The standard iterative method for solving large sparse least squares problems min ∈Rn ‖ −A ‖2, A ∈ Rm×n is the CGLS method, or its stabilized version LSQR, which applies the (preconditioned) conjugate gradient method to the normal equation ATA = AT . In this paper, we will consider alternative methods using a matrix B ∈ Rn×m and applying the Generalized Minimal Residual (GMRES) method to min ∈R...

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to anot...

We consider linear parameterized systems $A(\mu) x(\mu) = b$ for many different $\mu$, where $A$ is large and sparse depends nonlinearly on $\mu$. Solving such individually each $\mu$ would require great computational effort. In this work we propose to compute a partial parameterization $\tilde{x} \approx x(\mu)$, $\tilde{x}(\mu)$ cheap evaluate Our methods are based the observation that compan...

This paper introduces a monolithic compressible flow implicit scheme, capable of scaling up to a few thousand processors. The scheme is programmed in Alya, the BSC in-house code for simulating multiphysics problems in supercomputers [1,2,3]. It is monolithic, assembling a global matrix for the delta form of the conservative unknowns linear momentum, density and total energy and solving the resu...

Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently disco...

Grid computing in general is a special type of parallel computing. It intends to deliver high-performance computing over distributed platforms for computation and data-intensive applications by making use of a very large amount of resources. The GMRES method is used widely to solve the large sparse linear systems. In this paper, we present an effective parallel hybrid asynchronous method, which...

The block GMRES (BGMRES) method is a natural generalization of the GMRES algorithm for solving large nonsymmetric systems with multiple right-hand sides. Unfortunately, its cost increases significantly per iteration, frequently rendering the method impractical. In this paper we propose a hybrid block GMRES method which offers significant performance improvements over BGMRES. This method uses th...

We analyze the the convergence behavior of block GMRES and characterize the phenomenon of stagnation which is then related to the behavior of the block FOM method. We generalize the block FOM method to generate well-defined approximations in the case that block FOM would normally break down, and these generalized solutions are used in our analysis. This behavior is also related to the principal...

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...

In this paper, we consider some vector extrapolation methods for solving nonsymmetric systems of linear equations. When applied to sequences generated linearly, these methods namely the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE), are Krylov subspaces methods and are respectively equivalent to the method of Arnoldi and to the GCR and GMRES. By considering the...