In this paper we show how the properties of integral operators and their approximations are reeected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden's method and we present some comparisons of the two methods ...

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b i, which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing ste...

We study the convergence of GMRES for linear algebraic systems with normal matrices. In particular, we explore the standard bound based on a min-max approximation problem on the discrete set of the matrix eigenvalues. This bound is sharp, i.e. it is attainable by the GMRES residual norm. The question is how to evaluate or estimate the standard bound, and if it is possible to characterize the GM...

A Newton–Krylov algorithm is presented for two-dimensional Navier–Stokes aerodynamic shape optimization problems. The algorithm is applied to both the discrete-adjoint and the discrete  ow-sensitivity methods for calculating the gradient of the objective function. The adjoint and  ow-sensitivity equations are solved using a novel preconditioned generalized minimumresidual (GMRES) strategy. To...

A multiblock mortar approach to modeling multiphase ow in porous media decomposes the simulation domain into a series of blocks with possibly di erent physical and numerical models employed in each block. Matching conditions along the interfaces are imposed through the use of mortar nite elements. A parallel domain decomposition algorithm reduces the algebraic nonlinear system to an interface p...

The analysis of a non-overlapping domain decomposition method with optimized transmission conditions, applied to a simplified 1-D problem discretized by finite elements, is performed to better understand the spectral properties of the method. An approximate deflation preconditioner is then introduced to modify the spectrum of the iteration operator, and speed up the convergence of the GMRES alg...

The cuckoo search algorithm is a recently developedmeta-heuristic optimization algorithm, which is suitable forsolving optimization problems. To enhance the accuracy andconvergence rate of this algorithm, an improved cuckoo searchalgorithm is proposed in this paper. Normally, the parametersof the cuckoo search are kept constant. This may lead todecreasing the efficiency of the algorithm. To cop...

[1] We introduce the preconditioned generalized minimum residual (GMRES) method, along with an outer loop (OL) iteration to solve the sea-ice momentum equation. The preconditioned GMRES method is the linear solver. GMRES together with the OL is used to solve the nonlinear momentum equation. The GMRES method has low storage requirements, and it is computationally efficient and parallelizable. It...