On the H -LU-Based Fast Finite Element Direct Solver for 3-D Scattering Problems

Ming Lin Yang; Rui Qing Liu; Hong Wei Gao; Xin Qing Sheng

doi:10.1109/TAP.2018.2823774

On the H -LU-Based Fast Finite Element Direct Solver for 3-D Scattering Problems

Ming Lin Yang, Rui Qing Liu, Hong Wei Gao, Xin Qing Sheng^*

^*Corresponding author for this work

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

The nested dissection (ND) H -LU-based fast finite element (FE) direct solver is studied for scattering by large 3-D inhomogeneous objects. The special characteristics of the admissibility condition in FE method (FEM) are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional one. A better reduction scheme is presented for electrodynamic scattering problem. Numerical experiments show that our developed ND H -LU-based FE direct solver has O(NlogN) memory complexity and O(Nlog²N) CPU time complexity for a quasi-static problem, but a larger and irregular complexity for an electrodynamic problem. It has been compared with other most advanced direct sparse solvers and proved to have a better performance. A large realistic scattering problem with more than 10 million unknowns is calculated, showing the capability of our proposed ND-based H -LU direct FEM solver.

Original language	English
Pages (from-to)	3792-3797
Number of pages	6
Journal	IEEE Transactions on Antennas and Propagation
Volume	66
Issue number	7
DOIs	https://doi.org/10.1109/TAP.2018.2823774
Publication status	Published - Jul 2018

Keywords

3-D scattering
H-matrix
direct solution
finite element methods (FEMs)
nested dissection (ND)

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10.1109/TAP.2018.2823774

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title = "On the H -LU-Based Fast Finite Element Direct Solver for 3-D Scattering Problems",

abstract = "The nested dissection (ND) H -LU-based fast finite element (FE) direct solver is studied for scattering by large 3-D inhomogeneous objects. The special characteristics of the admissibility condition in FE method (FEM) are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional one. A better reduction scheme is presented for electrodynamic scattering problem. Numerical experiments show that our developed ND H -LU-based FE direct solver has O(NlogN) memory complexity and O(Nlog2N) CPU time complexity for a quasi-static problem, but a larger and irregular complexity for an electrodynamic problem. It has been compared with other most advanced direct sparse solvers and proved to have a better performance. A large realistic scattering problem with more than 10 million unknowns is calculated, showing the capability of our proposed ND-based H -LU direct FEM solver.",

keywords = "3-D scattering, H-matrix, direct solution, finite element methods (FEMs), nested dissection (ND)",

author = "Yang, {Ming Lin} and Liu, {Rui Qing} and Gao, {Hong Wei} and Sheng, {Xin Qing}",

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T1 - On the H -LU-Based Fast Finite Element Direct Solver for 3-D Scattering Problems

AU - Yang, Ming Lin

AU - Liu, Rui Qing

AU - Gao, Hong Wei

AU - Sheng, Xin Qing

PY - 2018/7

Y1 - 2018/7

N2 - The nested dissection (ND) H -LU-based fast finite element (FE) direct solver is studied for scattering by large 3-D inhomogeneous objects. The special characteristics of the admissibility condition in FE method (FEM) are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional one. A better reduction scheme is presented for electrodynamic scattering problem. Numerical experiments show that our developed ND H -LU-based FE direct solver has O(NlogN) memory complexity and O(Nlog2N) CPU time complexity for a quasi-static problem, but a larger and irregular complexity for an electrodynamic problem. It has been compared with other most advanced direct sparse solvers and proved to have a better performance. A large realistic scattering problem with more than 10 million unknowns is calculated, showing the capability of our proposed ND-based H -LU direct FEM solver.

AB - The nested dissection (ND) H -LU-based fast finite element (FE) direct solver is studied for scattering by large 3-D inhomogeneous objects. The special characteristics of the admissibility condition in FE method (FEM) are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional one. A better reduction scheme is presented for electrodynamic scattering problem. Numerical experiments show that our developed ND H -LU-based FE direct solver has O(NlogN) memory complexity and O(Nlog2N) CPU time complexity for a quasi-static problem, but a larger and irregular complexity for an electrodynamic problem. It has been compared with other most advanced direct sparse solvers and proved to have a better performance. A large realistic scattering problem with more than 10 million unknowns is calculated, showing the capability of our proposed ND-based H -LU direct FEM solver.

KW - 3-D scattering

KW - H-matrix

KW - direct solution

KW - finite element methods (FEMs)

KW - nested dissection (ND)

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JF - IEEE Transactions on Antennas and Propagation

IS - 7

ER -

On the H -LU-Based Fast Finite Element Direct Solver for 3-D Scattering Problems

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