论文标题
通过隐式runge-kutta方法离散的大型时间步骤和直流稳定的TD-Fefies
Large Time Step and DC Stable TD-EFIE Discretized with Implicit Runge-Kutta Methods
论文作者
论文摘要
时间域 - 电场积分方程（TD-FEFIE）及其差异化版本被广泛用于通过完美的电导体（PEC）模拟依赖性电磁场的瞬态散射。 TD-FEFIE的时间离散化可以通过时空Galerkin方法来实现，或者正如此贡献所考虑的那样，使用隐式runge-kutta方法来实现卷积正交。然后，使用时间（MOT）算法进行计算解决方案。差异化的TD-FEFIE有两个问题：（i）当时间步长增加（低频分解）时，系统矩阵会遭受不良条件的影响，并且（ii）它受到直流不稳定性的影响，即，该制剂允许在解决方案中缓慢生长的胎儿螺线管电流。在这项工作中，我们表明（i）和（ii）可以通过利用Quasi-Helmholtz投影仪将诱导电流的Helmholtz组件分开并独立缩回它们来缓解。该方法的功效通过包括基准和现实生活应用在内的数值示例来证明。
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 Electrical 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: (i) the system matrix suffers from ill-conditioning when the time step increases (low frequency breakdown) and (ii) 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 work, we show that (i) and (ii) 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.
