We consider the three-dimensional problem of diffraction of a monochromatic electromagnetic wave by a system of objects of various physical nature, including dielectric bodies (domains), perfectly conducting bodies, and perfectly conducting screens. The perfectly conducting bodies may be placed in an exterior medium or immersed into the dielectric domains. In addition, the perfectly conducting screens may reside at the interface of the dielectric domains, being part of each of those. We give a boundary value problem for the Maxwell equations that describes the electromagnetic field under consideration. Integral representations are derived for the electromagnetic field in terms of surface integrals, and the boundary value problem is reduced to a system of boundary integral equations containing weakly and strongly singular surface integrals. The integral equations are written on the dielectric and perfectly conducting parts of the interface between the dielectric domains, on the surfaces of the perfectly conducting bodies, and on the perfectly conducting screens.

中文翻译：

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单色电磁波衍射问题中的边界积分方程方法由完全导电和分段均匀介电物体系统

我们考虑由各种物理性质的物体组成的系统对单色电磁波的衍射的三维问题，包括介电体（域）、完美导电体和完美导电屏幕。完美导电体可以放置在外部介质中或浸入介电域中。此外，完美导电的屏幕可能位于介电域的界面处，是每个介电域的一部分。我们给出了描述所考虑的电磁场的麦克斯韦方程的边值问题。根据表面积分推导出电磁场的积分表示，并将边值问题简化为包含弱奇异和强奇异表面积分的边界积分方程组。