2023/11/27 by Pierrick Cordel, Alexandre Dély, Cordel, Pierrick +5
Engineering · Physics and Astronomy · #Advanced Antenna and Metasurface Technologies #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2311.15592
openalex publication_date 2023/11/27 · openalex created_date 2023/11/29 · openalex updated_date 2026/07/30
In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard schemes based on the electric field integral equation (EFIE). The standard time-domain EFIE-based approaches typically yield matrices that become increasingly ill-conditioned as the time-step or the mesh discretization density increase and suffer from the well-known DC instability. This work presents solutions to these issues that are based both on new Calderón strategies and quasi-Helmholtz projectors regularizations. In addition, to ensure an efficient computation of the marching-on-in-time, the proposed schemes leverage properties of the Z-transform -- involved in the convolution quadrature discretization scheme -- when computing the stabilized operators. The two resulting formulations compare favorably with standard, well-established schemes. The properties and practical relevance of these new formulations will be showcased through relevant numerical examples that include canonical geometries and more complex structures.