In this paper, the authors investigate ability of Waveform Relaxation method to deal with large power systems and assess its efficiency. As any domain decomposition methods, number iterations required by is strongly dependent on size system, subdomains, initialization values. To cope these dependencies, an technique reduce a preconditioning maintain high convergence rate for subsystems are here proposed. Applications European electricity network illustrate great efficiency proposed methods...

This paper deals with some improvements of the Waveform Relaxation method for large power systems transient stability analysis. In this context, classical iterative is usually not efficient due to its slow convergence. The convergence speed depends on a lot parameters such as model, disturbance nature, number subdomains created by decomposition, initialization, time domain length, etc. order make competitive usual and mastered sequential methods, important points are here investigated an...

All bell- and kink-shaped solitons sustained by an infinite periodic atomic chain of arbitrary anharmonicity are worked out solving a second-order, nonlinear differential equation involving advanced retarded terms. The asymptotic time decay behaves exponentially or as power law according to whether the potential has harmonic limit not. Excellent agreement is achieved with Toda's model. Illustrative examples also given for Fermi-Pasta-Ulam sine-Gordon potentials. Lattice continuum differ...

In this paper, the authors investigate ability of Schwarz relaxation (SR) methods to deal with large systems differential algebraic equations (DAEs) and assess their respective efficiency. Since number iterations required achieve convergence classical SR method is strongly related subdomains time step size, two new preconditioning techniques are here developed. A preconditioner based on a correction using first introduced leads independent subdomains. second Schur complement matrix makes...

The application of the generalized Roe scheme to numerical simulation two-phase flow models requires a fast and robust computation absolute value system matrix. In several such as two-fluid model or general multi-field model, this matrix has non trivial eigenstructure eigen decomposition is often ill conditioned. We give two algorithms avoiding diagonalization process: an iterative computation, which turns out be exact interpolation algorithm faster can handle case complex eigenvalues....

Toeplitz matrices are persymmetric belonging to the large class of so-called structured matrices, characterized by their displacement rank. This characterization was introduced 12 years ago Kailath and others. In this framework, properties singular investigated with goal proving possible existence fast algorithms for computing pseudo-inverses. Loosely speaking, it is proved that pseudo-inverses some rank r have a bounded $2r$.

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