A parallel multigrid solver for multi-patch Isogeometric Analysis

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.Comment: The first author would like to thank the Austrian Science Fund (FWF) for the financial support through the DK W1214-04, while the second author was supported by the FWF grant NFN S117-0

Beyond the Evidence of the New Hypertension Guidelines. Blood pressure measurement – is it good enough for accurate diagnosis of hypertension? Time might be in, for a paradigm shift (I)

Despite widespread availability of a large body of evidence in the area of hypertension, the translation of that evidence into viable recommendations aimed at improving the quality of health care is very difficult, sometimes to the point of questionable acceptability and overall credibility of the guidelines advocating those recommendations. The scientific community world-wide and especially professionals interested in the topic of hypertension are witnessing currently an unprecedented debate over the issue of appropriateness of using different drugs/drug classes for the treatment of hypertension. An endless supply of recent and less recent "drug-news", some in support of, others against the current guidelines, justifying the use of selected types of drug treatment or criticising other, are coming out in the scientific literature on an almost weekly basis. The latest of such debate (at the time of writing this paper) pertains the safety profile of ARBs vs ACE inhibitors. To great extent, the factual situation has been fuelled by the new hypertension guidelines (different for USA, Europe, New Zeeland and UK) through, apparently small inconsistencies and conflicting messages, that might have generated substantial and perpetuating confusion among both prescribing physicians and their patients, regardless of their country of origin. The overwhelming message conveyed by most guidelines and opinion leaders is the widespread use of diuretics as first-line agents in all patients with blood pressure above a certain cut-off level and the increasingly aggressive approach towards diagnosis and treatment of hypertension. This, apparently well-justified, logical and easily comprehensible message is unfortunately miss-obeyed by most physicians, on both parts of the Atlantic. Amazingly, the message assumes a universal simplicity of both diagnosis and treatment of hypertension, while ignoring several hypertension-specific variables, commonly known to have high level of complexity, such as: - accuracy of recorded blood pressure and the great inter-observer variability, - diversity in the competency and training of diagnosing physician, - individual patient/disease profile with highly subjective preferences, - difficulty in reaching consensus among opinion leaders, - pharmaceutical industry's influence, and, nonetheless, - the large variability in the efficacy and safety of the antihypertensive drugs. The present 2-series article attempts to identify and review possible causes that might have, at least in part, generated the current healthcare anachronism (I); to highlight the current trend to account for the uncertainties related to the fixed blood pressure cut-off point and the possible solutions to improve accuracy of diagnosis and treatment of hypertension (II)

Consistent patterns of common species across tropical tree communities

Trees structure the Earth’s most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations1,2,3,4,5,6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth’s 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories7, we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world’s most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees

Consistent patterns of common species across tropical tree communities

Trees structure the Earth's most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations1-6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth's 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories7, we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world's most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees