关于边界元法中对数奇点积分的更多信息

T. Rymarczyk, J. Sikora
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摘要

本文介绍了用两种方法计算具有对数奇异点的积分的精确度,即忽略奇异点的方法和减法(包括将奇异点部分与其余非奇异点部分分开)。本文只考虑了二维问题,如狄利克特问题,以及在频域中提出的声学问题。本文讨论了与计算精度有关的问题,并指出了频率以及分析区域几何形状对计算精度的影响。当我们谈到几何形状的影响时,我们指的不仅是离散化,还包括区域的配置,例如边界线的尖锐边缘,假定使用经典的边界元素法,不做任何修改。
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SOME MORE ON LOGARITHMIC SINGULARITY INTEGRATION IN BOUNDARY ELEMENT METOD
The accuracy of calculations of integrals with logarithmic singularities for two methods, namely the method of ignoring singularities and the method of subtraction (consisting in separating the singular part from the remaining non-singular), are presented in this paper. Only two-dimensional problems, like Dirichlet's problems, as well as acoustic problems formulated in the frequency domain are considered. Problems related to the accuracy of calculations are discussed and the influence of frequency, as well as the influence of the geometry of the analysed area on the accuracy of calculations, are indicated. When we talk about the influence of geometry, we mean not only discretization, but also the configuration of the area, such as the sharp edges of the boundary line, assuming the use of the classic, without any modifications, Boundary Element Method.
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