Characterizing Ultrawideband Scattering From Penetrable Objects Using a Stabilized and Well-Conditioned TDIE With Laguerre Polynomials

A novel approach is proposed to solve ultrawideband scattering problem of dielectric objects, which employs the time-domain integral equation (TDIE) method. The frequency band spans from ultralow frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-25}$ </tex-math></inline-formula> Hz) to microwave frequency. The application of the Calderón preconditioner ensures that the impedance matrix is well-conditioned. Furthermore, the Filon-type method is integrated into the Calderón preconditioner to guarantee the accuracy of the oscillatory integral. In addition, by incorporating a block-matrix constraint condition, we obtain stabilized and well-conditioned dielectric formulations based on marching-on-in-degree (MOD) method. Expanding on these techniques, we propose a universal static error current subtraction (SECS) method, characterized by its simplicity of implementation, to attain an accurate solution for ultrawideband scenarios. Notably, the accurate results can be obtained from ultralow to high frequencies through single temporal simulation. Numerical examples demonstrate that the proposed approach is able to achieve stable and accurate ultra broadband solutions.