Processing of Near Singular Integrals in 3D Boundary Elements Method - Ali, Jaafar Khalaf (Basrah Journal for Engineering Sciences, 2009)
In this work, the efficiency of double Gauss quadrature method, used to integrate over a rectangular element in 3D BEM, has been investigated. The efficiency of a quadrature or integration scheme is investigated by estimating the critical ratio for which the absolute relative error of the numerical integration is less than 1×10^-6. As small as the critical ratio is, the quadrature is more efficient. Also, special transformation techniques have been introduced and used to increase the accuracy and efficiency of double Gauss quadrature especially for near singular cases, where the source point is very close to the element under consideration. Three types of kernels were considered, weak, strong and hyper singular kernels which can be encountered in the integral equation of 3D elastodynamics BEM problems.