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Hierarchical LU decomposition‐based direct method with improved solution for 3D scattering problems in FEM
Author(s) -
Wan Ting,
Hu Xiao Qing,
Chen Ru Shan
Publication year - 2011
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.26122
Subject(s) - lu decomposition , finite element method , matrix (chemical analysis) , sparse matrix , logarithm , matrix decomposition , algorithm , scattering , decomposition , microwave , mathematics , computer science , computational science , mathematical optimization , mathematical analysis , physics , materials science , optics , eigenvalues and eigenvectors , quantum mechanics , ecology , telecommunications , composite material , biology , gaussian , thermodynamics
An efficient direct method based on hierarchical LU (H‐LU) Decomposition is developed for the solution of large sparse finite element systems.On the basis of hierarchical matrix (H‐matrix) technique, H‐LU direct method provides a data‐sparse way to approximate the LU‐factors of a finite element matrix which are dense originally. The approximate LU‐factors can be computed and stored in the algebra of H‐matrices with logarithmic‐linear complexity. The accuracy of this approximation is controllable related to the different choices of the H‐matrix parameters. A modification algorithm is proposed to efficiently improve the accuracy of the approximate solution computed by the H‐LU‐based direct method. Some numerical examples are provided to illustrate the accuracy and efficiency of the proposed method for finite element analysis of three‐dimensional (3D) electromagnetic scattering problems. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26122