Transformation of hypersingular integrals and black-box cubature
Transformation of hypersingular integrals and black-box cubature
复制标题
超奇异积分和黑盒体积的变换
作者：
S. Sauter;C. Lage
在本文中，我们将考虑由椭圆型边值问题转化为边界积分方程而产生的超奇异积分。首先，将推导这些积分的局部表示。这些表示包含了所谓的有限部分积分。第二步，将这些积分重新表述为反常积分。我们将证明这些积分可以用文献中存在的弱奇异积分的培养方法来处理。
In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals. In the second step, these integrals are reformulated as improper integrals. We will show that these integrals can be treated by cubature methods for weakly singular integrals as they exist in the literature.