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

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

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed

Mutation in Hemagglutinin Antigenic Sites in Influenza A pH1N1 Viruses from 2015–2019 in the United States Mountain West, Europe, and the Northern Hemisphere

H1N1 influenza A virus is a respiratory pathogen that undergoes antigenic shift and antigenic drift to improve viral fitness. Tracking the evolutionary trends of H1N1 aids with the current detection and the future response to new viral strains as they emerge. Here, we characterize antigenic drift events observed in the hemagglutinin (HA) sequence of the pandemic H1N1 lineage from 2015–2019. We observed the substitutions S200P, K147N, and P154S, together with other mutations in structural, functional, and/or epitope regions in 2015–2019 HA protein sequences from the Mountain West region of the United States, the larger United States, Europe, and other Northern Hemisphere countries. We reconstructed multiple phylogenetic trees to track the relationships and spread of these mutations and tested for evidence of selection pressure on HA. We found that the prevalence of amino acid substitutions at positions 147, 154, 159, 200, and 233 significantly changed throughout the studied geographical regions between 2015 and 2019. We also found evidence of coevolution among a subset of these amino acid substitutions. The results from this study could be relevant for future epidemiological tracking and vaccine prediction efforts. Similar analyses in the future could identify additional sequence changes that could affect the pathogenicity and/or infectivity of this virus in its human host

On maximum norm convergence of multigrid methods for elliptic boundary value problems

Multigrid methods applied to standard linear finite element discretizations of linear elliptic boundary value problems in two dimensions are considered. In the multigrid method, damped Jacobi or damped Gauss-Seidel is used as a smoother. It is proven that the two-grid method with v pre-smoothing interations has a contraction number with respect to the maximum norm that is (asymptotically) bounded by Cv-1/2|lnhk|2, with hk a suitable mesh size parameter. Moreover, it is shown that this bound is sharp in the sense that a factor |ln hk| is necessary

Soluble P-selectin predicts lower extremity peripheral artery disease incidence and change in the ankle brachial index: The Multi-Ethnic Study of Atherosclerosis (MESA)

ObjectiveTo determine the association of circulating P-selectin with prevalent and incident peripheral artery disease (PAD), the ankle brachial index (ABI), and change in the ABI.MethodsThe Multi-Ethnic Study of Atherosclerosis (MESA) is a prospective population-based cohort study including 6814 European descent, African American, Hispanic and Chinese men and women aged 45-84 at baseline. Four clinical exams took place after the baseline exam. After excluding those with ABI>1.4, prevalent and incident PAD were defined as an ABI≤0.90. ABI progression was defined as progression from a normal ABI (0.91-1.4) to abnormal (≤0.90 or >1.4) at a later exam.ResultsIn adjusted models, each SD (13 ng/mL) higher P-selectin was significantly associated with 0.007 lower ABI (95% CI ((-0.011, -0.004)), p < 0.001), and an average change in the ABI of -0.006 ((-0.010, -0.003, p < 0.001). P-selectin was significantly associated with a 1.17-fold greater odds of prevalent PAD ((1.02, 1.33), p = 0.03), and a 30% greater risk of incident PAD ((1.11, 1.53), p = 0.001), as well as progression from a normal ABI to an ABI≤ 0.90 (p = 0.003), but not to an ABI>1.4 (p = 0.96). Addition of P-selectin to models containing traditional PAD risk factors and markers of inflammation/coagulation significantly improved the net reclassification for ABI progression (p = 0.03), but was only marginally significant for incident PAD (p = 0.06).ConclusionsP-selectin is significantly associated with the development of PAD. However, further research is needed in population-based studies to confirm prospective associations of P-selectin with incident PAD and change in the ABI, as well as its potential predictive ability

Hepatocyte growth factor is associated with progression of atherosclerosis: The Multi-Ethnic Study of Atherosclerosis (MESA)

Background and aimsHepatocyte growth factor (HGF) has previously been associated with risk of stroke, coronary heart disease, and atherosclerosis. We hypothesized that higher circulating HGF is associated with greater progression of measures of atherosclerosis: coronary artery calcium (CAC) and carotid plaque.MethodsParticipants aged 45-84 years from the prospective cohort study Multi-Ethnic Study of Atherosclerosis had HGF measured at baseline (between 2000 and 2002) and were followed for progression of atherosclerosis for up to 12 years. CAC was measured at all five exams using the Agatston method. Mixed-effects models were used to examine the association of HGF and CAC progression among 6695 participants with available data. Relative risk regression was used to assess the association between HGF and new or additional carotid plaque between exams 1 and 5 in 3400 participants with available data. All point estimates were adjusted for potential confounding variables.ResultsEach standard deviation higher HGF at baseline was associated with 2.9 Agatston units/year greater CAC progression (95% CI: 1.6-4.2, p < 0.0001), and the magnitude of this association differed by race/ethnicity (p value for interaction by race = 0.003). Each standard deviation higher HGF at baseline was associated with a 4% higher risk of new or additional carotid plaque (95% CI: 1.01-1.08, p = 0.005).ConclusionsHigher levels of HGF were significantly associated with greater progression of atherosclerosis in this large and diverse population. Circulating HGF continues to show promise as a potential clinical biomarker for cardiovascular disease