A practical factorization of a Schur complement for PDE-constrained Distributed Optimal Control
Abstract
A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces two complex factors that are complex conjugate to each other. The proposed solution methodology involves the application of a parallel linear domain decomposition solver---FETI-DPH---for the solution of the subproblems with the complex factors. Numerical properties of FETI-DPH in this context are demonstrated, including numerical and parallel scalability and regularization dependence. The new factorization can be used to solve Schur complement systems arising in both range-space and full-space formulations. In both cases, numerical results indicate that the complex factorization is promising.
Cite
@article{arxiv.1312.5653,
title = {A practical factorization of a Schur complement for PDE-constrained Distributed Optimal Control},
author = {Youngsoo Choi and Charbel Farhat and Walter Murray and Michael Saunders},
journal= {arXiv preprint arXiv:1312.5653},
year = {2013}
}