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Abstract:
This paper aims to introduce a novel adaptive multigrid method for the elasticity eigenvalue problem. Different from the developing adaptive algorithms for the elasticity eigenvalue problem, the proposed approach transforms the elasticity eigenvalue problem into a series of boundary value problems in the adaptive spaces and some small-scale elasticity eigenvalue problems in a low-dimensional space. As our algorithm avoids solving large-scale elasticity eigenvalue problems, which is time-consuming, and the boundary value problem can be solved efficiently by the adaptive multigrid method, our algorithm can evidently improve the overall solving efficiency for the elasticity eigenvalue problem. Meanwhile, we present a rigorous theoretical analysis of the convergence and optimal complexity. Finally, some numerical experiments are presented to validate the theoretical conclusions and verify the numerical efficiency of our approach.
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Source :
BIT NUMERICAL MATHEMATICS
ISSN: 0006-3835
Year: 2022
Issue: 4
Volume: 62
Page: 2005-2033
1 . 5
JCR@2022
1 . 5 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:20
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 0
SCOPUS Cited Count:
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 12
Affiliated Colleges: