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We propose the recent progress in fast integral multiscale simulations in our group in this contribution. Firstly, a wideband fast kernel independent fast solver is proposed. The equivalence sources on designed equivalence surface are introduced to obtain the nested low rank approximation. At the low to mid frequency, thanks to the nested low rank approximation, the computation complexity of the proposed...
A nested complex source beam (NCSB) method based on the method of moment (MoM) solution is proposed for electromagnetic scattering analysis. In the finest level, the far field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed evenly on the equivalent surface for every group. Furthermore, the far-field coupling of CSBs in the son level group also...
A domain decomposition method based on equivalence principle algorithm is used for analyzing and calculating radiation problems of large-scale arrays. The adaptive cross approximation method is introduced to accelerate computing the translate operator, and the repeatability of the array is removed. Numerical results demonstrate that the time consumption and the memory usage are all reduced.
A fast wideband electromagnetic scattering analysis method based on Taylor expansion and higher order hierarchical vector basis functions is proposed. By extracting a phase term from the green function, the remaining exponent term can be approximated by its truncated Taylor expansion. After that, some computationally intensive matrices related to the geometry of the object can be computed in advance...
Wepresent a new developed rank based method, namely the Wideband Nested Equivalent Source Approximation (WNESA) method for multiscale problems. The low rank approximation of WNESA is constructed after introducing equivalent vector source distributions on properly defined equivalence surfaces enclosing the coupling groups. The equivalent vector sources are determined by an inverse-source process that...
A doubly hierarchical method of moments (MoM) is proposed for the analysis of large scale multiscale structures. The separate handling of the high and low frequency interactions of the MLMCM/MLFMA is exploited to efficiently analyze multi-scale structures; the resulting system is further preconditioned following the MR-ILU approach, which has proven successful for solving multi-scale complex structures...
The asymptotic waveform evaluation (AWE) technique is proposed with a preprocessing technique which is achieved by the arbitrarily dimensional fast lifting wavelet-like transform. With the new preprocessing technique, the sparse matrix equation in wavelet-domain is formed firstly. The wide band solution of this sparse linear system is obtained by application of AWE technique, and the actual induced...
A direct rational approximation method based on Thiele interpolating continued fractions theory is proposed for fast frequency sweep analysis of electromagnetic problems. And an adaptive algorithm is also formed. Compared with the conventional rational approximation method, the proposed method can get a rational approximation directly without a great number of matrix inverse computations and doesn't...
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