Preconditioning discrete approximations
of the Reissner-Mindlin plate model

Douglas N. Arnold
Deparpartment of Mathematics
Penn State University
University Park, PA 16802

Richard S. Falk
Deparpartment of Mathematics
Rutgers University
New Brunswick, NJ 08903

Ragnar Winther
Department of Informatics
University of Oslo
Oslo, Norway

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.

Key Words: preconditioner, Reissner, Mindlin, plate, finite element

Subject classification: 65N30, 65N22, 65F10, 73V05


Contributed June 28, 1996.