Sparsity-Aware Precorrected Tensor Train Algorithm for Fast Solution of 2-D Scattering Problems and Current Flow Modeling on Unstructured Meshes

Chen, Zhuotong; Gomez, Luis J.; Zheng, Shucheng; Yücel, Abdulkadir C.; Zhang, Zheng; Okhmatovski, Vladimir

doi:10.1109/tmtt.2019.2948873

Cited by 9 publications

(2 citation statements)

References 27 publications

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“…So far, a plethora of methods has been developed to lower the memory and CPU time requirements of VIE solvers [4]- [12]. These methods were primarily developed to expedite the matrix-vector multiplications during the iterative solution of the VIE system.…”

Section: Introductionmentioning

confidence: 99%

“…These methods were primarily developed to expedite the matrix-vector multiplications during the iterative solution of the VIE system. They leverage analytic or algebraic compression techniques, including the fast multipole method (FMM) [4], [5], fast Fourier transform [6]- [8], [13], low-rank compression [9], hierarchical matrices as kernel-free FMM [10], [11], and, more recently, tensor decompositions [12]. Despite the success of these methods in expediting matrixvector multiplications during iterative solution, the discretized VIE systems are often ill-conditioned.…”

Section: Introductionmentioning

confidence: 99%

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A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

Sayed,

Liu,

Gomez

et al. 2021

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A butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N ) construction cost of the HOD-BF-compressed system matrix and O(N 1.5 log N ) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

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Section: Introductionmentioning

confidence: 99%