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Iterative methods for solving large-scale problems of structural mechanics using multi-core computers

Fialko S. Y.

Archives of Civil and Mechanical Engineering

2014

Vol. 14, no. 1

190--203

The paper studies the conjugate gradient method for solving systems of linear algebraic equations with symmetric sparse matrices that arise when the finite-element method is applied to the problems of structural mechanics. The main focus is on designing effective preconditioning and parallelizing the method for multi-core desktop computers. Preconditioning is based on the incomplete Cholesky “by value” factorization method and implemented based on the technique of sparse matrices, which allows increasing convergence considerably without a significant increase of the computer's resources. Parallelization is implemented for the incomplete factorization as well as for iterative process stages. The method is integrated into the SCAD software package (www.scadsoft.com). The paper includes a discussion of the results of calculations done with direct and iterative methods for large-scale design models of tall buildings, originally from the SCAD Soft1 problem collection.

Numerical analysis of loadbearing systems of multistory buildings

Aliawdin P., Mordich A., Simbirkin V.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no 4

531-541

The paper presents a numerical evaluation of various reinforced concrete structural systems with reference to their response to gravity and wind loads. The structural systems considered are multistory cast-in-place, precast and mixed precast and in-situ skeletons with and without shear walls employed in current building practice. The results of static, dynamic, and stability FE-analyses of such systems are discussed. Cast-in-place and mixed skeletons are shown to be efficient loadbearing systems for multistory residential and office buildings.