In this article, we compare different iterative techniques enhanced by the CBFM, which are used to analyze finite arrays of disjoint antenna elements. These based on stationary-type methods (Jacobi, Gauss–Seidel, and macroblock Jacobi), nonstationary GMRES, hybrid alternating GMRES-Jacobi (AGJ) method that combines these two types. each iteration, reduced CBFM system is constructed previous ite...

We present a polynomial preconditioner for solving large systems of linear equations. The is derived from the minimum residual (the GMRES polynomial) and more straightforward to compute implement than many previous preconditioners. Our current implementation this using its roots naturally stable methods computing same polynomial. further stability control added roots, allows high degree polynom...

Three solvers for saddle point problems arising from the linearization and discretization of the steady state incompressible Navier–Stokes equations are numerically studied. The numerical tests are based on nonconforming finite element approximations of lowest order in two–dimensional domains using isotropic meshes. The investigated solvers are coupled multigrid methods with Vanka–type smoother...

The anisotropic and active properties of the perfectly matched layer (PML) absorbers significantly deteriorate the finite-element method (FEM) system condition and as a result, convergence of the iterative solver is substantially affected. To address this issue, we examine the generalized minimal residual (GMRES) solver for solving finite-element systems terminated with PML. A strong approximat...

Starting from the residual estimates for GMRES formulated by many authors, usually in terms of the quotient of the Hermitian part and the norm of a matrix or by using the field of values of a matrix, we present more general estimates which hold also for restarted and augmented GMRES. Sufficient conditions for convergence are formulated. All estimates are independent on the choice of an initial ...

In this paper we analyze the numerical behavior of several minimum residual methods, which are mathematically equivalent to the GMRES method. Two main approaches are compared: the one that computes the approximate solution (similar to GMRES) in terms of a Krylov space basis from an upper triangular linear system for the coordinates, and the one where the approximate solutions are updated with a...

In this report we describe the implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of simplicity, flexibility and efficiency the GMRES solvers have been implemented using the reverse communication mechanism for the matrixvector product, the preconditioning and ...