Preconditioned MDA-SVD-MLFMA for Analysis of Multi-Scale Problems

摘要

Multilevel fast multipole algorithm (MLFMA) has been widely used to solve electromagnetic scattering problems from the electrically large size objects. However, it consumes very large memory to store near the interaction matrix for the object with fine structures because the "low frequency breakdown" phenomenon would happen when the finest level box's size is below 0.2 wavelengths. The matrix decomposition algorithm - singular value decomposition (MDA-SVD) is one remedy to alleviate this pressure because it has no limit of the box's size. However, the matrix assembly time of MDA-SVD is much longer than that of the MLFMA. In this paper, a hybrid method called MDA-SVD-MLFMA is proposed to analyze multi-scale problems, which uses the main framework of MLFMA but adopts the MDA-SVD to deal with the near interaction of MLFMA. This method takes advantage of the virtues of both MLFMA and MDA-SVD and is more efficient than either conventional MLFMA or conventional MDA-SVD. An efficient preconditioning technique is combined into the inner-outer flexible generalized minimal residual (FGMRES) solver to speed up the convergence rate. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.