We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the controllability method determines iteratively a periodic solution in the time domain. At each conjugate gradient iteration, the gradient of the cost functional is simply computed by running any time-dependent simulation code forward and backward for one period, thus leading to a non-intrusive implementation easily integrated into existing software. Moreover, the proposed algorithm automatically inherits the parallelism, scalability, and low memory footprint of the underlying time-domain solver. Since the time-periodic solution obtained by minimization is not necessarily unique, we apply a cheap post-processing filtering procedure which recovers the time-harmonic solution from any minimizer. Finally, we present a series of numerical examples which show that our algorithm greatly speeds up the convergence towards the desired time-harmonic solution when compared to simply running the time-marching code until the time-harmonic regime is eventually reached.
翻译:我们建议了一种控制方法,用于在一阶配制中对时间-调和 Maxwell 的方程式进行数字解析。 通过最小化一个测量周期偏差的二次成本功能, 控制性方法在时间域中迭代地决定一个周期性解决方案。 在每一个交替梯度迭代时, 成本函数的梯度仅仅是通过运行任何时间依赖的模拟代碼向前和向后运行一个时期来计算, 从而导致一个不侵犯性的实施很容易融入现有软件。 此外, 拟议的算法自动继承了基础时间- 域解码的平行性、 缩放性和 低记忆足迹。 由于通过最小化获得的时间- 周期性解决方案不一定是独一无二的, 我们采用了一种廉价的后处理过滤程序, 从任何最小化器中恢复时间- 协调性解决方案。 最后, 我们提出了一系列数字实例, 表明我们的算法在与仅仅运行时间- 平衡系统最终达到时间- 调和 时间- 调制相比, 大大加快了我们所期望的时间- 的趋同 。