1016/j.cpc.2024.109391},