Multilevel Adaptive Cross Approximation (MLACA)

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

doi:10.1109/tap.2011.2165476

Cited by 74 publications

(25 citation statements)

References 18 publications

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“…Some approaches such as the Dual Modified Gram Schmidt block-QR-factorization [11] or the block IE-QR approach presented in [12] also offer the advantage of not having to assemble the full submatrix before performing the compression. The Adaptive Cross Approximation method [13] also presents the same advantage and has been extensively studied and applied in the last years, including error and convergence analysis [14,15], multilevel and hierarchical implementations [16,17] or combinations with other fast approaches such as MLFMA [18] or the Characteristic Basis Function Method [19].…”

Section: Improving the Efficiency Of The Moment Methodsmentioning

confidence: 99%

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

Delgado¹,

García²,

Moreno³

et al. 2015

PIER

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Abstract-This paper presents an evolution of the challenges and solutions found in the application of techniques based on the Method of Moments until the present day. The original MoM presented very high computational restrictions that have motivated the development of more efficient approaches. The main features of these newer improvements are presented, as well as other technical details regarding preconditioning and parallelization techniques. Some representative examples are shown in order to assert the suitability of these approaches for the analysis of complex and realistic scenarios.

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Section: Improving the Efficiency Of The Moment Methodsmentioning

confidence: 99%

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

Delgado¹,

García²,

Moreno³

et al. 2015

PIER

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“…HSS construction is implemented in a multilevel fashion as described in [34], and essentially, its multilevel compression can be considered comparable to the one used in the multilevel ACA (MLACA) algorithm [17]. Furthermore, so-called multilevel "butterfly" algorithms [37]- [38], as well as the fast solver presented in [39], have a similar basis to the multilevel compression coupled with low-rank matrix representation.…”

Section: Efficient Scalable Parallel Higher Order Directmentioning

confidence: 99%

Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

Manic

Smull

Rouet

et al. 2017

IEEE Trans. Antennas Propagat.

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Abstract-A novel fast scalable parallel algorithm is proposed for the solution of large 3-D scattering problems based on: 1) the double (geometrical and current-approximation) higher order (DHO) method of moments (MoM) in the surface integral equation (SIE) formulation and 2) a direct solver for dense linear systems utilizing hierarchically semiseparable (HSS) structures. Namely, an HSS matrix representation is used for compression, factorization, and solution of the system matrix. In addition, a rank-revealing QR decomposition for memory compression is used, with a stopping criterion in terms of the relative rank tolerance value. A method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the HSS algorithm accuracy and parallelization. Numerical examples show how the accuracy of the DHO HSS-MoM-SIE method is easily controllable by using the relative tolerance for the matrix compression. Moreover, the examples demonstrate low memory consumption, as well as much faster simulation time, when compared to the direct LU decomposition. The method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low-order discretizations. Finally, great scalability of the algorithm is demonstrated on more than one thousand processes.Index Terms-Curved parametric elements, direct solvers, fast solvers, hierarchically semiseparable (HSS) structures, higher order (HO) modeling, low-rank matrix approximation, method of moments (MoM), multilevel matrix compression, numerical algorithms, parallelization, polynomial basis functions, scalability, scattering, surface integral equation (SIE).

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“…Besides, this can be done in a recursive scheme (each subregion can be split into many subregions to exhibit smaller off-diagonal blocks to compress) with a Multi-Level ACA [13], or also with the formalism of H-matrix theory [16,17]. This is not applied here for the two impedance matricesZ 11 andZ 22 sincē Z 11 is quite small (for an object of small or moderate size) and applying MLACA or H-matrix theory can be more expensive than a direct inversion; and forZ 22 , the FBSA is already used which provides a low complexity: only O(P FB N 2 N s ) for the computation of the local interactions on S 2 (inversion ofZ 2 and computation of the matrix-vector productZ −1 2 u, where u is a vector).…”

Section: Epile+fbsa Combined With Acamentioning

confidence: 99%

“…Thus, in order to accelerate the matrix-vector products involved in the coupling steps, a recent algebraic method called Adaptive Cross Approximation (ACA) is applied to compress the coupling matrices. This method, developed in 2000 by Bebendorf [7,8], was then applied to electromagnetics [9][10][11][12][13] and can be seen as a truncated and partially pivoted Gaussian elimination [7].…”

Section: Introductionmentioning

confidence: 99%

A Fast Epile+fbsa Method Combined With Adaptive Cross Approximation for the Scattering From a Target Above a Large Ocean-Like Surface

Kubické¹,

Bourlier²,

Bellez³

et al. 2014

PIER M

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Abstract-The rigorous evaluation of the NRCS (Normalized Radar Cross Section) of an object above a one-dimensional sea surface (2D case) needs to numerically solve a set of discretized integral equations involving a large number of unknowns. Thus, the direct solution of the impedance matrix equation via LU decomposition becomes the most expensive step in the MoM (Method of Moments) procedure. So, in order to minimize the computation cost, the iterative domain decomposition method called EPILE (Extended Propagation-Inside-Layer Expansion) was used and then was combined with the FBSA (Forward-Backward with Spectral Acceleration) to calculate the local interactions on the rough sea surface. The resulting fast method is called EPILE+FBSA. In this paper, we take advantage of the rank-deficient nature of the coupling matrices, corresponding to the object-surface interactions, to further reduce the complexity of the method by using the ACA (Adaptive Cross Approximation). Thus, the coupling matrices are strongly compressed without a loss of accuracy and the memory requirement is then strongly reduced. For a cylinder above a rough sea surface, the results show the efficiency of the accelerated EPILE+FBSA+ACA method.

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Multilevel Adaptive Cross Approximation (MLACA)

Cited by 74 publications

References 18 publications

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

A Fast Epile+fbsa Method Combined With Adaptive Cross Approximation for the Scattering From a Target Above a Large Ocean-Like Surface

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