Contingency analysis (CA) plays a critical role to guarantee operation security in the modern power systems. With the high penetration of renewable energy, a real-time and comprehensive “N-1” CA is needed as a power system analysis tool to ensure system security. In this paper, a graph-based preconditioning conjugate gradient (GPCG) approach is proposed for the nodal parallel computing in “N-1”...

In both bubbly and porous media flow, the jumps in coefficients may yield an ill-conditioned linear system. The solution of this system using an iterative technique like the conjugate gradient (CG) is delayed because of the presence of small eigenvalues in the spectrum of the coefficient matrix. To accelerate the convergence, we use two levels of preconditioning. For the first level, we choose ...

A strategy for computing aeroelastic solutions is proposed. An implicit LU fac-torisation scheme for solving the time dependent Euler equations on unstructured triangular meshes is presented and coupled with a typical section aeroelastic wing model. EEciency is improved by coupling the LU factorisation scheme with a GM-RES algorithm. In this case the LU scheme plays the role of a preconditioner...

We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix A ∈ Cn×n. We are also able to predict which permutation matrices will be chosen by partial pivoting or complete pivoting Gaussian elimination. Our method uses maxplus algebra and is based purely on the modulii of the entries in the matrix. This approximation can be used ...

This paper describes a technique for constructing robust preconditioners for the CGLS method applied to the solution of large and sparse least squares problems. The algorithm computes an incomplete LDLT factorization of the normal equations matrix without the need to form the normal matrix itself. The preconditioner is reliable (pivot breakdowns cannot occur) and has low intermediate storage re...

The Finite Element modelling of geological faults by penalty contact elements may give rise to illconditioned stiffness matrices with the convergence of iterative solvers accelerated, or even allowed for, by the development and implementation of appropriate preconditioners. The present communication investigates the performance of three different block preconditioners in a realistic geomechanic...

In many astrophysical hydrodynamical and magnetohydro-dynamical problems explicit time integration is ineecient due to the dis-parate time scales, or because we are looking for a steady-state. Implicit schemes can ooer a viable alternative, which requires eecient solution of large linear systems. In multi-dimensional ows these linear systems cannot be solved with a direct method, so that iterat...

A special procedure for the numerical solution of two-dimensional obstacle scattering problems is considered. The original exterior problem is approximated by introducing a rectangular artiicial boundary and by imposing an absorbing boundary condition. The scatterer is assumed to have a dielectric coating of variable thickness. Finite element discretization is performed with a structured mesh, ...

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton li...