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This paper presents an approach for determining the linear stability of steady states of partial differential equations (PDEs) on massively parallel computers. Linearizing the transient behavior around a steady state solution leads to an eigenvalue problem. The eigenvalues with the largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration. This is done iteratively so that the algorithm scales with problem size. A representative model problem of three‐dimensional incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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N.B. Meisner D.S. Woo H.B. Huntington G.L. Salinger L.V. Meisel 《Journal of Physics and Chemistry of Solids》1973,34(8):1409-1416
Experiments are presented to establish that irradiation produced defects in lead not only pin dislocations but also can be trapped at the ends of dislocation lines in agreement with the model proposed by Thompson, Buck, Huntington and Barnes. This model indicates that there is a temperature T* at which there is a maximum pinning of dislocations. T* is found to be near 140 K. The data of Part I are analyzed according to this model using reasonable values of the dislocation density and the binding energy of the defect in the trap. The resulting activation energy for the region A process in the reaction kinetics model is found to be 0.15 eV which is consistent with the value found from an eigenvalue expansion model. 相似文献
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Jean-François Lemieux Stephen F. Price Katherine J. Evans Dana Knoll Andrew G. Salinger David M. Holland Antony J. Payne 《Journal of computational physics》2011,230(17):6531-6545
We have implemented the Jacobian-free Newton–Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8–3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods. 相似文献
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Maxime Crochemore Costas S. Iliopoulos Gonzalo Navarro Yoan J. Pinzon Alejandro Salinger 《Journal of Discrete Algorithms》2005,3(2-4):198-214
(δ,γ)-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P1…m and a text T1…n on an alphabet of integers, find the occurrences P′ of the pattern in the text such that (i) , and (ii) . The problem makes sense for δγδm. Several techniques for (δ,γ)-matching have been proposed, based on bit-parallelism or on skipping characters. We first present an O(mnlog(γ)/w) worst-case time and O(n) average-case time bit-parallel algorithm (being w the number of bits in the computer word). It improves the previous O(mnlog(δm)/w) worst-case time algorithm of the same type. Second, we combine our bit-parallel algorithm with suffix automata to obtain the first algorithm that skips characters using both δ and γ. This algorithm examines less characters than any previous approach, as the others do just δ-matching and check the γ-condition on the candidates. We implemented our algorithms and drew experimental results on real music, showing that our algorithms are superior to current alternatives with high values of δ. 相似文献
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A Gurtu P K Malhotra I S Mittra P M Sood SC Gupta VK Gupta GL Kaul LK Mangotra Y Prakash NK Rao ML Sharma 《Pramana》1974,3(5):311-322
This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR em = 〈n s〉/〈n ch〉, where 〈n ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R em = 1·71 implies an effectiveA-dependence ofR A =A 0.18,i.e., a very weak dependence. Predictions ofR em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production. 相似文献
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