Analytical removal of singularities and one-dimensional integration of three-dimensional boundary element method kernels

• Published in: Engineering analysis Vol. 4; no. 1; pp. 21 - 24
• Main Authors: Aliabadi, M.H., Hall, W.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1987
• ISSN: 0264-682X
• DOI: 10.1016/0264-682X(87)90028-1

The boundary element method for potential problems requires the evaluation of integrands which are singular due to the presence of the inverse of distances between points on the boundary. One method of dealing with the problem of evaluating these integrals numerically is to transform triangular surface elements to square local plane elements. Quadrilateral surface elements can also be treated by dividing them up into triangles. This introduces a Jacobian which has the form of a local plane distance and tends to zero so providing a cancelling effect. It is known that such cancelling is numerically8 effective. However, it has not been clear whether the local plance cancels tha distance exactly so that, as they each tend to zero, their ratio remains finite. It is shown here, using an expansion method, that cancelling is exact. It is further shown that the surface integration can be reduced to a regular line integration which implies a significant reduction in the amount of calculation.