Fast monostatic RCS computation in FEM based solvers using QR decomposition

Venkatarayalu, Neelakantam; Gan, Yeow-Beng; Zhao, Kun; Lee, Jin Fa

doi:10.1109/eucap.2006.4584497

Cited by 7 publications

(2 citation statements)

References 2 publications

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“…In addition to block iterative solvers, other efforts are underway, which reduce the dimension of multiple RHSs itself. Low-rank approximation with singular value decomposition (SVD) [12], asymptotic waveform evaluation (AWE) [13], [14], and model-based parameter estimation (MBPE) [15], [16] are well-known methods. In addition, [11] introduced a novel method that uses Fourier harmonics to construct excitation matrices.…”

Section: Introductionmentioning

confidence: 99%

An Efficient and Error-Controllable Angular Sweep Algorithm for Electromagnetic Wave Scattering and its Analysis

Lee

Kotulski

Dang

et al. 2023

IEEE Trans. Antennas Propagat.

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The angular sweep of electromagnetic wave scattering is formulated as a matrix equation with multiple right-hand sides (RHSs). Although the low-rank approximation of an RHS matrix is a popular choice for reducing the computational costs of multiple RHSs, only a small amount of research has been conducted to explore how this approximation impacts the solution quality. Furthermore, there has not been sufficient research on the quality of the solution as a function of the accuracy of the iterative solver. We present an error analysis of the approximated solution considering both the reduced number of RHSs and the tolerance of the iterative solver. Based on the error analysis, a new angular sweep algorithm is proposed with fine-tuned tolerances of the iterative solver for individual singular vectors. The different tolerances for each singular vector increase the efficiency of the proposed algorithm. Another benefit of the proposed algorithm is that the error can be bounded by a user-defined global tolerance. Additionally, a variant of the generalized conjugate residual method for multiple RHSs is introduced to accelerate iterative solvers. Finally, numerical validation is conducted with three examples in which the discontinuous Galerkin surface integral equation method is applied. The experiments support two conclusions: tight upper and lower bounds of the solution error exist, and fine-tuning the tolerances reduces the computational costs.

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Section: Introductionmentioning

confidence: 99%

An Efficient and Error-Controllable Angular Sweep Algorithm for Electromagnetic Wave Scattering and its Analysis

Lee

Kotulski

Dang

et al. 2023

IEEE Trans. Antennas Propagat.

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show abstract

“…Over the past few years, many algorithms have been developed to reduce the computational cost of the MRCS calculations [2][3][4][5][6][7][8][9][10][11][12]. In [2], the MRCS was evaluated approximately using the results of bistatic radar cross-sections.…”

Section: Introductionmentioning

confidence: 99%

Fast monostatic radar cross‐section computation for perfectly electric conducting targets using low‐rank compression and adaptive integral method

Lü

2014

IET Microwaves, Antennas & Propagation

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The adaptive integral method (AIM) in conjunction with the low‐rank compression method is developed to calculate the monostatic radar cross‐section (RCS) of arbitrarily shaped three‐dimensional perfectly electric conducting objects. For backscattering problems, the excitation matrix is usually highly rank‐deficient and can be compressed via low‐rank techniques without explicitly assembling the original matrix beforehand. Therefore, only the matrix equations corresponding to the linearly independent excitation vectors need to be solved, whose number is much less than that of incident angles. As a result, fast monostatic RCS calculation over a widely angular range can be achieved. To facilitate the analysis of electrical large problems, the AIM is applied to accelerate the matrix–vector product and reduce the memory usage. Numerical examples are presented to demonstrate the validity and efficiency of the method.

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Efficient Generation of Aggregative Basis Functions in the Marching-on-in-Degree Time-Domain Integral Equation Solver

et al. 2013

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Fast monostatic RCS computation in FEM based solvers using QR decomposition

Cited by 7 publications

References 2 publications

An Efficient and Error-Controllable Angular Sweep Algorithm for Electromagnetic Wave Scattering and its Analysis

An Efficient and Error-Controllable Angular Sweep Algorithm for Electromagnetic Wave Scattering and its Analysis

Fast monostatic radar cross‐section computation for perfectly electric conducting targets using low‐rank compression and adaptive integral method

Efficient Generation of Aggregative Basis Functions in the Marching-on-in-Degree Time-Domain Integral Equation Solver

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