Theoretically optimal inexact spectral deferred correction methods

Weiser, Martin; Ghosh, Sunayana

doi:10.2140/camcos.2018.13.53

Cited by 7 publications

(7 citation statements)

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“…We note that of course many further ideas could be exploited in this context, ranging from parallel SDC, MLSDC, and PFASST to more advanced spatial solvers [Gräser et al 2009] or adaptive selection of tolerances for inexact SDC [Weiser and Ghosh 2018]. However, for this paper and for pySDC the more relevant aspects are to show that implementing, testing and running multiple variants of SDC (and MLSDC and PFASST for that matter) is straightforward.…”

Section: Sdc For the Allen-cahn Equationmentioning

confidence: 99%

“…This solver can be used as a blackbox, treating (3) as implicit Euler formula with modified right-hand side. However, recent results indicate that the computational efficiency of SDC can be enhanced significantly, if the spatial solver is taken into account more carefully, see [Speck et al 2016a;Weiser and Ghosh 2018].…”

Section: Spectral Deferred Correctionsmentioning

confidence: 99%

“…Moreover, each variant is tested with (a) full and (b) reduced accuracy in the linear and/or nonlinear implicit solvers. The latter approach is called inexact SDC and has been investigated in [Speck et al 2016b;Weiser and Ghosh 2018]. We use Newton's method for the nonlinear systems and CG for the linear systems.…”

Section: Sdc For the Allen-cahn Equationmentioning

confidence: 99%

“…• convergence can be accelerated by GMRES [Huang et al 2006] or algebraic preconditioners [Weiser 2014], • high-order implicit-explicit or even multi-implicit splitting is straightforward [Bourlioux et al 2003;Minion 2003;Ruprecht and Speck 2016], • multirate integration allows effective treatment of different time-scales [Bouzarth and Minion 2010;Naumann et al 2018] • inexact spatial solvers enhance time-to-solution [Speck et al 2016a;Weiser and Ghosh 2018].…”

Section: Introductionmentioning

confidence: 99%

“…• multirate integration allows effective treatment of different time-scales [Bouzarth and Minion 2010;Naumann et al 2018] • inexact spatial solvers enhance time-to-solution [Speck et al 2016a;Weiser and Ghosh 2018].…”

Section: Introductionmentioning

confidence: 99%

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Inexact Spectral Deferred Corrections

Speck

Ruprecht

Minion

et al. 2016

Lecture Notes in Computational Science and Engineering

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In this paper we present the Python framework pySDC for solving collocation problems with spectral deferred correction methods (SDC) and their time-parallel variant PFASST, the parallel full approximation scheme in space and time. pySDC features many implementations of SDC and PFASST, from simple implicit time-stepping to high-order implicit-explicit or multi-implicit splitting and multi-level spectral deferred corrections. It comes with many different, pre-implemented examples and has seven tutorials to help new users with their first steps. Time-parallelism is implemented either in an emulated way for debugging and prototyping as well as using MPI for benchmarking. The code is fully documented and tested using continuous integration, including most results of previous publications. Here, we describe the structure of the code by taking two different perspectives: the user's and the developer's perspective. While the first sheds light on the front-end, the examples and the tutorials, the second is used to describe the underlying implementation and the data structures. We show three different examples to highlight various aspects of the implementation, the capabilities and the usage of pySDC. Also, couplings to the FEniCS framework and PETSc, the latter including spatial parallelism with MPI, are described.

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Section: Sdc For the Allen-cahn Equationmentioning

confidence: 99%

Section: Spectral Deferred Correctionsmentioning

confidence: 99%

Section: Sdc For the Allen-cahn Equationmentioning

confidence: 99%