Closed-form solutions are derived for the regular and adjacent-singular integrals involving the two-dimensional Laplacian’s Green’s function and its normal derivative that arise in the Galerkin BEM. Motivation for their use is provided by comparing the accuracy and time required to compute the BEM system matrix relative to traditional numerical integration. Specifically, it is shown that the use of the closed-form solutions reduces computation time to produce the influence matrices by approximately 95% relative to Gauss quadrature with similar accuracy. All elements of these matrices are then expressed in a form convenient for implementation.

中文翻译：

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Galerkin BEM 闭式二维势公式的积分评估

对于包含二维拉普拉斯格林函数及其在伽辽金边界元法中出现的正规导数的正则和相邻奇异积分，推导出封闭形式的解。通过比较计算边界元系统矩阵相对于传统数值积分所需的精度和时间，提供了使用它们的动机。具体而言，结果表明，相对于具有相似精度的高斯正交，使用封闭形式的解决方案将生成影响矩阵的计算时间减少了大约 95%。然后，这些矩阵的所有元素都以便于实现的形式表示。