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Christopher B. Davis

Publications and source records attributed to Christopher B. Davis.

3 recordsLinked to original sources
arXiv2018

Additive Schwarz preconditioners for a state constrained elliptic distributed optimal control problem discretized by a partition of unity method

We present additive Schwarz preconditioners for a class of elliptic optimal control problems discretized by a partition of unity method. The discrete problem is solved by a primal-dual active set algorithm, where the auxiliary system in each iteration is solved by a preconditioned conjugate gradient method based on additive Schwarz preconditioners. Condition number estimates are given and verified by a numerical example.

math.NA↗
arXiv2018

Additive Schwarz Preconditioners for the Obstacle Problem of Clamped Kirchhoff Plates

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.

math.NA↗