An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral

Rui Qing Liu; Ming Lin Yang; Bi Yi Wu; Xin Qing Sheng

doi:10.1109/NEMO49486.2020.9343483

An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral

Rui Qing Liu, Ming Lin Yang, Bi Yi Wu, Xin Qing Sheng

School of Integrated Circuits and Electronics

Beijing Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A flexible and efficient mathcal{H}-LU-based preconditioner (mathcal{H}-LU-P) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for solving 3D scattering by inhomogeneous objects in this paper. The formulation of FE-BI is firstly approximated by using locally approximated integral operators for the BI part to construct a FEM-ABC based precondition matrix. Then the precondition matrix equation is solved by the nested dissection (ND) accelerated mathcal{H}-LU-based fast direct solver. Performance of the mathcal{H}-LU-P is studied numerically for different problems, including the quasi-static problem, 2D extended and 3D extended electrodynamic problems, etc. Numerical experiments show the mathcal{H}-LU-P has an O(NlogN) memory complexity and an O(Nlog2N) CPU time complexity for the quasi-static, the 2D extended lossless and the 3D extended lossy problems. For the 3D extended lossless problems, the complexity is larger due to the increasing rank of the mathcal{H}-LU, but it still outperforms alternative direct solvers, such as the popular multifrontal-based solver MUMPS. Large realistic scattering problems with more than ten million unknowns are calculated, including a honeycomb structure with 8100 elements, showing the capability and efficiency of our proposed preconditioner.

Original language	English
Title of host publication	2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728169668
DOIs	https://doi.org/10.1109/NEMO49486.2020.9343483
Publication status	Published - 7 Dec 2020
Event	2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020 - Hangzhou, China Duration: 7 Dec 2020 → 9 Dec 2020

Publication series

Name	2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020

Conference

Conference	2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020
Country/Territory	China
City	Hangzhou
Period	7/12/20 → 9/12/20

Keywords

3D scattering
FE-BI-MLFMA
H-LU
nested dissection
preconditioner

Access to Document

10.1109/NEMO49486.2020.9343483

Cite this

Liu, R. Q., Yang, M. L., Wu, B. Y., & Sheng, X. Q. (2020). An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral. In 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020 Article 9343483 (2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/NEMO49486.2020.9343483

Liu, Rui Qing ; Yang, Ming Lin ; Wu, Bi Yi et al. / An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral. 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020. Institute of Electrical and Electronics Engineers Inc., 2020. (2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020).

@inproceedings{d90b35eb39054dfbb083b44360469266,

title = "An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral",

abstract = "A flexible and efficient mathcal{H}-LU-based preconditioner (mathcal{H}-LU-P) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for solving 3D scattering by inhomogeneous objects in this paper. The formulation of FE-BI is firstly approximated by using locally approximated integral operators for the BI part to construct a FEM-ABC based precondition matrix. Then the precondition matrix equation is solved by the nested dissection (ND) accelerated mathcal{H}-LU-based fast direct solver. Performance of the mathcal{H}-LU-P is studied numerically for different problems, including the quasi-static problem, 2D extended and 3D extended electrodynamic problems, etc. Numerical experiments show the mathcal{H}-LU-P has an O(NlogN) memory complexity and an O(Nlog2N) CPU time complexity for the quasi-static, the 2D extended lossless and the 3D extended lossy problems. For the 3D extended lossless problems, the complexity is larger due to the increasing rank of the mathcal{H}-LU, but it still outperforms alternative direct solvers, such as the popular multifrontal-based solver MUMPS. Large realistic scattering problems with more than ten million unknowns are calculated, including a honeycomb structure with 8100 elements, showing the capability and efficiency of our proposed preconditioner.",

keywords = "3D scattering, FE-BI-MLFMA, H-LU, nested dissection, preconditioner",

author = "Liu, {Rui Qing} and Yang, {Ming Lin} and Wu, {Bi Yi} and Sheng, {Xin Qing}",

note = "Publisher Copyright: {\textcopyright} 2020 IEEE.; 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020 ; Conference date: 07-12-2020 Through 09-12-2020",

year = "2020",

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language = "English",

series = "2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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address = "United States",

