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Preconditioning discrete approximations of the Reissner-Mindlin plate model. (English) Zbl 0877.73060

We consider iterative methods for the solution of the linear system of equations arising from the mixed finite element discretization of the Reissner-Mindlin plate model. We show how to construct a symmetric positive definite block diagonal preconditioner such that the resulting linear system has spectral condition number independent of both the mesh size \(h\) and the plate thickness \(t\). We further discuss how this preconditioner may be implemented and then apply it to solve the indefinite linear system. The presence of the small parameter \(t\) and the fact that the matrix in the upper left corner of the partition is only positive semidefinite introduce new complications.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
65F10 Iterative numerical methods for linear systems
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