Dual variational formulation of the electrostatic problem in an inhomogeneous anisotropic dielectric (Q2403570)

The authors develop a dual variational formulation of an electrostatic problem in an inhomogeneous anisotropic medium. Solutions to the Maxwell equations with this method can be obtained using numerical or approximate analytical techniques. The integral mean square error of the solution can also be estimated. This dual formulation includes two functionals, which allow for estimates of the capacity of a virtual capacitor with an inhomogeneous anisotropic dielectric. These functionals can also be used to obtain estimates for the dielectric permittivity of a material including a composite with randomly oriented anisotropic inclusions.