Low-Rank Matrix Factorization Method for Multiscale Simulations: A Review
| Autor: | Mengmeng Li, Giuseppe Vecchi, Jun Hu, Dazhi Ding, Rushan Chen, Alexander Heldring |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Teoria del Senyal i Comunicacions, Universitat Politècnica de Catalunya. ANTENNALAB - Grup d'Antenes i Sistemes Radio |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Multiscale
method of moments Computational complexity theory Computation Method of moments Equacions integrals low-rank Matrix decomposition lcsh:Telecommunication Computational complexity Low-rank Matrix (mathematics) Informàtica::Informàtica teòrica [Àrees temàtiques de la UPC] Kernel (image processing) Factorization multiscale lcsh:TK5101-6720 Applied mathematics Integral equation Algebraic number Integral equations Complexitat computacional Mathematics Sparse matrix |
| Zdroj: | IEEE Open Journal of Antennas and Propagation, Vol 2, Pp 286-301 (2021) UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| ISSN: | 2637-6431 6187-1222 |
| Popis: | In this paper, a review of the low-rank factorization method is presented, with emphasis on their application to multiscale problems. Low-rank matrix factorization methods exploit the rankdeficient nature of coupling impedance matrix blocks between two separated groups. They are widely used, because they are purely algebraic and kernel free. To improve the computation precision and efficiency of low-rank based methods, the improved sampling technologies of adaptive cross approximation (ACA), post compression methods, and the nested low-rank factorizations are introduced. O(N) and O (NlogN) computation complexity of the nested equivalence source approximation can be achieved in low and high frequency regime, which is parallel to the multilevel fast multipole algorithm, N is the number of unknowns. Efficient direct solution and high efficiency preconditioning techniques can be achieved with the low-rank factorization matrices. The trade-off between computation efficiency and time are discussed with respect to the number of levels for low-rank factorizations. This work was supported in part by the Natural Science Foundation of China under Grant 61871222, Grant 62025109, Grant 61890541, Grant 61931021, and Grant 61721001; and in part by the Spanish Government under Project TEC 2017-83343-C4-2-R and Project MDM-2016-0600. |
| Databáze: | OpenAIRE |
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