Numerical Quadrature Over Bounded Smooth Surfaces

This talk describes a high order accurate method to calculate integrals over smooth surfaces with boundaries. Given data locations that are arbitrarily distributed over the surface, together with some functional description of the surface and its boundary, the algorithm produces matching quadrature weights. This extends on our earlier methods for integrating over the surface of a sphere and over arbitrarily shaped smooth closed surfaces by now considering domain boundaries. The core approach consists of combining RBF-FD (radial basis function-generated finite difference) approximations for curved surface triangles, which together make up the full surface. A discussion of proposed applications is included.