A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements t...

An analysis of the regularized stokeslet method ⋆

A regularized boundary integral equation for exterior Stokes flow around rigid bodies in three dimensions is studied. The formulation is based on a free-space solution of the Stokes equations with concentrated, but smooth forcing and involves two regularization parameters that control the behavior of the free-space solution and the conditioning of the integral equation. The smooth free-space so...

The Boundary Integral Equation Method

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

k-Nearest Neighbour Classifiers

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier – classification is achieved by identifying the nearest neighbours to a query example and using those neighbours to determine the class of the query. This approach to classification is of particular importance today because issues of poor run-time performance is not such...