Using edge elements for modeling of 3-D magnetodynamic problem via a subproblem method

In this paper, the subproblem method with using edge finite elements is proposed for coupling subproblems via several steps to treat and deal with some troubles regarding to electromagnetic problems that gets quite difficulties when directly applying a finite element method. In the strategy subproblem method, it allows a complete problem to define into several subproblems with adapted dimensions. Each subproblem can be solved on its independent domain and mesh without performing in whole domain or mesh. This easily supports meshing and decreases computing time.
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Using edge elements for modeling of 3-D magnetodynamic problem via a subproblem methodScience & Technology Development Journal, 23(1):439-445 Open Access Full Text Article Research ArticleUsing edge elements for modeling of 3-D magnetodynamicproblem via a subproblem methodVuong Dang Quoc1,* , Christophe Geuzaine2 ABSTRACT Introduction: The mathematical modeling of electromagnetic problems in electrical devices are often presented by Maxwells equations and constitutive material laws. These equations are par- Use your smartphone to scan this tial differential equations linked to fields and their sources. In order to solve these equations and QR code and download this article simulate the distribution of magnetic fields and eddy current losses of electromagnetic problems, a subproblem method for modeling a 3-D magnetodymic problem with the b-conformal formula- tion is proposed. Methods: In this paper, the subproblem method with using edge finite elements is proposed for coupling subproblems via several steps to treat and deal with some troubles regard- ing to electromagnetic problems that gets quite difficulties when directly applying a finite element method. In the strategy subproblem method, it allows a complete problem to define into sev- eral subproblems with adapted dimensions. Each subproblem can be solved on its independent domain and mesh without performing in whole domain or mesh. This easily supports meshing and decreases computing time. Results: The obtained results, the subproblem method with edge elements indicates magnetic flux densities and the eddy current losses in the conducting region. The computed results is also compared with the measured results done by other authors. This can be shown that there is a very good agreement. Conclusion: The validated method has been successfully applied to a practical test problem (TEAM Problem 7). Key words: Eddy current, Magnetic field, TEAM problem 7, b-conformal formulation, finite ele- ment method, subproblem method1 Training Center of ElectricalEngineering, School of ElectricalEngineering, Hanoi University of Science INTRODUCTIONand Technology As we have known, the mathematical modeling of electromagnetic problems in electrical devices are often2 Electrical Engineering and Computer presented by Maxwell’s equations and constitutive material laws. These equations are partial differentialScience Department of the University of equations (PDEs) 1,2 linked to fields and their sources (such as: magnetic and electric fields, eddy currentLiège, Belgium losses).Correspondence In order to solve these equations and simulate the distribution of magnetic fields and eddy current losses,Vuong Dang Quoc, Training Center of many authors have been recently used a finite element method (FEM) for magnetodynamic problems. But,Electrical Engineering, School of the directly application of the FEM to an actual problem is still quite difficult 3,4 when the dimension of theElectrical Engineering, Hanoi Universityof Science and Technology computed conducting domains is very small in comparison with the whole problem.Email: vuong.dangquoc@hust.edu.vn In order to overcome this drawback, many authors have been recently proposed a subproblem method (SPM)History to divide a complete problem into subproblems (SPs) in one way coupling 5–7 . However, this proposal was• Received: 2019-10-16 done for thin shell models, where appearing errors near edge and corner effects 5–7 .• Accepted: 2019-12-10 In this study, the SPM is expanded for coupling SPs via two steps with using edge finite elements (FEs). The• Published: 2020-02-20 scenario of this method is also based on a SPM 5 , instead of solving a complete model (e.g, stranded inductorsDOI : 10.32508/stdj.v23i1.1718 and conducting regions) in a single mesh, it will be split into several problems with a series of changes. This means that the problem with a stranded inductor (coil) alone is first solved, and then the second problem with conducting regions is added. Thus, the complete solution is finally defined as a superposition of the SP solutions. From this SP to another is constrained by interface conditions (ICs) with surface sources (SSs) orCopyright volume sources (VSs), that express changes of permeability and conductivity material in conducting© VNU-HCM Press. This is an open- regions.The developed method is performed for the magnetic flux density formulation and is illustrated on aaccess article distributed under the practical test problem (TEAM problem 7) 3 .terms o ...