On a Hermite boundary integral approximation

A cubic Hermite approximation for two-dimensional boundary integral analysis is presented. The method differs from previous Hermite interpolation algorithms in that the gradient equations are sparse, significantly reducing the computational cost, and in that information about the surface normals is incorporated to effect a cubic interpolation of the geometry. A motivation for the development of this approximation is in the solution of moving boundary problems, as high accuracy and surface gradients are required for these simulations.