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Liu, RQ, Yang, ML , Wu, BY & Sheng, XQ 2020, An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral. in 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020., 9343483, 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020, Institute of Electrical and Electronics Engineers Inc., 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020, Hangzhou, China, 7/12/20. https://doi.org/10.1109/NEMO49486.2020.9343483

An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral. / Liu, Rui Qing; Yang, Ming Lin ; Wu, Bi Yi et al.
2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020. Institute of Electrical and Electronics Engineers Inc., 2020. 9343483 (2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral

AU - Liu, Rui Qing

AU - Yang, Ming Lin

AU - Wu, Bi Yi

AU - Sheng, Xin Qing

PY - 2020/12/7

Y1 - 2020/12/7

N2 - A flexible and efficient mathcal{H}-LU-based preconditioner (mathcal{H}-LU-P) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for solving 3D scattering by inhomogeneous objects in this paper. The formulation of FE-BI is firstly approximated by using locally approximated integral operators for the BI part to construct a FEM-ABC based precondition matrix. Then the precondition matrix equation is solved by the nested dissection (ND) accelerated mathcal{H}-LU-based fast direct solver. Performance of the mathcal{H}-LU-P is studied numerically for different problems, including the quasi-static problem, 2D extended and 3D extended electrodynamic problems, etc. Numerical experiments show the mathcal{H}-LU-P has an O(NlogN) memory complexity and an O(Nlog2N) CPU time complexity for the quasi-static, the 2D extended lossless and the 3D extended lossy problems. For the 3D extended lossless problems, the complexity is larger due to the increasing rank of the mathcal{H}-LU, but it still outperforms alternative direct solvers, such as the popular multifrontal-based solver MUMPS. Large realistic scattering problems with more than ten million unknowns are calculated, including a honeycomb structure with 8100 elements, showing the capability and efficiency of our proposed preconditioner.

AB - A flexible and efficient mathcal{H}-LU-based preconditioner (mathcal{H}-LU-P) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for solving 3D scattering by inhomogeneous objects in this paper. The formulation of FE-BI is firstly approximated by using locally approximated integral operators for the BI part to construct a FEM-ABC based precondition matrix. Then the precondition matrix equation is solved by the nested dissection (ND) accelerated mathcal{H}-LU-based fast direct solver. Performance of the mathcal{H}-LU-P is studied numerically for different problems, including the quasi-static problem, 2D extended and 3D extended electrodynamic problems, etc. Numerical experiments show the mathcal{H}-LU-P has an O(NlogN) memory complexity and an O(Nlog2N) CPU time complexity for the quasi-static, the 2D extended lossless and the 3D extended lossy problems. For the 3D extended lossless problems, the complexity is larger due to the increasing rank of the mathcal{H}-LU, but it still outperforms alternative direct solvers, such as the popular multifrontal-based solver MUMPS. Large realistic scattering problems with more than ten million unknowns are calculated, including a honeycomb structure with 8100 elements, showing the capability and efficiency of our proposed preconditioner.

KW - 3D scattering

KW - FE-BI-MLFMA

KW - H-LU

KW - nested dissection

KW - preconditioner

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U2 - 10.1109/NEMO49486.2020.9343483

DO - 10.1109/NEMO49486.2020.9343483

M3 - Conference contribution

AN - SCOPUS:85101255535

T3 - 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020

BT - 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020

Y2 - 7 December 2020 through 9 December 2020

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Liu RQ, Yang ML , Wu BY , Sheng XQ. An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral. In 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020. Institute of Electrical and Electronics Engineers Inc. 2020. 9343483. (2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization, NEMO 2020). doi: 10.1109/NEMO49486.2020.9343483

An H-LU Preconditioner for the Hybrid Finite Element-Bomdaty Integral

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