Inexact Spectral Deferred Corrections
Implicit integration methods based on collocation are attractive for a number of reasons, e.g. their ideal (for Gauss-Legendre nodes) or near ideal (Gauss-Radau or Gauss-Lobatto nodes) order and stability properties. However, straightforward application of a collocation formula with M nodes to an initial value problem with dimension d requires the solution of one large Md × Md system of nonlinear equations.
KeywordsStiff Problem Multigrid Solver Euler Step Viscous Burger Spectral Deferred Correction
This work was supported by the Swiss National Science Foundation (SNSF) under the lead agency agreement through the project “ExaSolvers” within the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) of the Deutsche Forschungsgemeinschaft (DFG). Matthew Emmett and Michael Minion were supported by the Applied Mathematics Program of the DOE Office of Advanced Scientific Computing Research under the U.S. Department of Energy under contract DE-AC02-05CH11231. Michael Minion was also supported by the U.S. National Science Foundation grant DMS-1217080. The authors acknowledge support from Matthias Bolten, who provided the employed multigrid solver.
- 1.R. Alexander, Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s. SIAM J. Numer. Anal. 14(6), 1006–1021 (1977)Google Scholar
- 6.M. Emmett, M.L. Minion, Efficient Implementation of a Multi-Level Parallel in Time Algorithm. Domain Decomposition Methods in Science and Engineering XXI, Lecture Notes in Computational Science and Engineering, vol. 98 (Springer, Switzerland, 2014), pp. 359–366Google Scholar
- 12.C. Oosterlee, T. Washio, On the use of multigrid as a preconditioner, in Proceedings of 9th International Conference on Domain Decomposition Methods, pp. 441–448 (1996)Google Scholar
- 13.D. Ruprecht, R. Speck, M. Emmett, M. Bolten, R. Krause, Poster: Extreme-scale space-time parallelism, in Proceedings of the 2013 Supercomputing Companion, SC ‘13 Companion, 2013 Google Scholar
- 14.R. Speck, D. Ruprecht, M. Emmett, M. Bolten, R. Krause. A space-time parallel solver for the three-dimensional heat equation. in Parallel Computing: Accelerating Computational Science and Engineering (CSE), Advances in Parallel Computing, vol. 25 (IOS Press, 2014), pp. 263–272. doi:10.3233/978-1-61499-381-0-263Google Scholar