ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows

We propose a C2-continuous alternating direction implicit (ADI) method for the solution of the streamfunction-vorticity equations governing steady 2D incompressible viscous fluid flows. Discretisation is simply achieved with Cartesian grids. Local two-node integrated radial basis function elements (IRBFEs) [D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong, A C2-continuous control-volume technique based on Cartesian grids and two-node integrated-RBF elements for second-order elliptic problems, CMES: Computer Modeling in Engineering & Sciences 72 (2011) 299-334] are used for the discretisation of the diffusion terms, and then the convection terms are incorporated into system matrices by treating nodal derivatives as unknowns. ADI procedure is applied for the time integration. Following ADI factorisation, the two-dimensional problem becomes a sequence of one-dimensional problems. The solution strategy consists of multiple use of a one-dimensional sparse matrix algorithm that helps saving the computational cost. High levels of accuracy and efficiency of the present methods are demonstrated with solutions of several benchmark problems defined on rectangular and non-rectangular domains

Trachoma in Viet Nam: results of 11 surveillance surveys conducted with the Global Trachoma Mapping Project.

PURPOSE: Following interventions against trachoma in Viet Nam, impact surveys conducted in 2003-2011 suggested that trachoma was no longer a public health problem. In 2014, we undertook surveillance surveys to estimate prevalence of trachomatous inflammation-follicular (TF) and trichiasis. METHODS: A population-based prevalence survey was undertaken in 11 evaluation units (EUs) encompassing 24 districts, using Global Trachoma Mapping Project methods. A two-stage cluster sampling design was used in each EU, whereby 20 clusters and 60 children per cluster were sampled. Consenting eligible participants (children aged 1-9 years and adults aged ≥50 years) were examined for trachoma. RESULTS: A total of 9391 households were surveyed, and 20,185 participants (98.8% of those enumerated) were examined for trachoma. EU-level TF prevalence in 1-9-year-olds ranged from 0% to 1.6%. In one cluster (in Hà Giang Province), the percentage of children with TF was 10.3%. The overall pattern of cluster-level percentages of children with TF, however, was consistent with an exponential distribution, which would be consistent with trachoma disappearing. Among people aged ≥50 years, prevalence of trichiasis by EU ranged from 0% to 0.75%; these estimates are equivalent to 0-0.13% in all ages. The prevalence of trichiasis unknown to the health system among people aged ≥50 years, by EU, ranged from 0% to 0.17%, which is equivalent to 0-0.03% in all ages. CONCLUSION: Findings suggest that trachoma is no longer a public health problem in any of the 11 EUs surveyed. However, given the high proportion of children with TF in one cluster in Hà Giang Province, further investigations will be undertaken

Safety and efficacy of fluoxetine on functional outcome after acute stroke (AFFINITY): a randomised, double-blind, placebo-controlled trial

Background Trials of fluoxetine for recovery after stroke report conflicting results. The Assessment oF FluoxetINe In sTroke recoverY (AFFINITY) trial aimed to show if daily oral fluoxetine for 6 months after stroke improves functional outcome in an ethnically diverse population. Methods AFFINITY was a randomised, parallel-group, double-blind, placebo-controlled trial done in 43 hospital stroke units in Australia (n=29), New Zealand (four), and Vietnam (ten). Eligible patients were adults (aged ≥18 years) with a clinical diagnosis of acute stroke in the previous 2–15 days, brain imaging consistent with ischaemic or haemorrhagic stroke, and a persisting neurological deficit that produced a modified Rankin Scale (mRS) score of 1 or more. Patients were randomly assigned 1:1 via a web-based system using a minimisation algorithm to once daily, oral fluoxetine 20 mg capsules or matching placebo for 6 months. Patients, carers, investigators, and outcome assessors were masked to the treatment allocation. The primary outcome was functional status, measured by the mRS, at 6 months. The primary analysis was an ordinal logistic regression of the mRS at 6 months, adjusted for minimisation variables. Primary and safety analyses were done according to the patient's treatment allocation. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12611000774921. Findings Between Jan 11, 2013, and June 30, 2019, 1280 patients were recruited in Australia (n=532), New Zealand (n=42), and Vietnam (n=706), of whom 642 were randomly assigned to fluoxetine and 638 were randomly assigned to placebo. Mean duration of trial treatment was 167 days (SD 48·1). At 6 months, mRS data were available in 624 (97%) patients in the fluoxetine group and 632 (99%) in the placebo group. The distribution of mRS categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio 0·94, 95% CI 0·76–1·15; p=0·53). Compared with patients in the placebo group, patients in the fluoxetine group had more falls (20 [3%] vs seven [1%]; p=0·018), bone fractures (19 [3%] vs six [1%]; p=0·014), and epileptic seizures (ten [2%] vs two [<1%]; p=0·038) at 6 months. Interpretation Oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and epileptic seizures. These results do not support the use of fluoxetine to improve functional outcome after stroke

RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients

Many important engineering problems have multiple-scale solutions. Thermal conductivity of composite materials, flow in porous media, and turbulent transport in high Reynolds number flows are examples of this type. Direct numerical simulations for these problems typically require extremely large amounts of CPU time and computer memory, which may be too expensive or impossible on the present supercomputers. In this paper, we develop a high order computational method, based on multiscale basis function approach and integrated radial-basis-function (IRBF) approximant, for the solution of multiscale elliptic problems with reduced computational cost. Unlike other methods based on multiscale basis function approach, sets of basis and correction functions here are obtained through $C^2$-continuous IRBF element formulations. High accuracy and efficiency of this method are demonstrated by several one- and two-dimensional examples

High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows

In this paper, 2-node integrated radial basis function elements (IRBFEs)[CMES, vol.72, no.4, pp.299-334, 2011] are further developed for the simulation of incompressible viscous flows in two dimensions. Emphasis is placed on (i) the incorporation of C2-continuous 2-node IRBFEs into the subregion and point collocation frameworks for the discretisation of the stream function-vorticity formulation on Cartesian grids; and (ii) the development of high order upwind schemes based on 2-node IRBFEs for the case of convection-dominant flows. High levels of accuracy and efficiency of the present methods are demonstrated by solutions of several benchmark problems defined on rectangular and non-rectangular domains

IRBFN-based multiscale solution of a model 1D elliptic equation

Many engineering problems have a wide range of length scales in their solutions. Direct numerical simulations for these problems typically require extremely-large amounts of CPU time and computer memory, which may be too expensive or impossible on the present supercomputers. In this paper, we present a high-order method, based on the multiscale basis function framework and integrated radial-basis-function networks, for solving multiscale elliptic problems in one dimension