Benefited from the accuracy improvement in modeling physical problem of complex geometry and integrating the discretization and simulation, the isogeometric analysis in boundary element method (IGABEM) has been drawn a great deal of attention. The nearly singular integrals of 2D potential problem in the IGABEM are addressed by a semianalytical scheme in the present work. We use the subtraction technique to separate the integrals to singular and nonsingular parts, where the singular parts can be calculated by the analytical formulae derived by utilizing a series of integration by parts, while the nonsingular parts are calculated numerically with fewer quadrature points. Comparing the present semianalytical results with the ones of exact solutions, we find that the present method can obtain precise potential and flux densities of inner points much closer to the boundary without refining the elements nearby. Sufficient comparisons with other regularization schemes, such as the exponential and sinh transformation methods, are also conducted. The results in the numerical examples show the competitiveness of the present method, especially when calculating the nearly strongly and highly singular integrals during the simulation of the flux density.

中文翻译：

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用等几何边界元方法对二维电势问题中的奇异积分进行半解析分析

得益于复杂几何模型物理问题建模以及离散化和仿真集成的准确性的提高，边界元方法（IGABEM）的等几何分析引起了广泛关注。IGABEM中2D潜在问题的几乎奇异积分在本工作中通过半解析方案解决。我们使用减法技术将积分分离为奇异部分和非奇异部分，其中奇异部分可以通过利用利用一系列零件积分的方法得出的解析公式来计算，而非奇异部分则用较少的正交点进行数值计算。将目前的半分析结果与精确的解决方案进行比较，我们发现，本方法可以获得精确的势能和更接近边界的内部点的通量密度，而无需细化附近的元素。还与其他正则化方案（例如指数和正弦变换方法）进行了充分比较。数值示例中的结果显示了本方法的竞争力，特别是在通量密度模拟过程中计算近强且高度奇异的积分时。