Abstract: A method and apparatus for simulating a mesh element of an anisotropic medium are provided. A unitary transformation is applied to an initial coordinate system of the mesh element by a transformation module to produce a transformed reference coordinate system of the mesh element. Maxwell's equations for the mesh element are solved by an update generation module using computational methods to obtain an electric field tensor and an electric displacement field tensor within the mesh element. A unitary transformation to the electric field tensor and the electric displacement tensor are performed by a transformation module to calculate a corresponding electric field tensor and electric displacement tensor for the mesh element in the initial coordinate system.