We present a variant of a boundary integral equation proposed by M. Herberthson in 2008–2010 for high-frequency plane wave scattering by perfectly conducting obstacles. This integral equation, as some of its predecessors, is entirely dedicated to a single direction of incidence. A significant reduction in the system size can then be obtained by looking for a pseudo-current, which is the actual surface current multiplied by the conjugate of the incident wave’s phase function. This advantage is mostly lost when multiincidence problems have to be solved because, in addition to the source terms, the discretized operator must be recomputed for every new incidence. In this article, we make an explicit representation of the new operator as the sum of a conventional electric field integral equation (EFIE) which is independent of the direction of incidence, and an additional operator, which is dependent on the direction of incidence. The latter can be computed very efficiently such that a net performance gain is obtained with respect to the EFIE even for multiincidence problems.

中文翻译：

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平面波散射专用积分方程

我们提出了 M. Herberthson 在 2008-2010 年提出的边界积分方程的变体，用于完美传导障碍物的高频平面波散射。这个积分方程，就像它的一些前辈一样，完全致力于单一的入射方向。然后可以通过寻找伪电流来显着减小系统尺寸，伪电流是实际表面电流乘以入射波相位函数的共轭。当必须解决多重发生问题时，这种优势通常会失去，因为除了源项之外，必须为每个新发生重新计算离散化算子。在本文中，我们将新算子明确表示为与入射方向无关的常规电场积分方程 (EFIE) 的总和，和一个额外的运算符，它取决于入射方向。后者可以非常有效地计算，这样即使对于多发病问题，也可以获得相对于 EFIE 的净性能增益。