===firstname:
Joseph
===firstname3:
Christopher
===affil6:

===lastname3:
Coley
===email:
Joseph.Benzaken@colorado.edu
===keyword_other2:

===lastname6:

===affil5:

===lastname4:
Evans
===lastname7:

===affil7:

===postal:
2805 Olson Dr. Unit B
Boulder, CO 80303
===ABSTRACT:
In this talk, we present a novel isogeometric approach to the numerical solution of the classical Reissner-Mindlin and Kirchhoff-Love plate equations. This approach eliminates the common issue of locking in thin plates, a numerical phenomenon resulting from an incompatibility between the finite element spaces for the translational and rotational displacement degrees of freedom. This locking-free implementation also permits the use of a simple geometric multigrid method for solving the resulting linear system in which Schwarz methods with intelligently-chosen subdomains are used for iterative smoothing in the multigrid V-cycles. In the thin plate limit, our multigrid approach automatically and exactly preserves the constraint that the shear strain is zero at every geometric level. This results in a method with convergence rates independent of the thickness. Moreover, this elucidates the problem as a network of coupled plates with Dirichlet boundary data specified by adjacent subdomains. Numerical results for both the Kirchhoff-Love and Reissner-Mindlin plates are presented. The results demonstrate the robustness of the numerical method through the invariance of convergence rates with respect to thickness.
===affil3:
The University of Colorado, Boulder
===title:
Multigrid Methods for Isogeometric Thin Plate Discretizations
===affil2:
The University of Colorado, Boulder
===lastname2:
Benzaken
===firstname4:
John A.
===keyword1:
APP_OTHER
===workshop:
no
===lastname:
Benzaken
===firstname5:

===keyword2:
Solvers for indefinite systems
===otherauths:

===affil4:
The University of Colorado, Boulder
===competition:
yes
===firstname7:

===firstname6:

===keyword_other1:
Iterative solvers for structural mechanics
===lastname5:

===affilother:

===firstname2:
Joseph