An Efficient Higher-Order Parallel MLFMA with Hybrid Singularity Cancellation Strategy

Applying higher-order technologies to method of moments (MoM) and multilevel fast multipole algorithm (MLFMA) will commonly encounter the crisis of singularity cancellation. To obtain satisfactory accuracy and computational efficiency, parallel MLFMA based on surface integral equations (SIEs) together with a hybrid singularity cancellation strategy (HSCS) is presented in this paper. For electric field integral equation (EFIE) singularities and near singularities, an improved Duffy's transform is employed; while for magnetic field integral equation (MFIE) singularities, nonoverlapping integration rules for source and field elements are adopted to calculate the principle value term. Performance of this proposed approach is demonstrated via preliminary numerical results.