On the computation of nearly singular integrals in 3D BEM collocation.

*(English)*Zbl 1195.74256Summary: We propose an efficient strategy to compute nearly singular integrals over planar triangles in \(\mathbb{R}^{3}\) arising in boundary element method collocation. The strategy is based on a proper use of various nonlinear transformations, which smooth or move away or quite eliminate all the singularities close to the domain of integration. We will deal with near singularities of the form 1/\(r\), \(1/r^{2}\) and \(1/r^{3}\), \(r=\| x - y \|\) being the distance between a fixed near observation point \(x\) and a generic point \(y\) of a triangular element. Extensive numerical tests and comparisons with some already existing methods show that the approach proposed here is highly efficient and competitive.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

65N38 | Boundary element methods for boundary value problems involving PDEs |

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\textit{L. Scuderi}, Int. J. Numer. Methods Eng. 74, No. 11, 1733--1770 (2008; Zbl 1195.74256)

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