A multilevel matrix decomposition algorithm for analyzing scattering from large structures

Michielssen, E.; Boag, Amir

doi:10.1109/8.511816

Cited by 320 publications

(282 citation statements)

References 18 publications

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“…When the criterion is met, the serial numbers of the sampled columns and rows are saved. With them, according to the matrix decomposition algorithm (MDA) [10], M can be decomposed into…”

Section: Principle Of Facamentioning

confidence: 99%

A Hybrid Method to Accelerate the Calculation of Two-Dimensional Monostatic Radar Cross Section on Pec Targets

Fei¹,

Chen²,

Zhang³

et al. 2016

PIER M

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Abstract-This paper proposes a hybrid method to accelerate the calculation of the monostatic radar cross section (RCS) of perfect electric conducting (PEC) targets. In a sense, the proposed method can be considered as a fast adaptive cross approximation (FACA)-based method. The FACA is firstly used to compress the excitation matrix which comes from the beforehand defined incident plane waves. It decreases the time and memory on decomposing the excitation matrix compared with the conventional adaptive cross approximation (ACA). Furthermore, the computational complexity of iterative solution is reduced by using the sparsified ACA (SPACA) algorithm after dividing the target into blocks. Consequently, the proposed method is efficient for calculating two-dimensional (2D) monostatic RCS.

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“…When the criterion is met, the serial numbers of the sampled columns and rows are saved. With them, according to the matrix decomposition algorithm (MDA) [10], M can be decomposed into…”

Section: Principle Of Facamentioning

confidence: 99%

A Hybrid Method to Accelerate the Calculation of Two-Dimensional Monostatic Radar Cross Section on Pec Targets

Fei¹,

Chen²,

Zhang³

et al. 2016

PIER M

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“…Altogether, the generation and compression of the impedance matrix is presently typically the bottleneck of the tool in terms of computational time. At UPC-UAB, an efficient implementation of the Matrix Decomposition Algorithm (MDA) [5,7] has been developed that highly accelerates the compression procedure, avoiding entirely the need to construct the full original matrix blocks. The next integration step within the ACE framework will be to release a version of MDA to the partners that can be integrated with their MoM code.…”

Section: Cbdmentioning

confidence: 99%

Integration of UPC-UAB fast solvers into the antenna simulation software of UNEX-UPM, KUL, UPV and EPFL ace partners

Heldring

Rius

Tamayo

et al. 2007

2nd European Conference on Antennas and Propagation (EuCAP 2007)

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Software integration between Antennas Centre of Excellence (ACE) partners is one of the main activities of the Antenna Software Initiative (ASI) work package. This paper will present the results of integrating the CBD fast direct solver for large systems of equations, developed at UPC AntennaLab, into the antenna simulation codes of UPM-UNEX, KUL, UPV and EPFL ACE partners. A non-ACE group (UAB) is closely cooperating with UPC in the development of fast solvers.

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“…It is directly applicable to almost any MoM formulation and substantially reduces the storage and computational cost with respect to straightforward LU decomposition. The method is based on a blockwise compression of the impedance matrix (see Section II), by the same technique as used in the matrix decomposition algorithm (MDA) [4]- [6]. The compressed matrix is then decomposed using an adapted version of the block LU algorithm previously published in [9] and [10], which allows to retain the original compression rate (see Section III-A).…”

Section: Introductionmentioning

confidence: 99%

“…Its main drawback, the costly construction, storage, and solution of a dense linear system, has led to the development of several fast algorithms such as AIM [2], MLFMA [3], and Multilevel MDA [4]- [6]. Most of these algorithms are based on some approximative compressed representation of the linear system matrix, or impedance matrix, that needs much less storage and highly accelerates the matrix-vector multiplications.…”

Section: Introductionmentioning

confidence: 99%

Fast direct solution of the method of moments linear system

Heldring

Tamayo

Rius

2006

2006 First European Conference on Antennas and Propagation

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Abstract-A novel algorithm, the compressed block decomposition (CBD), is presented for highly accelerated direct (noniterative) method of moments (MoM) solution of electromagnetic scattering and radiation problems. The algorithm is based on a block-wise subdivision of the MoM impedance matrix. Impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly, but approximated in a compressed form. Subsequently, the matrix is decomposed preserving the compression. Examples are presented of typical problems in the range of 5000 to 70 000 unknowns. The total execution time for the largest problem is about 1 h and 20 min for a single excitation vector. The main strength of the method is for problems with multiple excitation vectors (monostatic RCS computations) due to the negligible extra cost for each new excitation. For radiation and scattering problems in free space, the numerical complexity of the algorithm is shown to be 2 and the storage requirements scale with 3 2 . Index Terms-Fast solvers, impedance matrix compression, method of moments (MoM), numerical simulation.

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A multilevel matrix decomposition algorithm for analyzing scattering from large structures

Cited by 320 publications

References 18 publications

A Hybrid Method to Accelerate the Calculation of Two-Dimensional Monostatic Radar Cross Section on Pec Targets

A Hybrid Method to Accelerate the Calculation of Two-Dimensional Monostatic Radar Cross Section on Pec Targets

Integration of UPC-UAB fast solvers into the antenna simulation software of UNEX-UPM, KUL, UPV and EPFL ace partners

Fast direct solution of the method of moments linear system

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