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

作者：Fialko S Yu^*

来源：Archives of Civil and Mechanical Engineering, 2014, 14(1): 190-203.

DOI：10.1016/j.acme.2013.05.009

• Finite element method
• Preconditioned conjugate gradient method
• Sparse matrices
• Multi-core computers
• Multistory buildings

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 (http://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 Soft(1) problem collection.

• 出版日期2014-1