An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used ...

We introduce a method for constructing a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show that this polynomial-based NLLS-optimized (PBNO) preconditioner significantly improves the performance of 2-D continuous Galerkin (CG) and discontinuous Galerkin (DG) compressible Euler equation models when run in an implicit-explicit time integration mode. When employed ...

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...

The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection methods onto matrix Kr...

The Generalized Minimal Residual (GMRES) method is one of the most popular algorithms for the solution of large, sparse and unsymmetric linear systems of equations Ax = b [6]. The idea behind the GMRES is to construct an orthogonal matrix Vk such that its k columns span a Krylov subspace. The time and memory costs of computing Vk are proportional to k, so that, as k grows, the computational cos...

In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving time dependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution variants of the conjugate gradient algorithm and two convolution variants of the GMRES algorithm and analyze...

This paper presents a new preconditioning technique for the restarted GMRES algorithm. It is based on an invariant subspace approximation which is updated at each cycle. Numerical examples show that this deea-tion technique gives a more robust scheme than the restarted algorithm, at a low cost of operations and memory.

This paper presents a general framework for Shanks transformations of sequences of elements in a vector space. It is shown that the Minimal Polynomial Extrapolation (MPE), the Modified Minimal Polynomial Extrapolation (MMPE), the Reduced Rank Extrapolation (RRE), the Vector Epsilon Algorithm (VEA), the Topological Epsilon Algorithm (TEA), and Anderson Acceleration (AA), which are standard gener...

We present variants of the block-GMRES(m) algorithms due to Vital and the block-LGMRES(m,k) by Baker, Dennis and Jessup, obtained with replacing the standard QR factorization by a rank-revealing QR factorization in the Arnoldi process. The resulting algorithm allows for dynamic block deflation whenever there is a linear dependency between the Krylov vectors or the convergence of a right-handsid...

Grid computing attains high throughput computing by making use of a very large amount of unexploited computing resources. We present a typical parallel method GMRES to solve large sparse linear systems by the use of a lightweight GRID system XtremWeb. This global computing platform, just as many popular GRID systems, is mainly devoted to multi-parameters generic applications. We have implemente...