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Accelerated engineering design optimization using successive matrix inversion method
Author(s) -
Bae HaRok,
Grandhi Ramana V.,
Canfield Robert A.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1545
Subject(s) - preconditioner , iterative method , solver , mathematical optimization , inversion (geology) , robustness (evolution) , computation , computer science , algorithm , series (stratigraphy) , mathematics , structural basin , gene , biology , paleontology , biochemistry , chemistry
In a design optimization procedure, many repeated system analyses are conducted to evaluate certain performances of successively modified structural designs. To alleviate the high computational cost of structural reanalysis, an augmented preconditioner is introduced by using the successive matrix inversion (SMI) method. The SMI method, as an exact matrix solver, is successively applied to an iterative procedure to accelerate the solution convergence by improving the numerical condition of the reanalysis system. In this work, a new iterative technique, the binomial series iterative (BSI) method, is developed from the binomial series expansion by using the same concept as SMI. As a combined iterative (CI) method, SMI is incorporated in the procedure of BSI. The CI method, combined with SMI, shows sufficient efficiency and robustness through a stable iterative behaviour due to simple and straightforward computations in the iterative procedure. Published in 2005 by John Wiley & Sons, Ltd.