scholarly journals A mixed multiscale FEM for the eddy current problem with T,Φ-Φ and vector hysteresis

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Valentin Hanser ◽  
Markus Schöbinger ◽  
Karl Hollaus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eddy Current ◽  
Current Problem ◽  
Great Success ◽  
Content Type ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Eddy Current Problem ◽  
Element Method

Purpose This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis. Design/methodology/approach The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously. Findings As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced. Originality/value The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

scholarly journals An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1382
Author(s):  
Denis Spiridonov ◽  
Maria Vasilyeva ◽  
Aleksei Tyrylgin ◽  
Eric T. Chung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Reduction ◽  
Basis Functions ◽  
Computational Domain ◽  
Filtration Problem ◽  
Spectral Problems ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards equation. To approximate fractures we use the Discrete Fracture Model (DFM). Complex geometric features of the computational domain requires the construction of a fine grid that explicitly resolves the heterogeneities such as fractures. This approach leads to systems with a large number of unknowns, which require large computational costs. In order to develop a more efficient numerical scheme, we propose a model reduction procedure based on the Generalized Multiscale Finite element method (GMsFEM). The GMsFEM allows solving such problems on a very coarse grid using basis functions that can capture heterogeneities. In the GMsFEM, there are offline and online stages. In the offline stage, we construct snapshot spaces and solve local spectral problems to obtain multiscale basis functions. These spectral problems are defined in the snapshot space in each local domain. To improve the accuracy of the method, we add online basis functions in the online stage. The construction of the online basis functions is based on the local residuals. The use of online bases will allow us to get a significant improvement in the accuracy of the method. We present results with different number of offline and online multisacle basis functions. We compare all results with reference solution. Our results show that the proposed method is able to achieve high accuracy with a small computational cost.

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