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A multi-level spectral deferred correction method

Publikationstyp
Journal Article
Date Issued
2015-09-30
Sprache
English
Author(s)
Speck, Robert  
Ruprecht, Daniel  orcid-logo
Emmett, Matthew  
Minion, Michael  
Bolten, Matthias  
Krause, Rolf  
TORE-URI
http://hdl.handle.net/11420/10527
Journal
BIT  
Volume
55
Issue
3
Start Page
843
End Page
867
Citation
BIT Numerical Mathematics 55 (3): 843-867 (2015-09-30)
Publisher DOI
10.1007/s10543-014-0517-x
Scopus ID
2-s2.0-84942768082
Peer Reviewed
true
The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser levels are examined: reducing the degrees of freedom, reducing the order of the spatial discretization, and reducing the accuracy when solving linear systems arising in implicit temporal integration. Several numerical examples demonstrate the effect of multi-level coarsening on the convergence and cost of SDC integration. In particular, MLSDC can provide significant savings in compute time compared to SDC for a three-dimensional problem.
Subjects
FAS correction
Multi-level spectral deferred corrections
PFASST
Spectral deferred corrections
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