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arXiv · 1605.07795

A discretisation method with the $H_{\rm div}$ inner product for electric field integral equations

Kazuki Niino·Sho Akagi·Naoshi Nishimura
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Abstract

A discretisation method with the $H_{\rm div}$ inner product for the electric field integral equation~(EFIE) is proposed. The EFIE with the conventional Galerkin discretisation shows bad accuracy for problems with a small frequency, a problem known as the low-frequency breakdown. The discretisation method proposed in this paper utilises the $H_{\rm div}$ scalar product with a scalar coefficient for the Galerkin discretisation and overcomes the low-frequency problem with an appropriately chosen coefficient. As regards the preconditioning, we find that a naive use of the widely-used Calderon preconditioning is not efficient for reducing the computational time with the new discretisation. We therefore propose a new preconditioning which can accelerate the computation successfully. The efficiency of the proposed discretisation and preconditioning is verified through some numerical examples.

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Kazuki Niino, Sho Akagi, Naoshi Nishimura. 2016-05-25. A discretisation method with the $H_{\rm div}$ inner product for electric field integral equations. https://doi.org/10.1109/tap.2017.2696422

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