Adaptive time step selection for Spectral Deferred Correction
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866915483454799872 |
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| author | Saupe, Thomas Götschel, Sebastian Lunet, Thibaut Ruprecht, Daniel Speck, Robert |
| author_facet | Saupe, Thomas Götschel, Sebastian Lunet, Thibaut Ruprecht, Daniel Speck, Robert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive time step selection for Spectral Deferred Correction Saupe, Thomas Götschel, Sebastian Lunet, Thibaut Ruprecht, Daniel Speck, Robert Numerical Analysis Distributed, Parallel, and Cluster Computing 65Y05 G.1.0 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. |
| title | Adaptive time step selection for Spectral Deferred Correction |
| topic | Numerical Analysis Distributed, Parallel, and Cluster Computing 65Y05 G.1.0 |
| url | https://arxiv.org/abs/2403.13454 |