New preconditioners for semi-linear pde-constrained optimal control in annular geometries

Lasse Hjuler Christiansen*, John Bagterp Jørgensen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Optimization problems that are constrained by partial differential equations (PDEs) often pose significant computational challenges to black-box optimization algorithms. This is particular the case for non-linear problems that typically rely on multi-query solution of large-scale linearized subsystems. In this regard, this paper proposes a customized solution strategy for a class of semi-linear PDE-constrained optimization problems in annular domains. At its core, the strategy relies on a collection of new Poisson-like preconditioners that are based on boundary-adapted spectral Galerkin methods. The preconditioners are matrix-free and scale linearly with the problem size. To establish proof-of-concept, a case study solves a benchmark control problem for various model parameters. The results show that the preconditioners lead to fast solution strategies that outperform conventional direct approaches.

Original languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM Conference
EditorsSpencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
PublisherSpringer
Publication date2020
Pages441-452
ISBN (Print)9783030396466
DOIs
Publication statusPublished - 2020
Event12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, United Kingdom
Duration: 9 Jul 201813 Jul 2018

Conference

Conference12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
CountryUnited Kingdom
CityLondon
Period09/07/201813/07/2018
SeriesLecture Notes in Computational Science and Engineering
Volume134
ISSN1439-7358

Cite this

Christiansen, L. H., & Jørgensen, J. B. (2020). New preconditioners for semi-linear pde-constrained optimal control in annular geometries. In S. J. Sherwin, J. Peiró, P. E. Vincent, D. Moxey, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM Conference (pp. 441-452). Springer. Lecture Notes in Computational Science and Engineering, Vol.. 134 https://doi.org/10.1007/978-3-030-39647-3_35