Solution of a set of linear equations A x = b is a recurrent problem in power system analysis. Because of computational dependencies, direct methods have proven of limited value in both parallel and highly vectorized computing environments. The preconditioned conjugate gradient method has been suggested as a better alternative to direct methods. The preconditioning step itself is not particular...

The approximate solutions in standard iteration methods for linear systems Ax = b, with A an n by n nonsingular matrix, form a subspace. In this subspace, one may try to construct better approximations for the solution x. This is the idea behind Krylov subspace methods. It has led to very powerful and e$cient methods such as conjugate gradients, GMRES, and Bi-CGSTAB. We will give an overview of...

We conduct simulations for the 3D unsteady state anisotropic diffusion process with DT-MRI data in the human brain by discretizing the governing diffusion equation on Cartesian grid and adopting a high performance differential–algebraic equation (DAE) solver, the parallel version of implicit differential–algebraic (IDA) solver, to tackle the resulting large scale system of DAEs. Parallel precon...

Solution of a set of linear equations Ax = b is a recurrent problem in power system analysis. Because of computational dependencies, direct methods have proven of limited value in both parallel and highly vectorized computing environments. The preconditioned conjugate gradient method has been suggested as a better alternative to direct methods. The preconditioning step itself is not particularl...

We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1, 1) block of the saddle point matrix. We demonstrate performance of the preconditioner on prob...

BACKGROUND Classical and delayed preconditioning are powerful endogenous protection mechanisms against ischemia-reperfusion damage. However, it is still uncertain whether delayed preconditioning can effectively salvage myocardium in patients with co-morbidities, such as diabetes and the metabolic syndrome. We investigated delayed preconditioning in mice models of type II diabetes and the metabo...

To investigate the role of 12-lipoxygenase in preconditioning, we examined whether hearts lacking the "leukocyte-type" 12-lipoxygenase (12-LOKO) would be protected by preconditioning. In hearts from wild-type (WT) and 12-LOKO mice, left ventricular developed pressure (LVDP) and (31)P NMR were monitored during treatment (+/-preconditioning) and during global ischemia and reperfusion. Postischemi...

Linear systems with large differences between coefficients, called “discontinuous coefficients”, arise in many cases in which partial differential equations (PDEs) model physical phenomena involving heterogeneous media. The standard approach to solving such problems is to use domain decomposition (DD) techniques, with domain boundaries conforming to the boundaries between the different media. T...

This paper reports the development and performance of CaMEL_Aero, our truly matrix-free, parallel and vectorized unstructured finite volume solver for compressible flows. The Jacobian-free GMRES method is used to solve the linear systems of equations inside each nonlinear Newton-Raphson iteration. Furthermore, the matrix-free Lower-Upper Symmetric Gauss Seidel (LUSGS) method is employed as a pr...

Abstract. To efficiently solve second-order discrete elliptic PDEs by Krylov subspace-like methods, one needs to use some robust preconditioning techniques. Relaxed incomplete factorizations (RILU) are powerful candidates. Unfortunately, their efficiency critically depends on the choice of the relaxation parameter ω whose “optimal” value is not only hard to estimate but also strongly varies fro...