Partly approximate iteration technique for accelerating CG-MLFMA solution

To further expedite the solution of the conjugate gradient iteration multilevel fast multipole algorithm (CG-MLFMA), we have developed a partly approximate iteration technique. When the iterative error is lower than the critical iteration error (CIE), the matrix-vector multiplication can be computed approximately by the interactions from the nearby region. The CIE is determined by the contributions of the nearby region and the accuracy required. Compared to the interactions from the non-nearby region, the interactions from the nearby region only possess a very small portion of the total complexity. Because the number of iterations needed in the presented method does not increase dramatically, total CPU time can be reduced greatly. Numerical results are given to demonstrate the validity and efficiency of the presented method.