A Novel Multilevel Matrix Compression Method for Analysis of Electromagnetic Scattering From PEC Targets

Li, Mengmeng; Li, Chunyan; Ong, Chong‐Jin; Tang, Wanchun

doi:10.1109/tap.2011.2180310

Cited by 11 publications

(21 citation statements)

References 19 publications

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“…In this paper, we use two different and complementary fast factorization methods: The recently introduced MLMCM [11] is used to factorize the near-field region part, and the MLFMA is used for the far field region. For this class of hybrid MLFMA methods addressing multiscale problems, the state of the art is essentially in [13]- [22].…”

Section: Doubly Hierarchical Reciprocal Mlmcm (Rmlmcm) /Mlfma Anmentioning

confidence: 99%

“…Straightforward application of MoM would yield a dense matrix whose storage and computation efforts prohibit use with large practical problems. This calls for iterative solutions and fast factorizations; this is a largely studied field, with several solutions available for different frequency regimes [4]- [9], [11]- [30] (and references therein).…”

Section: Introductionmentioning

confidence: 99%

“…The solver is inspired by a recently proposed low-frequency fast solver, namely the multiLevel matrix compression method (MLMCM) [11]; in this study, it is combined with the multilevel fast multipole algorithm (MLFMA) [12] to efficiently treat large scale ("high frequency") interactions; the system is then effectively preconditioned with the MR-ILU approach [8], [9], a multiscale preconditioner which has proven very effective to tackle mixed frequency problems.…”

Section: Introductionmentioning

confidence: 99%

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A Doubly Hierarchical MoM for High-Fidelity Modeling of Multiscale Structures

Francavilla

Vipiana

et al. 2014

IEEE Trans. Electromagn. Compat.

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We propose a novel doubly hierarchical method of moments for the analysis of large and multiscale structures. A reciprocal multilevel matrix compression method (rMLMCM) is combined with the multilevel fast multipole algorithm (MLFMA), and they are used for the small-scale and large-scale cluster interactions, respectively. The resulting system is preconditioned following the hierarchical multiresolution-incomplete LU approach, which has proven successful for solving multiscale complex structures. The proposed method is applied to electromagnetic compatibility analysis of the real life, complex structures. Numerical results demonstrate the proposed preconditioned rMLMCM/MLFMA is effective also for large structures with strongly nonuniform discretization.Index Terms-Electromagnetic compatibility (EMC), fast solver, integral equations, method of moments (MoM), multiresolution (MR), multiscale, preconditioning.

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Section: Doubly Hierarchical Reciprocal Mlmcm (Rmlmcm) /Mlfma Anmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Doubly Hierarchical MoM for High-Fidelity Modeling of Multiscale Structures

Francavilla

Vipiana

et al. 2014

IEEE Trans. Electromagn. Compat.

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“…Fast factorizations, based on the compression of memory requirements and on the speed-up of Matrix-Vector (MV) products, obviously do not address the illconditioning problem (their intrinsic kernel approximation tends to worsen the conditioning of the system indeed). In particular, the approach proposed in [1], where the MultiLevel Matrix Compression Method (MLMCM) is combined with a MultiLevel Fast Multipole Approach (MLFMA) is a fast solver particularly well suited for multiscale problems, as it handles differently high and low frequency couplings, via MLFMA and MLMCM respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we fully ibridize the MLMCM/MLFMA fast solver proposed in [1] with the MR-ILU preconditioner proposed in [5].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical MoM for the analysis of high-definition multiscale structures

Fan

Chen

et al. 2013

2013 IEEE Antennas and Propagation Society International Symposium (APSURSI)

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A doubly hierarchical method of moments (MoM) is proposed for the analysis of large scale multiscale structures. The separate handling of the high and low frequency interactions of the MLMCM/MLFMA is exploited to efficiently analyze multiscale structures; the resulting system is further preconditioned following the MR-ILU approach, which has proven successful for solving multi-scale complex structures. Numerical results are shown to prove the effectiveness of the proposed approach.

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A fast direct matrix solver for surface integral equation methods for electromagnetic wave scattering from non‐penetrable targets

2012

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[1] The implementation details of a fast direct solver is described herein for solving dense matrix equations from the application of surface integral equation methods for electromagnetic field scatterings from non-penetrable targets. The proposed algorithm exploits the smoothness of the far field and computes a low rank decomposition of the off-diagonal coupling blocks of the matrices through a set of skeletonization processes. Moreover, an artificial surface (the Huygens' surface) is introduced for each clustering group to efficiently account for the couplings between well-separated groups. Furthermore, a recursive multilevel version of the algorithm is presented. Although asymptotically the algorithm would not alter the bleak outlook of the complexity of the worst case scenario, O(N 3 ) for required CPU time where N denotes the number of unknowns, for electrically large electromagnetic (EM) problems; through numerical examples, we found that the proposed multilevel direct solver can scale as good as O(N ) in CPU time for moderate-sized EM problems. Note that our conclusions are drawn based on a few sample examples that we have conducted and should not be taken as a true complexity analysis for general electrodynamic applications. However, for the fixed frequency (h-refinement) scenario, where the discretization size decreases, the computational complexities observed agree well with the theoretical predictions. Namely, the algorithm exhibits O(N ) and O(N

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A Novel Multilevel Matrix Compression Method for Analysis of Electromagnetic Scattering From PEC Targets

Cited by 11 publications

References 19 publications

A Doubly Hierarchical MoM for High-Fidelity Modeling of Multiscale Structures

A Doubly Hierarchical MoM for High-Fidelity Modeling of Multiscale Structures

Hierarchical MoM for the analysis of high-definition multiscale structures

A fast direct matrix solver for surface integral equation methods for electromagnetic wave scattering from non‐penetrable targets

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