On the parallel efficiency of the Frederickson-McBryan multigrid

To take full advantage of the parallelism in a standard multigrid algorithm requires as many processors as points. However, since coarse grids contain fewer points, most processors are idle during the coarse grid iterations. Frederickson and McBryan claim that retaining all points on all grid levels (using all processors) can lead to a superconvergent algorithm. The purpose of this work is to show that the parellel superconvergent multigrid (PSMG) algorithm of Frederickson and McBryan, though it achieves perfect processor utilization, is no more efficient than a parallel implementation of standard multigrid methods. PSMG is simply a new and perhaps simpler way of achieving the same results

Causes of the Violation of Integrity Constraints for Supporting the Quality of Databases

[EN] The quality of the information provided by databases can be captured by integrity constraints. Thus, violated cases of constraints may serve as a basis for measuring the quality of given database states. A quality metric with the potential of more accuracy is obtained by measuring the causes, i.e., data that are responsible for constraint violations. Such measures also serve for controlling quality impairment across updates.Partially supported by FEDER and the Spanish grants TIN2009-14460-C03 and TIN2010-17139Decker, H. (2011). Causes of the Violation of Integrity Constraints for Supporting the Quality of Databases. Lecture Notes in Computer Science. 6786:283-292. https://doi.org/10.1007/978-3-642-21934-4_24S2832926786Ceri, S., Gottlob, G., Tanca, L.: What you always wanted to know about Datalog (and never dared to ask). TKDE 1(1), 146–166 (1989)Christiansen, H., Martinenghi, D.: On simplification of database integrity constraints. Fundam. Inform. 71(4), 371–417 (2006)Decker, H.: Answers that Have Integrity in Databases that Violate Constraints. Presented at the ICALP Workshop SDKB 2010, to appear in the Post-Workshop Proceedings of SDKB (2011)Decker, H.: Toward a uniform cause-based approach to inconsistency-tolerant database semantics. In: Meersman, R., Dillon, T., Herrero, P. (eds.) OTM 2010. LNCS, vol. 6427, pp. 983–998. Springer, Heidelberg (2010)Decker, H.: Quantifying the Quality of Stored Data by Measuring their Integrity. In: Proc. DIWT 2009, Workshop SMM, pp. 823–828. IEEE, Los Alamitos (2009)Decker, H., Martinenghi, D.: Inconsistency-tolerant Integrity Checking. TKDE 23(2), 218–234 (2011)Decker, H., Martinenghi, D.: Modeling, measuring and monitoring the quality of information. In: Heuser, C.A., Pernul, G. (eds.) ER 2009. LNCS, vol. 5833, pp. 212–221. Springer, Heidelberg (2009)Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. J. Intelligent Information Systems 27(2), 159–184 (2006)Ramakrishnan, R., Gehrke, J.: Database Management Systems. McGraw-Hill, New York (2003

Multigrid for hypersonic inviscid flows

The use of multigrid methods to solve the Euler equations for hypersonic flow is discussed. The steady state equations are considered with a Runge-Kutta smoother based on the time accurate equations together with local time stepping and residual smoothing. The effect of the Runge-Kutta coefficients on the convergence rate was examined considering both damping characteristics and convection properties. The importance of boundary conditions on the convergence rate for hypersonic flow is discussed. Also of importance are the switch between the second and fourth difference viscosity. Solutions are given for flow around the bump in a channel and flow around a biconic section

A simplified analysis of the multigrid V-cycle as a fast elliptic solver

For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented

Three-dimensional computed tomography from interferometric measurements within a narrow cone of views

A theory to determine the properties of a fluid from measurements of its projections was developed and tested. Viewing cones as small as 10 degrees were evaluated, with the only assumption being that the property was space limited. The results of applying the theory to numerical and actual interferograms of a spherical discontinuity of refractive index are presented. The theory was developed to test the practicality and limits of using three-dimensional computer tomography in internal fluid dynamics

Electrical characteristics of a free-burning direct-current argon arc operating between 90 and 563 kilowatts with two types of cathodes

The electrical characteristics of a high-power, long-lived, free-burning dc argon arc are presented. Empirical formulas relating voltage to current, electrode separation, and operating pressure are given for two types of cathodes: a typical point tip cathode and a cathode with a 1.27-cm-(0.5-in.-) diameter crater in the tip. Power was varied from 90 to 563 kW. A discussion of the cathode with the crater tip is given

Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence