Title: Preconditioning discrete approximations of the Reissner-Mindlin
plate model
Authors: Douglas N. Arnold, Richard S. Falk, and Ragnar Winther.
Source: RAIRO Modél. Math. Anal. Numér., 31(4):517-557, 1997
Abstract: 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 efficiently solve this indefinite linear system. Although
the mixed formulation of the Reissner-Mindlin problem has a
saddle-point structure common to other mixed variational problems, 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
introduces new complications.
Keywords: preconditioner, Reissner, Mindlin, plate, finite element
URL: http://www.math.rutgers.edu/~falk/papers/prerm.pdf