Multiscale Compressed Block Decomposition Method With Characteristic Basis Function Method and Fast Adaptive Cross Approximation

In this paper, a fast adaptive cross approximation (FACA) algorithm and the characteristic basis function method (CBFM) are presented to accelerate the computing processing in using the multiscale compressed block decomposition (MS-CBD) method in direct solutions of electrically large problems. The impedance matrix or the reduced matrix can be compressed into block matrices of the MS-CBD structure using the FACA. With the recursive inversion processes on the reduced matrix, it is easy to obtain the solutions. Combined with the fast adaptive cross sampling and the matrix decomposition algorithm method, the speed of the calculation of FACA is proved much faster than that of the conventional adaptive cross approximation. The numerical results of several perfect electric conducting objects are validated to demonstrate the performance of this method. The simulation results show that the computational time of the proposed method is much less than the conventional MS-CBD method with the CBFM, while their computational storages are similar.