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Proposes a new parallelized incomplete Cholesky conjugate gradient (ICCG) solver effective on a small-scale multiprocessor system. The new method is based on a new reordering technique, namely the block red-black ordering method. Its parallel performance is evaluated in a finite edge-element eddy-current analysis. A numerical test shows that the proposed method is effective on a small number of processors due to fast convergence and low communication costs.