TY - JOUR
T1 - The method of subspace corrections
AU - Xu, Jinchao
N1 - Funding Information:
This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236 through Penn State university.
PY - 2001/3/1
Y1 - 2001/3/1
N2 - This paper gives an overview for the method of subspace corrections. The method is first motivated by a discussion on the local behavior of high-frequency components in a solution to an elliptic problem. A simple domain decomposition method is discussed as an illustrative example and multigrid methods are discussed in more detail. Brief discussion are also given to some non-linear examples including eigenvalue problems, obstacle problems and liquid crystal modelings. The relationship between the method of subspace correction and the method of alternating projects is observed and discussed.
AB - This paper gives an overview for the method of subspace corrections. The method is first motivated by a discussion on the local behavior of high-frequency components in a solution to an elliptic problem. A simple domain decomposition method is discussed as an illustrative example and multigrid methods are discussed in more detail. Brief discussion are also given to some non-linear examples including eigenvalue problems, obstacle problems and liquid crystal modelings. The relationship between the method of subspace correction and the method of alternating projects is observed and discussed.
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U2 - 10.1016/S0377-0427(00)00518-5
DO - 10.1016/S0377-0427(00)00518-5
M3 - Article
AN - SCOPUS:0035281551
SN - 0377-0427
VL - 128
SP - 335
EP - 362
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -