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A fast domain decomposition method based on orthogonal polynomials approximation for solving electromagnetic scattering problems
Author(s) -
Lü ZhiQing,
An Xiang
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.25734
Subject(s) - matrix (chemical analysis) , matrix decomposition , factorization , multiplication (music) , mathematics , domain decomposition methods , set (abstract data type) , algorithm , rank (graph theory) , domain (mathematical analysis) , computer science , computational science , finite element method , mathematical analysis , physics , combinatorics , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , thermodynamics , programming language
The partial basic solution vector based domain decomposition method (PBSV‐DDM) is well suited for solving large‐scale finite periodic electromagnetic problems.In this work, a new implementation scheme is developed to improve the efficiency of the PBSV‐DDM. A set of orthogonal polynomials is introduced to approximate the transmission condition between adjacent subdomains, which results in solving for the polynomial coefficients instead of the dual unknowns. The major advantages of the proposed method are: (i) the computational cost and the memory requirement for the PBSV matrix are decreased significantly; (ii) the computational efforts of the matrix‐vector multiplication during iterations can also be reduced greatly; (iii) in contrast with the rank‐revealing matrix factorization based DDM, this method does not need to explicitly produce the entire PBSV matrix in advance. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:357–361, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25734