The use of out-of-core iterative solvers for large 3D soil problems

TLDR: Numerical examples confirm the necessity of the developed algorithms for large soil problems and confirm the efficiency of the used iterative solvers.

Abstract: In this paper, out-of-core solution algorithms are used for analyzing large 3D soil problems. Such problems involve huge number of degrees of freedom. The soil continuum is modeled using 3D multi-region boundary element method. The overall stiffness matrix resulted from the multi-region boundary element problem is large, sparse and non-symmetric. The soil stiffness matrix is divided into series of sub-matrices according to the available computer memory. Each sub-matrix is assembled individually, hence only the non-zero elements are stored on the hard disk (out-of-core). The BiCGStab (l) and GMRES (m) iterative solvers are implemented to solve the overall system of equations. The innovative part in this paper is the coupling of the developed out-of-core solution with these iterative solvers. Read-in algorithms are developed where the non-zero elements of each sub-matrix are read-in element-by-element sequentially, to fit within relevant operations inside the used iterative solvers. Such a procedure reduces the used computer memory and accelerates the solvers time. The presented numerical examples confirm the necessity of the developed algorithms for large soil problems and confirm the efficiency of the used iterative solvers. In addition, the used iterative solvers give similar performance.