The Unimoment Method as Applied to Three-Dimensional Scattering in a Conductive Medium

Electromagnetic scattering is perhaps one of the most widely used techniques for remote sensing. It has been widely used for radar, medical imaging, and nondestructive testing. Historically many of these applications have required an empirical approach to development due to the lack of good methods for solving Maxwell's equations in all but the most trivial of cases. Recent advances in computer performance have made it possible to solve most problems numerically. This dissertation reports numerical solutions to three dimensional electromagnetic scattering problems. In particular, low frequency scattering in a conductive medium is addressed. No constraint is placed upon the geometry of the scattering object other than that it must be of finite extent. Solutions of two simple problems are reported and compared with analytical results to evaluate the performance of the techniques developed. The solution is carried out in the frequency domain by coupling a multipole expansion with a finite element expansion. This is accomplished by placing an artificial spherical boundary around the scattering object. The interior of the sphere is modeled by a series of linearly independent finite element solutions obtained by applying a linearly independent set of Dirichlet boundary conditions at the surface of the sphere. A multipole expansion is carried out for the scattered field in the region outside the sphere. The expansion coefficients for these two series solutions are obtained via a point matching algorithm. Numerical results are validated against analytical solutions. Excellent results are obtained for the tests cases reported. For both test cases reported the numerical and analytical solutions agree to within 5%. Further, the dissertation clearly demonstrates the computational efficiency of the Unimoment Method. To obtain comparable results via other methods would require the use of finite element meshes which are at least an order of magnitude larger.