Abstract
This paper describes a preconditioner of the conjugate gradient method which utilizes the sparse Cholesky factorization to solve particular dynamic soil-structure interaction problems. This preconditioner is designed for finite element models in which some building models consisting of beam or shell elements and a large soil model consisting of solid elements are combined together. The idea of the preconditioner is based on the two observations: 1) a sole building model can efficiently be solved by the sparse Cholesky factorization; and 2) the building models worsen the iteration behavior of the conjugate gradient method. Within an algebraic study, it is shown that the preconditioner reduces the coefficients with respect to the degrees of freedom of the building models into the identity and eliminates the terms related to the building models from the preconditioned coefficient matrix. This algebraic property is expected to facilitate improving the iteration behavior of the conjugate gradient method applied to the combined model. Numerical studies are also performed to demonstrate that this property holds in the actual computation. The other beneficial characteristics of the preconditioner are also qualitatively discussed through the results of residual force and moment.
