The convergence rate of iterative methods can vary in an unpredictable way. It is related to the matrix condition number, which is notoriously bad for the electric field integral equation in the large-scale electromagnetic problems. Therefore, an efficient direct solution—a multilevel compressed block decomposition (MLCBD) algorithm based on the adaptive cross-approximation algorithm—is applied to overcome this problem; it is very efficient for the monostatic problems. Simulation results of the objects up and below ground in half space demonstrate that the proposed MLCBD method is efficient for analyzing electromagnetic problems. Copyright © 2013 John Wiley & Sons, Ltd.