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At least 73 records · Page 4

An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Radespiel, R.↗

A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations

The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.

Borzi, A.↗

Vertex Movement for Mission Status Graphics: A Polar-Star Display

Humans are traditionally bad monitors, especially over long periods of time on reliable systems, and they are being called upon to do this more and more as systems become further automated. Because of this, there is a need to find a way to display the monitoring information to the human operator in such a way that he can notice pertinent deviations in a timely manner. One possible solution is to use polar-star displays that will show deviations from normal in a more salient manner. A polar-star display uses a polygon's vertices to report values. An important question arises, though, of how the vertices should move. This experiment investigated two particular issues of how the vertices should move: (1) whether the movement of the vertices should be continuous or discrete and (2) whether the parameters that made up each vertex should always move in one direction regardless of parameter sign or move in both directions indicating parameter sign. The results indicate that relative movement direction is best. Subjects performed better with this movement type and they subjectively preferred it to the absolute movement direction. As for movement type, no strong preferences were shown.

Trujillo, Anna↗

Vertex Reordering for Real-world Graphs and Applications: An Empirical Evaluation

Vertex reordering is a way to improve locality in graph computations. Given an input (or ``natural'') order, reordering aims to compute an alternate permutation of the vertices that is aimed at maximizing a locality-based objective. Given decades of research on this topic, there are tens of graph reordering schemes, and there are also several linear arrangement ``gap'' measures for treatment as objectives. However, a comprehensive empirical analysis of the efficacy of the ordering schemes against the different gap measures, and against real-world applications is currently lacking. In this study, we present an extensive empirical evaluation of up to 11 ordering schemes, taken from different classes of approaches, on a set of 34 real-world graphs emerging from different application domains. Our study is presented in two parts: a) a thorough comparative evaluation of the different ordering schemes on their effectiveness to optimize different linear arrangement gap measures, relevant to preserving locality; and b) extensive evaluation of the impact of the ordering schemes on two real-world, parallel graph applications, namely, community detection and influence maximization. Our studies show a significant divergence among the ordering schemes (up to $40\times$ between the best and the poor) in their effectiveness to reduce the gap measures; and a wide ranging impact of the ordering schemes on various aspects including application runtime (up to $4\times$), memory and cache use, load balancing, and parallel work and efficiency. The comparative study also help reveal the nuances of a parallel environment (compared to serial) on the ordering schemes and their role in optimizing applications.

Barik, Reet↗

Test of Harmonic Coil Accuracy Using a Multi Vertex Probe

Magnets are integral components of particle accelerators, with different multipoles used to perform various beam conditioning functions, like steering and focusing. Testing accelerator magnets to ensure compliance with specification is a crucial step of fabrication. One of the most popular techniques for verifying magnetic field strength and integrity is the harmonic coil probe. Harmonic coil probes are comprised of passive loops that are rotated around the aperture of a magnet and are used to measure magnetic flux. Oftentimes the measurements of the harmonic coil probe are affected by transverse vibrations along the axis of rotation and torsional vibrations of the position closure sensor, both causing spurious harmonics. To make matters challenging, it is difficult to distinguish between the real harmonics of the magnet and the spurious harmonics during analysis. This research explores the use of a novel configuration of harmonic coil probe, Multi-Vertex Probe (MVP), to address multiple factors that affect the accuracy and repeatability of harmonic coil probe measurement. Most of the results are based on simulation data, in which artificial torsional distortions are introduced and removed with the proposed processing method. In addition to implementing torsional vibration removal in simulation, laboratory analysis regarding the source of vibrations was performed using a pre-fabricated MVP. More specifically, various mechanical conditions were used to explore the standard deviation of main harmonic’s flux amplitude. The conditions included: coupling type (rigid or soft), rotation speed, probe starting position within magnetic field, and cabling location inside the magnetic field. Along with this, the MVP’s measured noise floor in and outside a magnetic field was quantified.

Lofquist, Claire [Northern Illinois U.]↗

Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Determining the range of validity of Migdal’s approximation for electron-phonon (e-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the e-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal’s approximation holds. Our results demonstrate that questions regarding the validity of Migdal’s approximation go hand in hand with questions of the validity of a linear e-ph interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vertex-finding and reconstruction of contained two-track neutrino events in the MicroBooNE detector

In this work, we describe algorithms developed to isolate and accurately reconstruct two-track events that are contained within the MicroBooNE detector. This method is optimized to reconstruct two tracks of lengths longer than 5cm. This code has applications to searches for neutrino oscillations and measurements of cross sections using quasi-elastic-like charged current events. The algorithms we discuss will be applicable to all detectors running in Fermilab's Short Baseline Neutrino program (SBN), and to any future liquid argon time projection chamber (LArTPC) experiment with beam energies ~ 1 GeV. The algorithms are publicly available on a GITHUB repository. This reconstruction offers a complementary and independent alternative to the Pandora reconstruction package currently in use in LArTPC experiments, and provides similar reconstruction performance for two-track events.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