Speck, R, Ruprecht, D, Emmett, M et al. (3 more authors) (2015) A multi-level spectral deferred correction method. BIT Numerical Mathematics, 55 (3). 843 - 867. ISSN 0006-3835
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014, Springer Science+Business Media Dordrecht. This is an author produced version of a paper published in BIT Numerical Mathematics. The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-014-0517-x |
Keywords: | Spectral deferred corrections; Multi-level spectral deferred corrections; FAS correction; PFASST; 65M55; 65M70; 65Y05 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Oct 2015 10:16 |
Last Modified: | 16 Jan 2018 20:06 |
Published Version: | http://dx.doi.org/10.1007/s10543-014-0517-x |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10543-014-0517-x |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90443 |