  The extended boundary condition method (EBCM) was formulated for the
perturbation of a source electric potential by a
  3D object composed of a homogeneous anisotropic dielectric medium whose
relative permittivity dyadic is positive definite. The formulation required the
application of Green's second identity to the exterior region to deduce the
electrostatic counterpart of the Ewald--Oseen extinction theorem. The electric
potential inside the object was represented using a basis obtained by
implementing an affine bijective transformation of space to the Gauss equation
for the electric field. The EBCM yields a transition matrix that depends on the
geometry and the composition of the 3D object, but not on the source potential.
