Fast algorithm for electrically small inhomogeneous medium structures

A fast algorithm is developed to solve electrically small composite object problems by applying low-frequency multilevel fast multipole algorithm (LF-MLFMA).; Firstly, contact-region modeling is applied to overcome the difficulty in determining loop bases on the complicated surface with branches and junctions of a composite object. A generalized surface integral equation formulation is presented based on contact-region modeling. Consequently, the interface boundary conditions are satisfied automatically by solving the integral equations and there is no need to express any interface or junction conditions explicitly.; Secondly, a scheme is presented to apply LF-MLFMA to composite object problems and O(N) CPU time and memory usage are obtained. Different MLFMA tree structures are applied to different regions, so that the efficiency of the algorithm is improved by not involving unnecessary bases in the calculation for each region.; Thirdly, a new implementation of basis rearrangement is presented, and problems with a large number of unknowns can be solved efficiently and accurately. A new method is also presented to analytically remove the cancellation in the excitation terms of both small and large loops, so that the excitation terms for practical structures with complicated geometries can be calculated accurately.; A new surface integral equation formulation for highly conductive materials is proposed by tuning the weighting coefficients of the integral equations for each region. Thus, the integration error due to small skin depth can be suppressed in the impedance matrix. Correct results are obtained over a significantly extended range of skin depths.; Finally, the conditions for low-frequency multilevel fast multipole algorithm and near-interaction approximation are determined from numerical tests and a low-cost approach for diagonal element estimation for highly conductive media is presented.; With the above accomplishments, electrically small composite structures involving lossless or lossy materials can be solved with O( N) computational cost.