TY - JOUR
T1 - An enhanced parareal algorithm based on the deferred correction methods for a stiff system
AU - Bu, Sunyoung
AU - Lee, June Yub
N1 - Funding Information:
This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009-0093827 ).
PY - 2014
Y1 - 2014
N2 - In this study, we consider a variant of the hybrid parareal algorithm based on deferred correction techniques in order to increase the convergence order even for the stiff system. A hybrid parareal scheme introduced by Minion (2011) [20] improves the efficiency of the original parareal by utilizing a Spectral Deferred Correction (SDC) strategy for a fine propagator within the parareal iterations. In this paper, we use Krylov Deferred Correction (KDC) for a fine propagator to solve the stiff system and Differential Algebraic Equations (DAEs) stably. Also we employ a deferred correction technique based on the backward Euler method for a coarse propagator in order to make the global order of accuracy reasonably high while limiting the cost of sequential steps as small as possible. Numerical experiments on the efficiency of our method are promising.
AB - In this study, we consider a variant of the hybrid parareal algorithm based on deferred correction techniques in order to increase the convergence order even for the stiff system. A hybrid parareal scheme introduced by Minion (2011) [20] improves the efficiency of the original parareal by utilizing a Spectral Deferred Correction (SDC) strategy for a fine propagator within the parareal iterations. In this paper, we use Krylov Deferred Correction (KDC) for a fine propagator to solve the stiff system and Differential Algebraic Equations (DAEs) stably. Also we employ a deferred correction technique based on the backward Euler method for a coarse propagator in order to make the global order of accuracy reasonably high while limiting the cost of sequential steps as small as possible. Numerical experiments on the efficiency of our method are promising.
KW - Differential algebraic equation
KW - Hybrid parareal algorithm
KW - Krylov deferred correction
KW - Spectral deferred correction
KW - Stiff system
UR - http://www.scopus.com/inward/record.url?scp=84879078640&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2013.05.001
DO - 10.1016/j.cam.2013.05.001
M3 - Article
AN - SCOPUS:84879078640
SN - 0377-0427
VL - 255
SP - 297
EP - 305
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -