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...

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...

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...

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...

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...