Multispace and multilevel BDDC

The Balancing Domain Decomposition by Constraints (BDDC) method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.     

Studies of the methods used for the determination of the digestibility of crude fats in calves

An investigation was made of methods used for the exact determination of the crude content and crude extract of faeces. The following methods were examined: (1) Following treatment with hydrochloric acid a 1:1 mixture of ether and petroleum ether was used. (2) Following hydrolysis with hydrochloric acid extraction with ether was carried out immediately from the aqueous phases. (3) The analysis was carried out with Folch's solvent. A 1:1 mixture of methanol and chloroform was used. (4) The faeces were dried with infrared lamps and crude fat extraction was carried out with Folch's solvent. A 1:1 mixture of methanol and chloroform was used. (5) The faeces were dried with infrared lamps and extraction with ether was done in a Soxhlet apparatus. Nearly identical results were obtained with methods 1 and 2 or 3 and 4 in determining the content of crude extract, the acid number and the percentage proportion of fatty acids. Essential differences were found between methods 1 and 2 and methods 3 and 4. The most reliable results were obtained by using method (2). Method (5) was found to be most suitable for large-scale testing. Values for the content of crude extract in the faeces were somewhat lower (0.78%-1.2%) when determined by method (5). These variations were not significant statistically. (P greater than 5%). No significant differences were observed between methods (2) and (5). It was thus established that method (5) is best suited for estimating the crude extract of the faces. The faeces of calves were found to contain a high proportion of unsaponifiable matter. This proportion was subtracted from the percentage of crude extract and the amount of faecal crude fat was thus estimated. Very small but statistically significant differences were found by converting digestibility data of crude extract into those of crude fat. Hence, for future work the most appropriate method appears to be the estimation of the crude extract in feedingstuffs.     

Near-infrared photoluminescence in germanium oxide enclosed germanium nano- and micro-crystals

We have studied the near-infrared photoluminescence properties of free-standing germanium nano-crystals (20?nm on average) and micro-crystals (60?μm on average) at 80-300?K. Two peaks were observed at ～1.0 and ～1.4?eV from both the nano-?and micro-crystals. The integrated PL (I(PL)) intensity of the nano-crystals is about an order of magnitude stronger than that of the micro-crystals and the I(PL) is also enhanced by ageing in air for both crystals. The ～1.0?eV peak position does not change with either the crystal size or temperature. We suggest that the deep traps located at the interfacial region between the surface GeO(2) layer and the bulk crystal Ge is responsible for the near-infrared PL.     

High-performance flat-panel solar thermoelectric generators with high thermal concentration

The conversion of sunlight into electricity has been dominated by photovoltaic and solar thermal power generation. Photovoltaic cells are deployed widely, mostly as flat panels, whereas solar thermal electricity generation relying on optical concentrators and mechanical heat engines is only seen in large-scale power plants. Here we demonstrate a promising flat-panel solar thermal to electric power conversion technology based on the Seebeck effect and high thermal concentration, thus enabling wider applications. The developed solar thermoelectric generators (STEGs) achieved a peak efficiency of 4.6% under AM1.5G (1 kW m(-2)) conditions. The efficiency is 7-8 times higher than the previously reported best value for a flat-panel STEG, and is enabled by the use of high-performance nanostructured thermoelectric materials and spectrally-selective solar absorbers in an innovative design that exploits high thermal concentration in an evacuated environment. Our work opens up a promising new approach which has the potential to achieve cost-effective conversion of solar energy into electricity.     

Activity of the enzymes participating in purine metabolism of cancerous and noncancerous human kidney tissues

CONTEXT: Heart failure is often preceded by isolated systolic hypertension, but the effectiveness of antihypertensive treatment in preventing heart failure is not known. OBJECTIVE: To assess the effect of diuretic-based antihypertensive stepped-care treatment on the occurrence of heart failure in older persons with isolated systolic hypertension. DESIGN: Analysis of data from a multicenter, randomized, double-blind, placebo-controlled clinical trial. PARTICIPANTS: A total of 4736 persons aged 60 years and older with systolic blood pressure between 160 and 219 mm Hg and diastolic blood pressure below 90 mm Hg who participated in the Systolic Hypertension in the Elderly Program (SHEP). INTERVENTION: Stepped-care antihypertensive drug therapy, in which the step 1 drug is chlorthalidone (12.5-25 mg) or matching placebo, and the step 2 drug is atenolol (25-50 mg) or matching placebo. MAIN OUTCOME MEASURES: Fatal and nonfatal heart failure. RESULTS: During an average of 4.5 years of follow-up, fatal or nonfatal heart failure occurred in 55 of 2365 patients randomized to active therapy and 105 of the 2371 patients randomized to placebo (relative risk [RR], 0.51; 95% confidence interval [CI], 0.37-0.71; P<.001; number needed to treat to prevent 1 event [NNT], 48). Among patients with a history of or electrocardiographic evidence of prior myocardial infarction (MI), the RR was 0.19 (95% CI, 0.06-0.53; P=.002; NNT, 15). Older patients, men, and those with higher systolic blood pressure or a history of or electrocardiographic evidence of MI at baseline had higher risk of developing heart failure. CONCLUSION: In older persons with isolated systolic hypertension, stepped-care treatment based on low-dose chlorthalidone exerted a strong protective effect in preventing heart failure. Among patients with prior MI, an 80% risk reduction was observed.     

Authoring Hierarchical Road Networks

We present a procedural method for generating hierarchical road networks connecting cities, towns and villages over large terrains. Our approach relies on an original geometric graph generation algorithm based on a non‐Euclidean metric combined with a path merging algorithm that creates junctions between the different types of roads. Unlike previous work, our method allows high level user control by manipulating the density and the pattern of the network. The geometry of the highways, primary and secondary roads as well as the interchanges and intersections are automatically created from the graph structure by instantiating generic parameterized models.     

Adaptive-Multilevel BDDC and its parallel implementation

We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a preconditioner based on standard components of the BDDC. The effectiveness of the method is illustrated on several engineering problems. It appears that the Adaptive-Multilevel BDDC algorithm is able to effectively detect troublesome parts on each decomposition level and improve convergence of the method. The developed open-source parallel implementation shows a good scalability as well as applicability to very large problems and core counts.     

An intuitive polygon morphing

We present a new algorithm for morphing simple polygons that is inspired by growing forms in nature. While previous algorithms require user-assisted definition of complicated correspondences between the morphing objects, our algorithm defines the correspondence by overlapping the input polygons. Once the morphing of one object into another is defined, very little or no user interaction is necessary to achieve intuitive results. Our algorithm is suitable namely for growth-like morphing. We present the basic algorithm and its three variations. One of them is suitable mainly for convex polygons, the other two are for more complex polygons, such as curved or spiral polygonal forms.