Methods for computing singular and nearly singular integrals

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....

Journal of Turbulence Jot Methods for Computing Singular and Nearly Singular Integrals *

Many scientific problems are formulated in terms of singular integrals. We describe a simple method for computing such integrals. Our approach is to replace a singularity, or near singularity, with a regularized version, compute a sum in a standard way, and then add correction terms, which are found by asymptotic analysis near the singularity. We have used this approach for a single-layer poten...

Evaluating Singular and Nearly Singular Integrals Numerically

A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with a regularized kernel and corrections are added for regularization and discretization, which are found from analysis near the singular point. The surface inte...

On Computing Smooth, Singular, and Nearly Singular Integrals on Implicitly Defined Surfaces

Mathematics) On Computing Smooth, Singular, and Nearly Singular Integrals on Implicitly Defined Surfaces by Jason R. Wilson Department of Mathematics Duke University