The approximate cardinal basis function (ACBF) preconditioning technique has been used to solve partial differential equations (PDEs) with radial basis functions (RBFs). In [31], a preconditioning scheme that is based upon constructing the least-squares approximate cardinal basis function from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. This p...

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton–Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower–...

In the work of solving a uniformly elliptic differential equations Au := − u+ a1ux + a2uy + a0u = f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix whe...

We study preconditioning strategies for linear systems with positive-deenite matrices of the form Z T GZ, where Z is rectangular and G is symmetric but not necessarily positive deenite. The preconditioning strategies are designed to be used in the context of a conjugate-gradient iteration, and are suitable within algorithms for constrained optimization problems. The techniques have other uses, ...

Preconditioning techniques are discussed for symmetric eigenvalue problems. The methods Davidson, Jacobi-Davidson, Rayleigh quotient iteration, and preconditioned Lanczos are considered. Some relationships are given between these different approaches, and some experimental comparisons are done. Jacobi-Davidson appears to be efficient in both expense and storage. A hybrid method may be helpful f...

Large CFD problems are often solved using iterative methods. Preconditioning is mandatory to accelerate the convergence of iterative methods. This paper presents new results using several preconditioning techniques. These preconditoners are non-standard in the CFD community. Several numerical tests were carried out for solving three-dimensional incompressible, compressible and magneto-hydrodyna...

Protein kinase C (PKC) has been proposed as a primary cellular mediator of ischemic preconditioning. However, the role of PKC in eliciting cardioprotection remains controversial. In this review, we summarize the evidence for and against the 'PKC hypothesis' of preconditioning, discuss the important technical limitations currently hampering PKC research, and suggest new approaches (i.e. PKC isof...

introduction: ischemic preconditioning mediated by potassium channels is a physiological protective mechanism, . it is hypothesized that nicorandil, which is a potassium channel activator, could protect the heart via preconditioning. materials and methods:this clinical trial was conducted on 162 patients undergoing percutaneous coronary intervention (pci) in quem hospital, from jan2013 to jan 2...