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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.06978 |
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| _version_ | 1866912753474600960 |
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| author | Christmann, Jan-Magnus D'Angelo, Laura A. M. De Gersem, Herbert Pfeiffer, Sven Mirza, Sajjad H. |
| author_facet | Christmann, Jan-Magnus D'Angelo, Laura A. M. De Gersem, Herbert Pfeiffer, Sven Mirza, Sajjad H. |
| contents | The homogenized harmonic balance finite element (FE) method enables efficient nonlinear eddy-current simulations of 3-D devices with lamination stacks by combining the harmonic balance method with a frequency-domain-based homogenization technique. This approach avoids expensive time stepping of the eddy-current field problem and allows the use of a relatively coarse FE mesh that does not resolve the individual laminates. In this paper, we extend the method to handle excitation signals with a dc bias. To achieve this, we adapt the original homogenization technique to better account for ferromagnetic saturation. The resulting formula for the homogenized reluctivity is evaluated using a look-up table computed from a 1-D FE simulation of a lamination and containing the average magnetic flux density in the lamination and the corresponding skin depth. We compare the results of the proposed method to those from a fine-mesh transient reference simulation. The tests cover different levels of ferromagnetic saturation and frequencies between 50 Hz and 10 kHz. For moderate ferromagnetic saturation, the method gives a good approximation of the eddy-current losses and the magnetic energy, with relative errors below 10%, while reducing the required number of degrees of freedom at 10 kHz by 1.5 orders of magnitude. This results in a reduction in simulation time from 2 days on a contemporary server to 90 minutes on a standard workstation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DC-Biased Homogenized Harmonic Balance Finite Element Method Christmann, Jan-Magnus D'Angelo, Laura A. M. De Gersem, Herbert Pfeiffer, Sven Mirza, Sajjad H. Computational Engineering, Finance, and Science The homogenized harmonic balance finite element (FE) method enables efficient nonlinear eddy-current simulations of 3-D devices with lamination stacks by combining the harmonic balance method with a frequency-domain-based homogenization technique. This approach avoids expensive time stepping of the eddy-current field problem and allows the use of a relatively coarse FE mesh that does not resolve the individual laminates. In this paper, we extend the method to handle excitation signals with a dc bias. To achieve this, we adapt the original homogenization technique to better account for ferromagnetic saturation. The resulting formula for the homogenized reluctivity is evaluated using a look-up table computed from a 1-D FE simulation of a lamination and containing the average magnetic flux density in the lamination and the corresponding skin depth. We compare the results of the proposed method to those from a fine-mesh transient reference simulation. The tests cover different levels of ferromagnetic saturation and frequencies between 50 Hz and 10 kHz. For moderate ferromagnetic saturation, the method gives a good approximation of the eddy-current losses and the magnetic energy, with relative errors below 10%, while reducing the required number of degrees of freedom at 10 kHz by 1.5 orders of magnitude. This results in a reduction in simulation time from 2 days on a contemporary server to 90 minutes on a standard workstation. |
| title | DC-Biased Homogenized Harmonic Balance Finite Element Method |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2512.06978 |