Optimal Control of Heat Equation by Coupling FVM and FEM Codes
In this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite volume OpenFOAM code and the adjo...
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| Format: | Article |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Samuele Baldini Giacomo Barbi Antonio Cervone Federico Giangolini Sandro Manservisi Lucia Sirotti |
| author_facet | Samuele Baldini Giacomo Barbi Antonio Cervone Federico Giangolini Sandro Manservisi Lucia Sirotti |
| author_sort | Samuele Baldini |
| collection | DOAJ |
| description | In this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite volume OpenFOAM code and the adjoint-control equation using a variational formulation of the problem with the in-house finite element FEMuS code. The variational formulation of the problem is the natural framework for accurately capturing the control correction while OpenFOAM guarantees the accuracy of the state solution. This coupling is facilitated through the open-source MED and MEDCoupling libraries of the SALOME platform. The code coupling is implemented with the MED libraries and additional routines added in the FEMuS and OpenFOAM codes. We demonstrate the accuracy, robustness, and performance of the proposed approach with examples targeting different objectives using distributed and boundary controls in each case. |
| format | Article |
| id | doaj-art-69ea3efd90bc4b8e9f9229e182909440 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-69ea3efd90bc4b8e9f9229e1829094402025-01-24T13:39:51ZengMDPI AGMathematics2227-73902025-01-0113223810.3390/math13020238Optimal Control of Heat Equation by Coupling FVM and FEM CodesSamuele Baldini0Giacomo Barbi1Antonio Cervone2Federico Giangolini3Sandro Manservisi4Lucia Sirotti5Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyLaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyLaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyLaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyLaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyLaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyIn this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite volume OpenFOAM code and the adjoint-control equation using a variational formulation of the problem with the in-house finite element FEMuS code. The variational formulation of the problem is the natural framework for accurately capturing the control correction while OpenFOAM guarantees the accuracy of the state solution. This coupling is facilitated through the open-source MED and MEDCoupling libraries of the SALOME platform. The code coupling is implemented with the MED libraries and additional routines added in the FEMuS and OpenFOAM codes. We demonstrate the accuracy, robustness, and performance of the proposed approach with examples targeting different objectives using distributed and boundary controls in each case.https://www.mdpi.com/2227-7390/13/2/238heat equationoptimal controlcoupling codesFVMFEM |
| spellingShingle | Samuele Baldini Giacomo Barbi Antonio Cervone Federico Giangolini Sandro Manservisi Lucia Sirotti Optimal Control of Heat Equation by Coupling FVM and FEM Codes Mathematics heat equation optimal control coupling codes FVM FEM |
| title | Optimal Control of Heat Equation by Coupling FVM and FEM Codes |
| title_full | Optimal Control of Heat Equation by Coupling FVM and FEM Codes |
| title_fullStr | Optimal Control of Heat Equation by Coupling FVM and FEM Codes |
| title_full_unstemmed | Optimal Control of Heat Equation by Coupling FVM and FEM Codes |
| title_short | Optimal Control of Heat Equation by Coupling FVM and FEM Codes |
| title_sort | optimal control of heat equation by coupling fvm and fem codes |
| topic | heat equation optimal control coupling codes FVM FEM |
| url | https://www.mdpi.com/2227-7390/13/2/238 |
| work_keys_str_mv | AT samuelebaldini optimalcontrolofheatequationbycouplingfvmandfemcodes AT giacomobarbi optimalcontrolofheatequationbycouplingfvmandfemcodes AT antoniocervone optimalcontrolofheatequationbycouplingfvmandfemcodes AT federicogiangolini optimalcontrolofheatequationbycouplingfvmandfemcodes AT sandromanservisi optimalcontrolofheatequationbycouplingfvmandfemcodes AT luciasirotti optimalcontrolofheatequationbycouplingfvmandfemcodes |