Mass-lumping discretization and solvers for distributed elliptic optimal control problems
Numerical Analysis
2023-05-01 v1 Numerical Analysis
Optimization and Control
Abstract
The purpose of this paper is to investigate the effects of the use of mass-lumping in the finite element discretization of the reduced first-order optimality system arising from a standard tracking-type, distributed elliptic optimal control problem with regularization. We show that mass-lumping will not affect the error between the desired state and the computed state, but will lead to a Schur-complement system that allows for a fast matrix-by-vector multiplication. We show that the use of the Schur-Complement Preconditioned Conjugate Gradient method in a nested iteration setting leads to an asymptotically optimal solver with respect to the complexity.
Cite
@article{arxiv.2304.14664,
title = {Mass-lumping discretization and solvers for distributed elliptic optimal control problems},
author = {Ulrich Langer and Richard Löscher and Olaf Steinbach and Huidong Yang},
journal= {arXiv preprint arXiv:2304.14664},
year = {2023}
}