Accelerated engineering design optimization using successive matrix inversion method

Abstract

SUMMARYIn 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.

An approach for structural static reanalysis with unchanged number of degrees of freedom

“…For large modifications, however, the PCG method which utilizes the initial stiffness matrix as the preconditioner may converge slowly. In order to accelerate the solution convergence, the successive matrix inversion method (Bae and Grandhi 2004;Bae et al 2006a) is exploited to construct the preconditioner (Bae et al 2006b). Since the incremental stiffness matrix is divided by columns of interest, the preconditioner may be non-symmetric and indefinite.…”