FAST, PROVABLY HIGH-ORDER ACCURATE METHODS FOR VOLUME INTEGRAL OPERATORS

Volume integral operators (VIOs) are fundamental tools for solving volumetric problems with integral equation methods, including wave scattering problems in inhomogeneous media. We will discuss a treatment using Green’s third identity and a local polynomial interpolant of the density function that transforms a VIO into regularized VIOs (as well as layer potentials, and a polynomial PDE solution): the regularized operators can be evaluated to provably high- order accuracy using entirely generic volumetric quadrature and can make efficient use of fast algorithms. Detailed error and stability analysis is provided in two dimensions, including connections to quadrature of functions of limited regularity at isolated points.