The time domain-electric field integral equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a perfect electric conductor (PEC). The time discretization of the TD-EFIE can be achieved by a space-time Galerkin approach or, as it is considered in this contribution, by a convolution quadrature using implicit Runge–Kutta methods. The solution is then computed using the marching-on-in-time (MOT) algorithm. The differentiated TD-EFIE has two problems: 1) the system matrix suffers from ill-conditioning when the time step increases (low frequency breakdown) and 2) it suffers from the DC instability, i.e., the formulation allows for the existence of spurious solenoidal currents that grow slowly in the solution. In this article, we show that 1) and 2) can be alleviated by leveraging quasi-Helmholtz projectors to separate the Helmholtz components of the induced current and rescale them independently. The efficacy of the approach is demonstrated by numerical examples including benchmarks and real-life applications.

中文翻译：

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使用隐式 Runge-Kutta 方法离散的大时间步长和 DC 稳定 TD-EFIE

时域-电场积分方程 (TD-EFIE) 及其微分版本被广泛用于模拟理想电导体 (PEC) 对瞬态电磁场的瞬态散射。TD-EFIE 的时间离散化可以通过时空 Galerkin 方法来实现，或者，正如本贡献中所考虑的那样，通过使用隐式 Runge-Kutta 方法的卷积正交来实现。然后使用按时前进 (MOT) 算法计算解决方案。微分 TD-EFIE 有两个问题：1) 当时间步长增加时，系统矩阵会出现病态 (低频击穿) 和 2) 它会受到 DC 不稳定性的影响，即公式允许存在虚假螺线管在溶液中缓慢增长的电流。在本文中，我们表明，1) 和 2) 可以通过利用准亥姆霍兹投影仪分离感应电流的亥姆霍兹分量并独立重新调整它们来缓解。该方法的有效性通过包括基准测试和实际应用在内的数值示例来证明。