The T-matrix for electromagnetic scattering is most commonly computed using the Extended Boundary Condition Method (EBCM), but this approach is numerically unstable for finite cylinders of high aspect ratio. In the electrostatics limit, we show that this instability is caused by catastrophic cancellations in the numerical calculations of oscillatory integrals. We find that the problematic integrals can instead be evaluated by integrating over the complement surface that extends from the cylinder to infinity. The resulting integrals are stable and we are then able to compute the electrostatic T-matrix accurately. The polarizability of the finite cylinder is then derived from this T-matrix and validated against results obtained via discretization. As an alternative, we also investigate the T-matrix on a basis of spheroidal harmonics, which is stable on its own and converges more quickly than on the spherical basis. Since the integrals are analytic, we moreover derive a simple analytic approximation based on truncation of the T-matrix on this basis. Beyond the direct benefits of analytic expressions for the electrostatic cylinder polarizability, this work should pave the way for a stable formulation of the full-wave T-matrix/EBCM approach for cylinders.

中文翻译：

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有限圆柱体的静电 T 矩阵和极化率的解析结果


电磁散射的 T 矩阵最常使用扩展边界条件法 （EBCM） 计算，但对于高纵横比的有限圆柱体，这种方法在数值上不稳定。在静电极限中，我们表明这种不稳定性是由振荡积分的数值计算中的灾难性抵消引起的。我们发现，有问题的积分可以通过对从圆柱体延伸到无穷大的补体表面进行积分来计算。得到的积分是稳定的，然后我们能够准确地计算静电 T 矩阵。然后从这个 T 矩阵中得出有限圆柱体的极化率，并根据通过离散化获得的结果进行验证。作为替代方案，我们还在球谐的基础上研究了 T 矩阵，它本身是稳定的，并且比球基收敛得更快。由于积分是解析的，因此我们还在此基础上基于 T 矩阵的截断推导出一个简单的解析近似。除了静电圆柱极化率的解析表达式的直接好处外，这项工作还为圆柱体全波 T 矩阵/EBCM 方法的稳定公式铺平了道路。