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<span id="BaumannEtAl2024">T. Baumann, S. Götschel, T. Lunet, D. Ruprecht, and R. Speck, “Adaptive time step selection for spectral deferred correction,” <i>Numerical Algorithms</i>, Oct. 2024, doi: 10.1007/s11075-024-01964-z. [Online]. Available at: <a href="https://doi.org/10.1007/s11075-024-01964-z" target="_blank">https://doi.org/10.1007/s11075-024-01964-z</a></span>
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BibTeX entry <code>BaumannEtAl2024</code>
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<pre class="abstract">@article{BaumannEtAl2024,
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title = {Adaptive time step selection for spectral deferred correction},
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issn = {1572-9265},
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url = {https://doi.org/10.1007/s11075-024-01964-z},
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doi = {10.1007/s11075-024-01964-z},
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journal = {Numerical Algorithms},
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author = {Baumann, Thomas and G{\"o}tschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Speck, Robert},
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month = oct,
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year = {2024}
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}
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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.
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<span id="BaumannEtAl2024b">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: <a href="https://arxiv.org/abs/2412.00529" target="_blank">https://arxiv.org/abs/2412.00529</a></span>
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<pre class="abstract">@misc{BaumannEtAl2024b,
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title = {Resilience Against Soft Faults through Adaptivity in Spectral Deferred Correction},
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author = {Baumann, Thomas and G{\"o}tschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Speck, Robert},
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year = {2024},
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eprint = {2412.00529},
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url = {https://arxiv.org/abs/2412.00529}
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