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Spectral deferred correction methods for second-order problems
Citation Link: https://doi.org/10.15480/882.15091
Publikationstyp
Doctoral Thesis
Date Issued
2025
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2025-04-16
Institute
TORE-DOI
Citation
Technische Universität Hamburg: (2025)
Peer Reviewed
false
In this thesis, we present a spectral deferred correction (SDC) method for second-order problems. We provide a complete theoretical analysis of the method, demonstrating its convergence and stability for general second-order problems, and we validate our theoretical results with numerical examples.
We also introduce a multi-level SDC (MLSDC) method for second-order problems and compare its residual and convergence properties with those of the standard SDC method.
Finally, we extend the SDC framework to multiscale problems using the micro–macro MLSDC (M3LSDC) method, which couples fine and coarse models with tailored FAS corrections. In numerical experiments, we show that M3LSDC achieves a smaller residual than both SDC and MLSDC with the same number of iterations.
We also introduce a multi-level SDC (MLSDC) method for second-order problems and compare its residual and convergence properties with those of the standard SDC method.
Finally, we extend the SDC framework to multiscale problems using the micro–macro MLSDC (M3LSDC) method, which couples fine and coarse models with tailored FAS corrections. In numerical experiments, we show that M3LSDC achieves a smaller residual than both SDC and MLSDC with the same number of iterations.
Subjects
Spectral deferred corrections (SDC)
Picard Iteration
velocity-Verlet
multi-level SDC (MLSDC)
micro-macro MLSDC (M3LSDC)
DDC Class
510: Mathematics
515: Analysis
518: Numerical Analysis
004: Computer Sciences
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