A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems
Abstract
1. Introduction
2. Problem Formulation
2.1. Discretization
2.2. Previous Work
3. New Preconditioning Method
3.1. New Preconditioners
3.2. Spectral Analysis
4. Numerical Results
4.1. Test Problem 1
4.2. Test Problem 2
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Method | MINRES (I) | MINRES () [6] | MINRES () [7] | GMRES () | ||||||||
DoF/ | ||||||||||||
3267 | 2278 (1.90) | 4662 (3.04) | -- | 11 (0.29) | 27 (0.59) | 129 (1.76) | 19 (0.42) | 25 (0.46) | 25 (0.31) | 6 (0.28) | 8 (0.12) | 8 (0.15) |
12,675 | -- | -- | -- | 11 (0.92) | 27 (1.66) | 132 (7.58) | 19 (1.57) | 27 (1.82) | 27 (1.96) | 6 (0.60) | 8 (0.73) | 8 (0.60) |
49,923 | -- | -- | -- | 13 (4.16) | 27 (7.78) | 139 (38.4) | 21 (7.98) | 27 (8.67) | 29 (9.18) | 6 (2.48) | 8 (3.35) | 8 (2.63) |
198,147 | -- | -- | -- | 13 (20.2) | 27 (34.6) | 143 (176) | 21 (30.5) | 29 (41.5) | 29 (41.3) | 6 (10.6) | 8 (12.9) | 8 (13.0) |
Method | MINRES (I) | MINRES () [6] | MINRES () [7] | GMRES () | ||||||||
DoF/ | ||||||||||||
3267 | 1371 (1.12) | 1422 (1.13) | 1423 (0.84) | 45 (0.59) | 283 (2.63) | 636 (5.64) | 11 (0.20) | 11 (0.15) | 9 (0.14) | 8 (0.15) | 9 (0.10) | 7 (0.09) |
12,675 | 4914 (9.39) | -- | -- | 45 (2.68) | 325 (18.8) | 1845 (106) | 11 (0.62) | 11 (0.74) | 11 (0.71) | 8 (0.56) | 9 (0.54) | 9 (0.73) |
49,923 | -- | -- | -- | 45 (11.5) | 336 (83.9) | 2750 (676) | 11 (3.07) | 11 (3.04) | 13 (3.33) | 9 (2.55) | 9 (2.73) | 9 (2.83) |
198,147 | -- | -- | -- | 43 (56.8) | 327 (424) | 3011 (3923) | 11 (15.7) | 11 (15.8) | 13 (18.6) | 9 (13.4) | 9 (14.7) | 9 (14.5) |
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Wang, C.; Chen, J.; Sun, S. A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems. Mathematics 2023, 11, 2599. https://doi.org/10.3390/math11122599
Wang C, Chen J, Sun S. A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems. Mathematics. 2023; 11(12):2599. https://doi.org/10.3390/math11122599
Chicago/Turabian StyleWang, Chaojie, Jie Chen, and Shuen Sun. 2023. "A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems" Mathematics 11, no. 12: 2599. https://doi.org/10.3390/math11122599
APA StyleWang, C., Chen, J., & Sun, S. (2023). A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems. Mathematics, 11(12), 2599. https://doi.org/10.3390/math11122599