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Application of a two‐step preconditioning strategy to the finite element analysis for electromagnetic problems
Author(s) -
Rui P. L.,
Chen R. S.,
Yung Edward K. N.,
Chan C. H.
Publication year - 2006
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.21683
Subject(s) - preconditioner , conjugate gradient method , finite element method , iterative method , mathematics , matrix (chemical analysis) , linear system , helmholtz equation , convergence (economics) , computer science , algorithm , mathematical analysis , engineering , boundary value problem , materials science , structural engineering , economics , composite material , economic growth
A two‐step preconditioning strategy is presented for the conjugate gradient (CG) iterative method to solve a large system of linear equations resulting from the use of edge‐based finite‐element discretizations of Helmholtz equations. The key idea is to combine both the factorized sparse approximate inverse (FSAI) and the symmetric successive overrelaxation (SSOR) preconditioning techniques in two successive steps in order to obtain a better preconditioner for the original matrix equations. The newly constructed preconditioner combines the advantages of both the FSAI and SSOR preconditioners with less computational complexity without the breakdowns of incomplete factorization technique. Numerical simulations show that this jointly preconditioned CG iterative method has a faster convergence speed than both FSAI and SSOR preconditioned CG methods. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1623–1627, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21683