Additive Schwarz Preconditioners for the Obstacle Problem of Clamped Kirchhoff Plates

TL;DR

This paper develops and analyzes additive Schwarz preconditioners to efficiently solve discretized obstacle problems for clamped Kirchhoff plates using a primal-dual active set algorithm, supported by numerical validation.

Contribution

It introduces novel additive Schwarz preconditioners tailored for the systems in each primal-dual active set iteration, enhancing computational efficiency.

Findings

Preconditioners improve convergence rates.

Numerical results confirm theoretical estimates.

Method accelerates solving obstacle problems.

Abstract

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.