TY - JOUR
T1 - A new mixed preconditioning method for finite element computations
AU - Tezduyar, T. E.
AU - Behr, M.
AU - Aliabadi, S. K.
AU - Mittal, S.
AU - Ray, S. E.
N1 - Funding Information:
Correspondence to: Professor Tayfun E. Tezduyar, Department of Aerospace Engineering and Mechanics, Minnesota Supercomputer Institute, 1200 Washington Avenue South, Minneapolis, MN 55415, USA. * This research was sponsored by NASA-Johnson Space Center (under grant NAG 9-449) and NSF (under grant MSM-8796352).
PY - 1992/8
Y1 - 1992/8
N2 - A new mixed clustered element-by-element (CEBE)/cluster companion (CC) preconditioning method for finite element computations is introduced. In the CEBE preconditioning, the elements are merged into clusters of elements, and the preconditioners are defined as series products of cluster level matrices. The CC preconditioning method, which is also introduced in this paper, shares a common philosophy with the multi-grid methods. The CC preconditioners are based on companion meshes associated with different levels of clustering. For each level of clustering, we construct a CEBE preconditioner and an associated CC preconditioner. Because these two preconditioners in a sense complement each other, when they are used in a mixed way, they can be expected to give better performance. In fact, our numerical tests, for two- and three-dimensional problems governed by the Poisson equation, demonstrate that the mixed CEBE/CC preconditioning results in convergence rates which are, in most cases, significantly better than the convergence rates obtained with the best of the CEBE and CC preconditioning methods.
AB - A new mixed clustered element-by-element (CEBE)/cluster companion (CC) preconditioning method for finite element computations is introduced. In the CEBE preconditioning, the elements are merged into clusters of elements, and the preconditioners are defined as series products of cluster level matrices. The CC preconditioning method, which is also introduced in this paper, shares a common philosophy with the multi-grid methods. The CC preconditioners are based on companion meshes associated with different levels of clustering. For each level of clustering, we construct a CEBE preconditioner and an associated CC preconditioner. Because these two preconditioners in a sense complement each other, when they are used in a mixed way, they can be expected to give better performance. In fact, our numerical tests, for two- and three-dimensional problems governed by the Poisson equation, demonstrate that the mixed CEBE/CC preconditioning results in convergence rates which are, in most cases, significantly better than the convergence rates obtained with the best of the CEBE and CC preconditioning methods.
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U2 - 10.1016/0045-7825(92)90121-Y
DO - 10.1016/0045-7825(92)90121-Y
M3 - Article
AN - SCOPUS:0026910211
SN - 0374-2830
VL - 99
SP - 27
EP - 42
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 1
ER -