论文标题
对几何学对电磁体中皮肤效应的影响
On the influence of the geometry on skin effect in electromagnetism
论文作者
论文摘要
我们考虑在电导率较大的机制中，在由电介质和导体子域制成的域上设置的电磁方程。假设介电 - 导电器界面的平滑度依赖于最近的作品，我们证明，麦克斯韦方程的解决方案可以接收一个多尺度渐近扩张，其轮廓术语迅速衰减导体内部。通过引入皮肤深度功能来衡量这种皮肤效果，该功能取决于导体边界的平均曲率。然后，我们通过各种轴对称构型中的数值实验来确认这些渐近结果。我们还以数值方式研究了非平滑界面的情况，即圆柱形导体。
We consider the equations of electromagnetism set on a domain made of a dielectric and a conductor subdomain in a regime where the conductivity is large. Assuming smoothness for the dielectric--conductor interface, relying on recent works we prove that the solution of the Maxwell equations admits a multiscale asymptotic expansion with profile terms rapidly decaying inside the conductor. This skin effect is measured by introducing a skin depth function that turns out to depend on the mean curvature of the boundary of the conductor. We then confirm these asymptotic results by numerical experiments in various axisymmetric configurations. We also investigate numerically the case of a nonsmooth interface, namely a cylindrical conductor.
