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This work investigates the feasibility of utilising the multilevel compressed block decomposition algorithm (MLCBD) to increase the efficiency of solving the matrix equation obtained from the finite-element method in the electromagnetic analysis. The MLCBD takes advantage of the low-rank approximation of each sub-matrix of the inverse matrix by truncating the information relative to the minor singular values. The choice of truncating tolerance will affect the accuracy and efficiency of the solution. Original MLCBD requires a small truncating threshold and uses a large amount of memory to yield a satisfying result. A novel technique is proposed to improve the solving efficiency by combining a less accurate truncating threshold in MLCBD with a rapid and cheap iterative refinement process. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed technique.