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Classical scattering theory of waves from the viewpoint of an eigenvalue problem and a

机译：从特征值问题和问题的角度看经典的波散射理论

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Abstract: The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWEs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology is explained in detail and examples are presented. !13
机译：摘要：亥姆霍兹-庞加莱波动方程（H-PWE）出现在经典波散射理论的许多领域。特别是对于浸没在边界的物体的声散射和物体的电磁散射的情况。扩展边界积分方程（EBIE）方法是通过考虑H-PWE的外部和内部解而得出的。这种耦合的表达式集的优点不仅在于为获得外部散射问题提供了解决方案的处方，而且还消除了与虚拟内部特征值相对应的不规则值的问题。一旦导出耦合方程，就可以通过将所有相关项扩展为部分波展开（包括格林函数的双正交展开）而以矩阵形式获得。然而，在表面膨胀的选择上有一些选择的自由度，因为只要获得封闭，未知的表面量可以以各种方式膨胀。在许多可能的选择中，我们基于与物体表面有关的最佳本征函数，开发了一种获得此类扩展的最佳方法。实际上，我们将部分问题（与第一类Fredholms积分方程相关联的问题）转换为相关Hermition算符的特征值问题。对该方法进行了详细说明，并提供了示例。 ！13

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