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 Calder\'on 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.

翻译：本文针对理想电导散射体的时域建模，提出基于卷积求积法的新积分公式，克服了基于电场积分方程（EFIE）的标准方案中一些最关键的缺陷。基于标准时域EFIE的方法通常会产生随时间步长或网格离散密度增加而病态程度加剧的矩阵，并遭受众所周知的直流不稳定性问题。本文提出了基于新的Calderón策略和准亥姆霍兹投影器正则化的解决方案。此外，为确保时域步进迭代的高效计算，所提方案在计算稳定化算子时利用了Z变换（涉及卷积求积离散方案）的特性。两种公式与标准成熟的方案相比具有优势。通过包含典型几何结构和更复杂结构的数值示例，将展示这些新公式的性质和实际相关性。