TY - JOUR
T1 - Linear iterations as smoothers in multigrid methods
T2 - Theory with applications to incomplete decompositions
AU - Wittum, Gabriel
PY - 1989/6
Y1 - 1989/6
N2 - In the present paper we discuss smoothing and the construction of smoothers in a general framework. The main results apply to general symmetric smoothers. They yield proofs of the smoothing smoperty for point- and blockwise incomplete decompositions, in particular for 5-point, 7-point, and block ILU applied to the anisotropic model problem. Further we give proofs for the V cycle with pointwise ILU smoothers, we present strategies to construct a smoother from a general symmetric iterative scheme, and we establish a general connection between convergent iterations and smoothers.
AB - In the present paper we discuss smoothing and the construction of smoothers in a general framework. The main results apply to general symmetric smoothers. They yield proofs of the smoothing smoperty for point- and blockwise incomplete decompositions, in particular for 5-point, 7-point, and block ILU applied to the anisotropic model problem. Further we give proofs for the V cycle with pointwise ILU smoothers, we present strategies to construct a smoother from a general symmetric iterative scheme, and we establish a general connection between convergent iterations and smoothers.
UR - http://www.scopus.com/inward/record.url?scp=0007370521&partnerID=8YFLogxK
U2 - 10.1016/0899-8248(89)90029-3
DO - 10.1016/0899-8248(89)90029-3
M3 - Article
AN - SCOPUS:0007370521
SN - 0899-8248
VL - 1
SP - 180
EP - 215
JO - IMPACT of Computing in Science and Engineering
JF - IMPACT of Computing in Science and Engineering
IS - 2
ER -