Volume 49, pp. 274-290, 2018.

Additive Schwarz preconditioners for the obstacle problem of clamped Kirchhoff plates

Susanne C. Brenner, Christopher B. Davis, and Li-Yeng Sung

Abstract

When the obstacle problem of clamped Kirchhoff plates is discretized by a partition of unity method, the resulting discrete variational inequalities can be solved by a primal-dual active set algorithm. In this paper we develop and analyze additive Schwarz preconditioners for the systems that appear in each iteration of the primal-dual active set algorithm. Numerical results that corroborate the theoretical estimates are also presented.

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Key words

partition of unity, additive Schwarz, displacement obstacle problem for clamped Kirchhoff plates, fourth-order variational inequality

AMS subject classifications

65N30, 65K15

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