Hierarchical quadrature for multidimensional singular integrals

Composite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions

The computation of wavelet coefficients of a function typically requires the computation of a large number of integrals. These integrals represent the inner product of that function with a wavelet function on different scales, or with the corresponding scaling function on a fine scale. We develop quadrature rules for those integrals that converge fast for piecewise smooth and singular functions...

Hierarchical quadrature for multidimensional singular integrals - Part II

In a previous part I, we introduced a method for the evaluation of singular integrals arising in the discretization of integral equations based on the repeated subdivision of domains. The integrals defined on these subdomains are classified such that a class of integrals can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the rela...

Evaluation of Singular Integrals by Hyperbolic Tangent Based Transformations

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations...

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...

Quadrature Rules for Fuzzy Integrals