A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916016455417856 |
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| author | Nolte, Maximilian Torchio, Riccardo Schöps, Sebastian Dölz, Jürgen Wolf, Felix Ruehli, Albert E. |
| author_facet | Nolte, Maximilian Torchio, Riccardo Schöps, Sebastian Dölz, Jürgen Wolf, Felix Ruehli, Albert E. |
| contents | This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an exact representation of the model geometry described in terms of non-uniform rational B-splines without meshing. This is particularly useful when high accuracy is required or when meshing is cumbersome for instance during optimization of electric components. The augmented electric field integral equation is adopted and the deflation method is applied, so the low-frequency breakdown is avoided. The extension to higher-order basis functions is analyzed and the convergence rate is discussed. Numerical experiments on academic and realistic test cases demonstrate the high accuracy of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation Nolte, Maximilian Torchio, Riccardo Schöps, Sebastian Dölz, Jürgen Wolf, Felix Ruehli, Albert E. Computational Engineering, Finance, and Science Numerical Analysis This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an exact representation of the model geometry described in terms of non-uniform rational B-splines without meshing. This is particularly useful when high accuracy is required or when meshing is cumbersome for instance during optimization of electric components. The augmented electric field integral equation is adopted and the deflation method is applied, so the low-frequency breakdown is avoided. The extension to higher-order basis functions is analyzed and the convergence rate is discussed. Numerical experiments on academic and realistic test cases demonstrate the high accuracy of the proposed approach. |
| title | A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation |
| topic | Computational Engineering, Finance, and Science Numerical Analysis |
| url | https://arxiv.org/abs/2401.10735 |