A discretization method with the $H_{\mathrm{ div}}$ inner product for the electric field integral equation (EFIE) is proposed. The EFIE with the conventional Galerkin discretization shows bad accuracy for problems… Click to show full abstract
A discretization method with the $H_{\mathrm{ div}}$ inner product for the electric field integral equation (EFIE) is proposed. The EFIE with the conventional Galerkin discretization shows bad accuracy for problems with a small frequency, a problem known as the low-frequency breakdown. The discretization method proposed in this paper utilizes the $H_{\mathrm{ div}}$ scalar product with a scalar coefficient for the Galerkin discretization 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 Calderón preconditioning is not efficient for reducing the computational time with the new discretization. We therefore propose a new preconditioning which can accelerate the computation successfully. The efficiency of the proposed discretization and preconditioning is verified through some numerical examples.
