  A boundary integral formulation of electromagnetics that involves only the
components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use
of surface currents that appear in the classical PMCHWT formulation. The
kernels of the boundary integral equations for $\boldsymbol{E}$ and
$\boldsymbol{H}$ are non-singular so that all field quantities at the surface
can be determined to high precision and also geometries with closely spaced
surfaces present no numerical difficulties. Quadratic elements can readily be
used to represent the surfaces so that the surface integrals can be calculated
to higher numerical precision than using planar elements for the same numbers
of degrees of freedom.
