The Galerkin method for a regularised combined field integral equation without a dual basis function
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arXiv
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| Formato: | Preprint |
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2024
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| _version_ | 1866929382820413440 |
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| author | Niino, Kazuki Yamamoto, Shunpei |
| author_facet | Niino, Kazuki Yamamoto, Shunpei |
| contents | We propose discretisation of a regularised combined field integral equation (regularised CFIE) only with the Rao-Wilton-Glisson (RWG) basis function. The CFIE is a formulation of integral equations, which avoids the so-called ficticious frequencies of integral equations. The most typical CFIE, which is a linear combination of the electric field integral equation (EFIE) and magnetic field integral equation (MFIE), is known to be ill-conditioned and requires many iterations when solved with iteration methods such as the generalised minimum residual (GMRES) method. The regularised CFIE is another formulation of the CFIE to solve this problem by applying a regularising operator to the part of the EFIE. In several previous studies the regularising operator is determined based on the Calderon preconditioning. This regularising operator however takes much more computatonal time than the standard CFIE since discretising the EFIE with the Calderon preconditioner requires the dual basis function. In this article we propose a formulation of the regularised CFIE, which can be discretised with the Galerkin method without the dual basis function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Galerkin method for a regularised combined field integral equation without a dual basis function Niino, Kazuki Yamamoto, Shunpei Numerical Analysis We propose discretisation of a regularised combined field integral equation (regularised CFIE) only with the Rao-Wilton-Glisson (RWG) basis function. The CFIE is a formulation of integral equations, which avoids the so-called ficticious frequencies of integral equations. The most typical CFIE, which is a linear combination of the electric field integral equation (EFIE) and magnetic field integral equation (MFIE), is known to be ill-conditioned and requires many iterations when solved with iteration methods such as the generalised minimum residual (GMRES) method. The regularised CFIE is another formulation of the CFIE to solve this problem by applying a regularising operator to the part of the EFIE. In several previous studies the regularising operator is determined based on the Calderon preconditioning. This regularising operator however takes much more computatonal time than the standard CFIE since discretising the EFIE with the Calderon preconditioner requires the dual basis function. In this article we propose a formulation of the regularised CFIE, which can be discretised with the Galerkin method without the dual basis function. |
| title | The Galerkin method for a regularised combined field integral equation without a dual basis function |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.07924 |