A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations has been developed for steady aerodynamic flows. The solution is computed through a Jacobian-free inexact-Newton method with an approximate-Newton method for startup. The linear system at each outer iteration is solved using a Generalized Minimal Residual (GMRES) Krylov subspace algorithm. An incomplete lower/uppe...

Krylov subspace methods are among the most efficient present-day solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace method algorithms do not scale well on massively parallel hardware due to the synchronization bottlenecks induced by the computation of dot products throughout the algorithms. Communication-hiding pipelined Krylov subspace methods offer increase...

In optimizing the iteration parameters of the SIMPLE-like numerical procedure, a genetic algorithm (GA) which searches for a minimum calculation time in a space of iteration numbers was developed. A methodology has been presented for the numerical solution of natural convection in a squeezed cavity at Rayleigh number of 10 and Pr number of 10.0. The pressure correction equation was employed in ...

When solving a linear algebraic system Ax = b with GMRES, the relative residual norm at each step is bounded from above by the so-called ideal GMRES approximation. This worstcase bound is sharp (i.e. it is attainable by the relative GMRES residual norm) in case of a normal matrix A, but it need not characterize the worst-case GMRES behavior if A is nonnormal. Characterizing the tightness of thi...

This note describes the usage of the GMRES solver using reverse communication protocol. The GMRES control flow is outlined, and an example calling sequence explained.

In the past few years new methods have been proposed that can be seen as combinations of standard Krylov subspave methods, such as Bi{ CG and GMRES. One of the rst hybrid schemes of this type is CGS, actually the Bi{CG squared method. Other such hybrid schemes include BiCGSTAB (a combination of Bi{CG and GMRES(1)), QMRS, TFQMR, Hybrid GMRES (polynomial preconditioned GMRES) and the nested GMRES...

Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the modified GMRES(m), GMRESH(m) procedure, alone and as part of an inexact Newton procedure with several choices for the forcing term, demonstrate ...

We propose a variant of GMRES which we call MPGMRES, whereby multiple (two or more) preconditioners are applied simultaneously, while maintaining minimal residual optimality properties. To accomplish this, a block version of Flexible GMRES is used, but instead of considering blocks starting with multiple right hand sides, we start with the initial residual and grow the space by applying each of...