TY - JOUR
T1 - A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem
JO - Communications in Computational Physics
VL - 1
SP - 143
EP - 167
PY - 2018
DA - 2018/04
SN - 19
DO - http://doi.org/10.4208/cicp.190914.080415a
UR - https://global-sci.org/intro/article_detail/cicp/11083.html
KW - 
AB - <p style="text-align: justify;">In this paper we consider PDE-constrained optimization problems which incorporate
an $\mathcal{H}_1$ regularization control term. We focus on a time-dependent PDE, and
consider both distributed and boundary control. The problems we consider include
bound constraints on the state, and we use a Moreau-Yosida penalty function to handle
this. We propose Krylov solvers and Schur complement preconditioning strategies
for the different problems and illustrate their performance with numerical examples.</p>