Journal Article

FZJ-2018-03898

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Parallelizing spectral deferred corrections across the method

Speck, R. (Corresponding author)FZJ*

2018
Springer Berlin

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Please use a persistent id in citations: http://hdl.handle.net/2128/19505  doi:10.1007/s00791-018-0298-x

Abstract: In this paper we present two strategies to enable “parallelization across the method” for spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an iterative fashion, SDC can be seen as preconditioned Picard iteration for the collocation problem. Typically, a serial Gauß–Seidel-like preconditioner is used, computing updates for each collocation node one by one. The goal of this paper is to show how this process can be parallelized, so that all collocation nodes are updated simultaneously. The first strategy aims at finding parallel preconditioners for the Picard iteration and we test three choices using four different test problems. For the second strategy we diagonalize the quadrature matrix of the collocation problem directly. In order to integrate non-linear problems we employ simplified and inexact Newton methods. Here, we estimate the speed of convergence depending on the time-step size and verify our results using a non-linear diffusion problem.

Note: Online first

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)
2. DFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162) (450829162)

Appears in the scientific report 2018

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Database coverage:
; ; Ebsco Academic Search ; Emerging Sources Citation Index ; Nationallizenz ; SCOPUS ; Thomson Reuters Master Journal List ; Web of Science Core Collection

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