Two Krylov subspace iterative methods, GMRES and QMR, were studied in conjunction with several preconditioning techniques for solving the linear system raised from the finite element discretisation of incompressible Navier-Stokes equations for hydrodynamic problems. The preconditioning methods under investigation were the incomplete factorisation methods such as ILU(0) and MILU, the Stokes prec...

Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the stationary smoothers of the standard multigrid method. This results in a robust and efficient solver for a complex shifted or stretched Helmholtz problem that can ...

In this paper we apply the generalized Taylor–Galerkin finite element model to simulate bore wave propagation in a domain of two dimensions. For stability and accuracy reasons, we generalize the model through the introduction of four free parameters. One set of parameters is rigorously determined to obtain the high-order finite element solution. The other set of free parameters is determined fr...

In this paper, we propose an efficient parallel implementation of the GMRES method for GPU clusters. This implementation requires us to parallelize the GMRES algorithm between CPUs of the cluster. Hence, all parallel and intensive computations on local data are performed on GPUs and reduction operations to compute global results are carried out by CPUs. The performances of our parallel GMRES so...

To date, the most efficient solver used in the weather sciences for the resolution of linear system in numerical weather prediction is the generalized minimal residual method called GMRES. However, difficulties still appear in matrix resolution when the GMRES iterative method is used without an appropriate preconditioner. For improving the computation speed in numerically solving weather equati...

Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface bound charge from a matrix equation using the Generalized Minimal Residue method (GMRES). Empirically, we find that GMRES converges very quickly. Indeed, our de...

In this paper, we propose a Newton-Krylov solver and a Picard-Krylov solver for finite element discrete problem of stationary incompressible magnetohydrodynamic equations in three dimensions. Using a mixed finite element method, we discretize the velocity and the pressure by H1(Ω)-conforming finite elements and discretize the magnetic field by H(curl,Ω)-conforming edge elements. An efficient pr...

In this paper we report on the design and analysis of a multilevel method for the solution of the OrnsteinZernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method.

Abstract A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by using a variety solvers. scalability analysis performed both direct and preconditioned iterative solvers four different pancakes with varying number turns mesh elements. It found that even two extremely time scales in system an solver com...

In this paper, we present some numerical studies on two partitioned fluid-structure interaction solvers: a preconditioned GMRES solver and a Newton based solver, for the fluid-structure interaction problems employing a nearly incompressible elasticity model in a classical mixed displacementpressure formulation. Both are highly relying on robust and efficient solvers for the fluid and structure ...