Application of multilevel directional adaptive cross approximation technique for electromagnetic problems. (English) Zbl 1403.78034
Summary: In this paper, a novel scheme is presented for forming the matrix equations of multilevel adaptive cross approximation (MLACA) algorithm. The main idea of the proposed technique is to use the directional grouping scheme to subdivide the far-field domain of MLACA algorithm. By using the grouping scheme, the far-field interaction domain can be divided into many cone structures. The matrix between the observation group and far-field group in the cone structure is low-rank, which meets the directional far-field requirement. At the same time, the near-field interaction matrices are formed by the SVD(T) method to further reduce the total memory requirements. With the given techniques, the memory requirement of the novel grouping scheme for the far-field is much less than half of traditional MLACA algorithm. Meanwhile, the memory requirement of the SVD(T) method for the near-field is only about one-third of direct filling.
MSC:
| 78M25 | Numerical methods in optics (MSC2010) |
| 65R20 | Numerical methods for integral equations |
| 45E05 | Integral equations with kernels of Cauchy type |
| 78A25 | Electromagnetic theory (general) |
Keywords:
multilevel directional adaptive cross approximation (MLDACA) algorithm; low-rank; directional grouping schemeReferences:
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