论文标题
麦克斯韦系统以高频的线性逆电导率问题
A linearised inverse conductivity problem for the Maxwell system at a high frequency
论文作者
论文摘要
我们考虑在高时谐波频率下，在三维有限域中电磁波的线性逆电导率问题。得出了完整的麦克斯韦系统中电导率系数和简化横向电动模式的电导率系数的增加。这些边界包含一个Lipschitz项，其因子，持有人项和对数项的频率为多项式增长，该术语相对于频率作为功率而衰减。为了从数值上验证这种提高的稳定性，我们提出了一种重建算法，目的是恢复足够多的电导率模式。数值证据阐明了增长频率的影响，并确认了在较高频率下的分辨率改善。
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system and in a simplified transverse electric mode are derived. These bounds contain a Lipschitz term with a factor growing polynomially in terms of the frequency, a Holder term, and a logarithmic term which decays with respect to the frequency as a power. To validate this increasing stability numerically, we propose a reconstruction algorithm aiming at the recovery of sufficiently many Fourier modes of the conductivity. A numerical evidence sheds light on the influence of the growing frequency and confirms the improved resolution at higher frequencies.
