Multilevel adaptive cross approximation (MLACA)

Tamayo, Jose M.; Heldring, A.; Rius, J.M.

doi:10.1109/aps.2009.5172344

Cited by 22 publications

(36 citation statements)

References 3 publications

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“…In this paper, a multilevel version of the FACA, termed as the MLFACA, is proposed to mitigate this problem. The MLFACA is based on the butterfly algorithm [4], [12] and can reduce both CPU time and storage of compressing…”

Section: B Mlfacamentioning

confidence: 99%

“…More recently, the multilevel ACA (MLACA) [12] and the sparsified ACA (SPACA) [13], [14] have been proposed to mitigate this problem. The MLACA uses the butterfly algorithm [4] and ACA-singular value decomposition (ACA-SVD) [15]- [17] to get a very high compression ratio of the impedance matrix, which results in an O(N log 2 N ) storage.…”

Section: Introductionmentioning

confidence: 99%

“…The MLACA uses the butterfly algorithm [4] and ACA-singular value decomposition (ACA-SVD) [15]- [17] to get a very high compression ratio of the impedance matrix, which results in an O(N log 2 N ) storage. However, its construction time of the compressed impedance matrix is still O(N 2 ) [12]. Therefore, the MLACA is faster than the single-level ACA only for large targets with more than a million unknowns [12].…”

Section: Introductionmentioning

confidence: 99%

“…However, its construction time of the compressed impedance matrix is still O(N 2 ) [12]. Therefore, the MLACA is faster than the single-level ACA only for large targets with more than a million unknowns [12]. The SPACA [13], [14] provides a faster and sparser truncated SVD of the impedance submatrix than the ACA-SVD, because it does not directly deal with the submatrix but an approximate expression of the submatrix.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this work is to present a more efficient ACAbased method, termed as multilevel fast ACA (MLFACA), which is based on the fast adaptive cross-sampling (FACS) [14] and the butterfly algorithm [4], [12]. The MLFACA can reduce both computational cost and storage to O(N log 2 N ).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

Chen

Ding

et al. 2015

IEEE Trans. Antennas Propagat.

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His research interests include computational electromagnetics, electromagnetic compatibility, antenna design, metamaterials and metasurfaces, spoof surface plasmon polaritons, and localized spoof plasmons.Ji Ding was born in Jiangsu, China, in 1984. He received the B.S. degree in electronic information science and technology, M.E. degree in electromagnetic field and microwave technology, and Ph.D. degree in communication and information system from

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Section: B Mlfacamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

Chen

Ding

et al. 2015

IEEE Trans. Antennas Propagat.

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Multiscale electromagnetic computations using a hierarchical multilevel fast multipole algorithm

2014

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A hierarchical multilevel fast multipole method (H-MLFMM) is proposed herein to accelerate the solutions of surface integral equation methods. The proposed algorithm is particularly suitable for solutions of wideband and multiscale electromagnetic problems. As documented in Zhao and Chew (2000) that the multilevel fast multipole method (MLFMM) achieves O(N log N) computational complexity in the fixed mesh size scenario, hk = cst, where h is the mesh size and k is the corresponding wave number, for problems discretized under conventional mesh density. However, its performance deteriorates drastically for overly dense meshes where the couplings between different groups are dominated by evanescent waves or circuit physics. In the H-MLFMM algorithm, two different types of basis functions are proposed to address these two different natures of physics corresponding to the electrical size of the elements. Specifically, for the propagating wave couplings, the plane wave basis function adopted by MLFMM are effective and they are inherited by H-MLFMM. Whereas in the circuit physics and for the evanescent waves, H-MLFMM employs the so-called skeleton basis. Moreover, the proposed H-MLFMM unifies the procedures to account for the couplings using these two distinct types of basis functions. O(N) complexity is observed for both memory and CPU time from a set of numerical examples with fixed mesh sizes. Numerical results are included to demonstrate that H-MLFMM is error controllable and robust for a wide range of applications.

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Multilevel adaptive cross approximation for efficient modeling of 3D arbitrary shaped eddy current NDE problems

Bao

Liu

Bowler

et al. 2019

NDT & E International

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In this article, the multilevel adaptive cross approximation (MLACA) algorithm is presented to accelerate the boundary element method (BEM) for eddy current nondestructive evaluation (NDE) 3D problems involving arbitrary shapes. The Stratton-Chu formula, which does not have the low frequency breakdown issue, has been selected for modeling. The equivalent electric and magnetic surface currents are expanded with Rao-Wilton-Glisson (RWG) vector basis functions while the normal component of the magnetic field is expanded with pulse basis functions. The MLACA compresses the rank deficient matrices with the ACA and the butterfly algorithm. We improve the efficiency of MLACA by truncating the integral kernels after a certain distance and applying the multi-stage (level) algorithm adaptively based on the criteria for different operators to further decrease the memory and CPU time requirements while keeping almost the same accuracy comparing with the traditional MLACA. The proposed method is especially helpful to deal with the large solution domain issue of the BEM for eddy current problems. Numerical predictions are compared with the analytical, the semi-analytical predictions and the experimental results for 3D eddy current NDE problems of practical interest to demonstrate the robustness and efficiency of the proposed method.Keywords-multilevel adaptive cross approximation (MLACA) algorithm, truncated integral kernels, boundary element method (BEM), eddy current testing (ECT), nondestructive testing (NDT)

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Multilevel adaptive cross approximation (MLACA)

Cited by 22 publications

References 3 publications

Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

Multiscale electromagnetic computations using a hierarchical multilevel fast multipole algorithm

Multilevel adaptive cross approximation for efficient modeling of 3D arbitrary shaped eddy current NDE problems

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