TY  - JOUR
AU  - Speck, Robert
TI  - Parallelizing spectral deferred corrections across the method
JO  - Computing and visualization in science
VL  - 19
IS  - 3-4
SN  - 1433-0369
CY  - Berlin
PB  - Springer
M1  - FZJ-2018-03898
SP  - 75-83
PY  - 2018
N1  - Online first
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000439461000002
DO  - DOI:10.1007/s00791-018-0298-x
UR  - https://juser.fz-juelich.de/record/849786
ER  -