The system of equations of electrodynamics is considered for a nonmagnetic nonconducting medium. For this system, the problem is under study of determining the permittivity ε from the given modulus of the electric intensity vector of the electromagnetic field that is the result of the interference of the two fields generated by some point sources of an extraneous current. It is assumed that permittivity is different from a given positive constant ε₀ only inside a compact domain Ω₀ ⊂ ℝ³, whereas the modulus of the electric field intensity vector is given for all frequencies starting from a fixed frequency ω₀ on the boundary S of some domain Ω that includes Ω₀. It is shown that this information allows us to reduce the original problem to the well-known inverse kinematic problem of determining the refraction index inside Ω by the travel time of the electromagnetic wave between the points of the boundary of this domain. The algorithm for numerical solution of the inverse problem is constructed, and the test calculations on the simulated data are presented.

中文翻译：

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用电磁场强度矢量模量确定介电常数的一种数值方法。

对于非磁性非导电介质，应考虑电动力学方程组。对于该系统，正在研究根据给定的电磁场电强度矢量模量确定介电常数ε的方法，该模量是由外部电流的某些点源产生的两个场的干扰的结果。据推测，介电常数为从给定的正的常数不同ε ₀仅在一个紧凑域Ω ₀ ⊂ℝ ³，而电场强度矢量的模，给出了从一个固定频率开始的所有频率ω ₀的边界小号包含Ω的某个域Ω的₀。结果表明，该信息使我们能够将原始问题简化为众所周知的逆运动学问题，该逆运动学问题是通过电磁波在该区域边界点之间的传播时间来确定Ω内的折射率的。构建了反问题数值求解算法，并给出了对仿真数据的测试计算。