A New Straightforward Method for Evaluating Singular Integrals

Evaluating Singular and Nearly Singular Integrals Numerically

A General New Algorithm for Regulaization of Singular Integrals in Three-Dimensional Boundary Elemnts

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

A Method for Computing Nearly Singular Integrals

We develop a method for computing a nearly singular integral, such as a double layer potential due to sources on a curve in the plane, evaluated at a point near the curve. The approach is to regularize the singularity and obtain a preliminary value from a standard quadrature rule. We then add corrections for the errors due to smoothing and discretization, which are found by asymptotic analysis....

A General New Algorithm for Regulaization of Singular Integrals in Three-Dimensional Boundary Elemnts

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

An efficient method for evaluating BEM singular integrals on curved elements with application in acoustic analysis

The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the aspect ratio of the element is large or (2) the field point is closed to the element boundary; thus a large number of quadrature points are needed to achieve a...