  I present an accurate and efficient technique for numerical evaluation of
singular 6-dimensional integrals over tetrahedon-product domains, with
applications to calculation of Galerkin matrix elements for discretized
volume-integral-equation (VIE) solvers using Schaubert-Wilton-Glisson (SWG) and
other tetrahedral basis functions. My method extends the generalized
Taylor-Duffy strategy---used to handle the singular \textit{triangle}-product
integrals arising in discretized surface-integral-equation (SIE)
formulations---to the tetrahedron-product case; it effects an exact
transformation of a singular 6-dimensional integral to an nonsingular
lower-dimensional integral that may be evaluated by simple numerical cubature
The method is highly general and may---with the aid of automatic code
generation facilitated by computer-algebra systems---be applied to a wide
variety of singular integrals arising in various VIE formulations with various
types of tetrahedral basis function, of which I present several examples. To
demonstrate the accuracy and efficiency of my method, I apply it to the
calculation of matrix elements for the volume electric-field integral equation
(VEFIE) discretized with SWG basis functions, where the method yields 12-digit
or higher accuracy with low computational cost---an improvement of many orders
of magnitude compared to existing techniques.
