TY - GEN
T1 - A direct solver for the heat equation with domain decomposition in space and time
AU - Garbey, Marc
PY - 2008/12/1
Y1 - 2008/12/1
N2 - In this paper we generalize the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation for the heat equation. The domain decomposition is in space and time. The standard Schwarz waveform relaxation algorithm has a linear rate of convergence and low numerical efficiency. This algorithm is, however, friendly to cache use and scales with the memory in parallel environments. We show that our new acceleration procedure of the waveform acceleration algorithm results in a fast direct solver.
AB - In this paper we generalize the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation for the heat equation. The domain decomposition is in space and time. The standard Schwarz waveform relaxation algorithm has a linear rate of convergence and low numerical efficiency. This algorithm is, however, friendly to cache use and scales with the memory in parallel environments. We show that our new acceleration procedure of the waveform acceleration algorithm results in a fast direct solver.
UR - http://www.scopus.com/inward/record.url?scp=78651526560&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78651526560&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-75199-1_63
DO - 10.1007/978-3-540-75199-1_63
M3 - Conference contribution
AN - SCOPUS:78651526560
SN - 9783540751984
T3 - Lecture Notes in Computational Science and Engineering
SP - 501
EP - 508
BT - Domain Decomposition Methods in Science and Engineering XVII
T2 - 17th International Conference on Domain Decomposition Methods
Y2 - 3 July 2006 through 7 July 2006
ER -