Tucker-FMM-FFT -Accelerated SIE Solver for Large-Scale Electromagnetic Analysis

A tensor decomposition methodology is combined with the fast multipole method-fast Fourier transform (FMM-FFT) technique to accelerate the surface integral equation (SIE) solvers. The proposed methodology leverages Tucker and hierarchical Tucker (H-Tucker) decompositions to compress the three-dimensional (3D) arrays storing the far-fields and five-dimensional (5D) arrays storing the translation operator samples, respectively. The compressed tensors are then used in the matrix-vector and element-wise products in aggregation/disaggregation and translation stages. By doing so, all stages of the FMM-FFT are performed via the Tucker-compressed tensors. The resulting Tucker-FMM-FFT-accelerated SIE simulator is far more memory and CPU efficient than the traditional FMM-FFT-accelerated SIE simulators. Preliminary results show that the Tucker-Fmm - Fftacceleration technique requires 12x less memory and 17x less CPU time compared to the traditional FMM-FFT acceleration technique for the electromagnetic (EM) scattering analysis of a frequency-selective surface.