Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

Weathering of hydrocarbons in mangrove sediments: testing the effects of using dispersants to treat oil spills

This field study was a combined chemical and biological investigation of the relative effects of using dispersants to treat oil spills impacting mangrove habitats. The aim of the chemistry was to determine whether dispersant affected the short- or long-term composition of a medium range crude oil (Gippsland) stranded in a tropical mangrove environment in Queensland, Australia. Sediment cores from three replicate plots of each treatment (oil only and oil plus dispersant) were analyzed for total hydrocarbons and for individual molecular markers (alkanes, aromatics, triterpanes, and steranes). Sediments were collected at 2 days, then 1, 7, 13 and 22 months post-spill. Over this time, oil in the six treated plots decreased exponentially from 36.6 +/- 16.5 to 1.2 +/- 0.8 mg/g dry wt. There was no statistical difference in initial oil concentrations, penetration of oil to depth, or in the rates of oil dissipation between oiled or dispersed oil plots. At 13 months, alkanes were >50% degraded, aromatics were similar to 30% degraded based upon ratios of labile to resistant markers. However, there was no change in the triterpane or sterane biomarker signatures of the retained oil. This is of general forensic interest for pollution events. The predominant removal processes were evaporation (less than or equal to 27%) and dissolution (greater than or equal to 56%), with a lag-phase of 1 month before the start of significant microbial degradation (less than or equal to 7%). The most resistant fraction of the oil that remained after 7 months (the higher molecular weight hydrocarbons) correlated with the initial total organic carbon content of the soil. Removal rate in the Queensland mangroves was significantly faster than that observed in the Caribbean and was related to tidal flushing. (C) 1999 Elsevier Science Ltd. All rights reserved.

Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O-2 (J=0) state-to-state reaction probabilities

An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann-Schwinger equation [Kouri , Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O-2 system (J=0), and the results indicate the approach is accurate and stable. (C) 2002 American Institute of Physics.