Additive Schwarz Preconditioners for the Obstacle Problem of Clamped Kirchhoff Plates
Provides preconditioners for solving discrete variational inequalities in plate obstacle problems, an incremental contribution to numerical methods for PDE-constrained optimization.
The paper develops and analyzes additive Schwarz preconditioners for systems arising in primal-dual active set algorithms for obstacle problems of clamped Kirchhoff plates, with numerical results confirming theoretical estimates.
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.