Block Diagonalization of the Electromagnetic Impedance Matrix of a Symmetric Buried Body Using Group Theory

A major problem with the volume-current integral-equation technique of three-dimensional electromagnetic modeling is the computational time and-storage required to form and solve the impedance matrix equation for the scattering currents. If the horizontal cross sections of a body with vertical sides all possess a certain symmetry, the matrix contains information about the effect of the symmetry on the scattering currents. This information can be deduced easily using group representation theory independent of any numerical computation or particular incident field geometry, and the original matrix, containing redundant informnation, can be replaced by a block-diagonal matrix. A straightforward example is used to illustrate this general technique. The computer storage requirements and solution time for the block-diagonalized matrix equation are significantly smaller than those for the original matrix equation.