Publisher DOI: 10.1007/s10543-014-0517-x
Title: A multi-level spectral deferred correction method
Language: English
Authors: Speck, Robert 
Ruprecht, Daniel  
Emmett, Matthew 
Minion, Michael 
Bolten, Matthias 
Krause, Rolf 
Keywords: FAS correction;Multi-level spectral deferred corrections;PFASST;Spectral deferred corrections
Issue Date: 30-Sep-2015
Source: BIT Numerical Mathematics 55 (3): 843-867 (2015-09-30)
Journal: BIT Numerical Mathematics 
Abstract (english): 
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.
ISSN: 0006-3835
Document Type: Article
Peer Reviewed: Yes
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