Krylov Subspace Methods in Distributed Computing Environments
Y Saad · 2026
In the last few years, substantial progress has been made in replacing direct solution methods for solving the large sparse linear systems that arise from fluid dynamics equations by iterative solvers. indeed, a general current consensus seems to be that for three-dimensional models and 2-dimensional pde&s;s with several degrees of freedom per grid point, iterative methods are essentially mandatory, mainly because of the enormous memory requirements of direct methods in such cases. among standard iterative methods, those based on krylov subspace techniques coupled with suitable preconditioners are generally considered to offer the best compromise between efficiency and robustness. in addition to their overwhelming advantage over direct methods, in terms of memory and computational cost, iterative methods are also attractive because of the simplicity with which they can be adapted to high performance computers.