The application of Krylov subspace iterative methods to unsteady three-dimensional Navier–Stokes codes on massively parallel and distributed computing environments is investigated. Previously, the Euler mode of the Navier–Stokes flow solver Transonic Unsteady Rotor Navier–Stokes (TURNS) has been coupled with a Newton–Krylov scheme which uses two Conjugate-Gradient-like (CG) iterative methods. F...

This report describes a new family of Newton-Krylov methods for solving nonlinear systems of equations arising from the solution of Richards’ equation and in fully implicit formulations in air-water systems. The basic approach is to perform secant (Broyden) updates restricted to the Krylov subspace generated by the GMRES iterative solver. This approach is introduced as Krylov-secant methods. On...

In this paper we discuss preconditioners for the incompressible Navier-Stokes equations. In combination with Krylov subspace methods, they give a fast convergence for the solution of the Navier -Stokes equations. With the help of numerical experiments, we report some new findings regarding the convergence of these preconditioners. Besides that, a renumbering scheme for direct solvers and ILU pr...

Let Mn(R) and Sn(R) be the spaces of n × n real matrices and real symmetric matrices respectively. We continue to study d(n, n − 2,R): the minimal number such that every -dimensional subspace of Sn(R) contains a nonzero matrix of rank n−2 or less. We show that d(4, 2,R) = 5 and obtain some upper bounds and monotonicity properties of d(n, n − 2,R). We give upper bounds for the dimensions of n − ...

This paper proposes two new algorithms for the direction of arrival (DOA) estimation of P radiating sources. Unlike the classical subspace-based methods, they do not resort to the eigen-decomposition of the covariance matrix of the received data. Indeed, the proposed algorithms involve the building of the signal subspace from the Krylov subspace of order P associated with the covariance matrix ...

We present a novel method to compute the overlap Dirac operator at zero and nonzero quark chemical potential. To approximate the sign function of large, sparse matrices, standard methods project the operator on a much smaller Krylov subspace, on which the matrix function is computed exactly. However, for large lattices this subspace can still be too large for an efficient calculation of the sig...

We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et al. SISC 2005], which is an iterative method allowing for the efficient minimization of the the residual over an augmented block Krylov subspace. We offer a clean derivation of the method and discuss methods of selecting recycling subspaces at restart as well as implementation decisions in the context of high...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

Krylov subspace methods play an important role in many areas of scientific computing, including numerical solution of linear algebraic systems arising from discretization of partial differential and/or integral equations. By their nature they represent model reductions based on matching moments. Such view naturally complements, to our opinion, the standard description using the projection proce...