New developments on BE/BE multi-zone algorithms based on krylov solvers: applications to 3D frequency-dependent problems

Abstract

In this paper, new developments concerning the use of BE/BE coupling algorithms for solving 3D time–harmonic problems are reported. The algorithms are derived by considering different iterative solvers. Their chief idea is to work with the global sparse matrix of the coupled system, however without considering the many zero blocks associated with the non–coupled nodes of different subregions. The use of iterative solvers makes it possible to store and manipulate only the block matrices with non–zero coefficients. Preconditioned iterative solvers based on the Lanczos, bi-conjugate gradient, and GMRES (generalized minimal residual) methods are used to derive the BE/BE coupling algorithms. A description of the formulation of these solvers, which are completely general and can be applied to any non–singular, non–hermitian systems of equations, is provided. The performance of the algorithms is verified by solving some foundation–soil interaction problems. Important parameters for estimating the efficiency of the algorithms as required CPU times, matrix sparsity, and accuracy of the obtained responses are presented in the results of the paper.