caa a22 4500 605496951 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10543-014-0517-x doi (NATIONALLICENCE)springer-10.1007/s10543-014-0517-x A multi-level spectral deferred correction method [Elektronische Daten] [Robert Speck, Daniel Ruprecht, Matthew Emmett, Michael Minion, Matthias Bolten, Rolf Krause] 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. Springer Science+Business Media Dordrecht, 2014 Spectral deferred corrections nationallicence Multi-level spectral deferred corrections nationallicence FAS correction nationallicence PFASST nationallicence Speck Robert Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany aut Ruprecht Daniel Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland aut Emmett Matthew Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, USA aut Minion Michael Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA aut Bolten Matthias Department of Mathematics and Science, University of Wuppertal, 42097, Wuppertal, Germany aut Krause Rolf Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland aut BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 843-867 0006-3835 55:3<843 2015 55 10543 https://doi.org/10.1007/s10543-014-0517-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0517-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Speck Robert Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany aut NATIONALLICENCE 700 1- Ruprecht Daniel Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland aut NATIONALLICENCE 700 1- Emmett Matthew Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, USA aut NATIONALLICENCE 700 1- Minion Michael Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA aut NATIONALLICENCE 700 1- Bolten Matthias Department of Mathematics and Science, University of Wuppertal, 42097, Wuppertal, Germany aut NATIONALLICENCE 700 1- Krause Rolf Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 843-867 0006-3835 55:3<843 2015 55 10543