Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems
In this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem. A new Schur complement is proposed for this algebraic system, extending it to both the block-triangula...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/3/375 |
| _version_ | 1827354719312412672 |
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| author | Xin-Hui Shao Jian-Rong Dong |
| author_facet | Xin-Hui Shao Jian-Rong Dong |
| author_sort | Xin-Hui Shao |
| collection | DOAJ |
| description | In this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem. A new Schur complement is proposed for this algebraic system, extending it to both the block-triangular preconditioner and the structured preconditioner. A theoretical analysis proves that the eigenvalues of block-triangular and structured preconditioned matrices are located in the interval [1/2, 1]. Numerical simulations show that two new preconditioners coupled with a Krylov subspace acceleration have good feasibility and effectiveness and are superior to some existing efficient algorithms. |
| first_indexed | 2024-03-08T03:52:47Z |
| format | Article |
| id | doaj.art-7a151d8a548145f8b6961e5584ce8c83 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:52:47Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7a151d8a548145f8b6961e5584ce8c832024-02-09T15:18:07ZengMDPI AGMathematics2227-73902024-01-0112337510.3390/math12030375Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control ProblemsXin-Hui Shao0Jian-Rong Dong1Department of Mathematics, College of Sciences, Northeastern University, Shenyang 100098, ChinaDepartment of Mathematics, College of Sciences, Northeastern University, Shenyang 100098, ChinaIn this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem. A new Schur complement is proposed for this algebraic system, extending it to both the block-triangular preconditioner and the structured preconditioner. A theoretical analysis proves that the eigenvalues of block-triangular and structured preconditioned matrices are located in the interval [1/2, 1]. Numerical simulations show that two new preconditioners coupled with a Krylov subspace acceleration have good feasibility and effectiveness and are superior to some existing efficient algorithms.https://www.mdpi.com/2227-7390/12/3/375PDE-constrained optimizationKrylov subspace methodseddy currentspreconditioner |
| spellingShingle | Xin-Hui Shao Jian-Rong Dong Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems Mathematics PDE-constrained optimization Krylov subspace methods eddy currents preconditioner |
| title | Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems |
| title_full | Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems |
| title_fullStr | Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems |
| title_full_unstemmed | Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems |
| title_short | Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems |
| title_sort | two preconditioners for time harmonic eddy current optimal control problems |
| topic | PDE-constrained optimization Krylov subspace methods eddy currents preconditioner |
| url | https://www.mdpi.com/2227-7390/12/3/375 |
| work_keys_str_mv | AT xinhuishao twopreconditionersfortimeharmoniceddycurrentoptimalcontrolproblems AT jianrongdong twopreconditionersfortimeharmoniceddycurrentoptimalcontrolproblems |