Adaptive Mixed-Form Fast Multipole Method for the Analysis of Electromagnetic Scattering - Chen, H.; Fan, Z. H.; Chen, R. S.; Jiang, Z. N.; Li, M. M. (Applied Computational Electromagnetics Society Journal (ACES), 2022)
To analyze an electrically large object with local fine structures, the conventional mixed form fast multipole algorithm requires that the boxes of the finest level are all with the same size, which belongs to the low-frequency region. This scheme is deficient since the mesh size is limited by the box size of the finest level, which is related to the finest parts of the object. In this paper, an efficient adaptive grouping scheme is introduced into a mixed-form fast multipole algorithm. In an adaptive mixed-form fast multipole algorithm, the number of unknowns in each non-empty box of the finest level is almost the same which results in the box of the finest level may be in a different frequency regime with a different size. Hence multipole expansions are employed, if the boxes located in the low frequency regime while the plane wave expansions are employed if the boxes located in the mid-frequency regime. Numerical results are given to show that the proposed approach is efficient to analyze the objects with many fine structures.