An Iterative Random Sampling Algorithm for Rapid and Scalable Estimation of Matrix Spectra

Kelley, Jon T.; Yılmaz, Ali E.; Brick, Yaniv

doi:10.1109/jmmct.2023.3263152

Cited by 6 publications

(2 citation statements)

References 41 publications

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“…Lastly, we consider a U-shaped scatterer as shown in Figure 11, which, when an octree is used for partitioning, will produce block-structured sub-matrices of the forms ( 16), (17), and (23). The outer side length of the U-profile is 1 m, and its thickness is 0.1 m. We consider discretizations with ranging from 3219 to 145 791 for testing.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The standard choice, also in the case of the EFIE [10], to select the rows and columns used for the approximation is the so-called partial pivoting [9], [10], [17], [18], where given a row (or column) the next column (or row) is selected by searching for the maximal element in modulo. However, when partial pivoting is used, the ACA is not error-controllable, and numerous works deal with improving convergence without jeopardizing the complexity [19]- [22]; in addition to those works, rapid rank-estimations such as in [23] have been suggested to be used as "guard rails" to prevent premature convergence [24].…”

Section: Introductionmentioning

confidence: 99%

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On the Adaptive Cross Approximation for the Magnetic Field Integral Equation

Tetzner,

Adrian

2024

Preprint

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We present an adaptive cross approximation (ACA) strategy for the magnetic field integral equation (MFIE), where an application of the standard ACA strategy can suffer from early convergence, in particular, due to block-structured interaction matrices associated with well-separated source and test domains. Our scheme relies on a combination of three pivoting strategies, where the active strategy is determined by a convergence criterion that extends the standard criterion with a mean-based random sampling criterion; the random samples give rise to one of the pivoting strategies, while the other two are based on (standard) partial pivoting and fill-distance pivoting. In contrast to other techniques, the purely algebraic nature as well as the quasilinear complexity of the ACA for electrically small problems are maintained. Numerical results show the effectiveness of our approach.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Adaptive Cross Approximation for the Magnetic Field Integral Equation

Tetzner,

Adrian

2024

Preprint

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Multi-Mode Analysis of Scattering by Bodies of Revolutions via the Combined-Field Integral Equation

Sepehripour

Hon

Beurden

2023

IEEE J. Multiscale Multiphys. Comput. Tech.

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Nested Pseudo Skeleton Approximation Algorithm for Generating ${\mathcal H}^{2}$-Matrix Representations of Electrically Large Surface Integral Equations

Yang,

Jiao

2024

IEEE J. Multiscale Multiphys. Comput. Tech.

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An Iterative Random Sampling Algorithm for Rapid and Scalable Estimation of Matrix Spectra

Cited by 6 publications

References 41 publications

On the Adaptive Cross Approximation for the Magnetic Field Integral Equation

On the Adaptive Cross Approximation for the Magnetic Field Integral Equation

Multi-Mode Analysis of Scattering by Bodies of Revolutions via the Combined-Field Integral Equation

Nested Pseudo Skeleton Approximation Algorithm for Generating ${\mathcal H}^{2}$-Matrix Representations of Electrically Large Surface Integral Equations

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