Analysis of preconditioners for saddle-point problems

Mixed finite element formulations give rise to large, sparse, block linear systems of equations the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the formulation of the finite element method (the Babuska-Brezzi, or inf-sup conditions)

Preconditioning the Advection-Diffusion Equation: the Green's Function Approach

We look at the relationship between efficient preconditioners (i.e., good approximations to the discrete inverse operator) and the generalized inverse for the (continuous) advection-diffusion operator -- the Green's function. We find that the continuous Green's function exhibits two important properties -- directionality and rapid downwind decay -- which are preserved by the discrete (grid) Green's functions, if and only if the discretization used produces non-oscillatory solutions. In particular, the downwind decay ensures the locality of the grid Green's functions. Hence, a finite element formulation which produces a good solution will typically use a coefficient matrix with almost lower triangular structure under a "with-the-flow" numbering of the variables. It follows that the block Gauss-Seidel matrix is a first candidate for a preconditioner to use with an iterative solver of Krylov subspace type

Schur complement preconditioning for elliptic systems of partial differential equations

One successful approach in the design of solution methods for saddle-point problems requires the efficient solution of the associated Schur complement problem. In the case of problems arising from partial differential equations the factorization of the symbol of the operator can often suggest useful approximations for this problem. In this work we examine examples of preconditioners for regular elliptic systems of partial differential equations based on the Schur complement of the symbol of the operator and highlight the possibilities and some of the difficulties one may encounter with this approach

A preconditioner for the 3D Oseen equations

We describe a preconditioner for the linearised incompressible Navier-Stokes equations (the Oseen equations) which requires as components only a preconditioner/solver for each of a discrete Laplacian and a discrete advection-diffusion operator. With this preconditioner, convergence of an iterative method such as GMRES is independent of the mesh size and depends only mildly on the viscosity parameter (the inverse Reynolds number). Thus when the component preconditioner/solvers are effective on their respective subproblems (as one expects with an appropriate multigrid cycle for instance) a fast Oseen solver results

Modelling the Fluid Mechanics of Cilia and Flagella in Reproduction and Development

Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscous-dominated microscale flow, including time-reversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higher order multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: (1) left-right symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and (2) motility of microswimmers through non-Newtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a body-conforming finite element framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a three-sphere model swimmer and a model sperm are similarly affected by shear-thinning; in both cases swimming due to a prescribed beat is enhanced by shear-thinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shear-thickening hindering cell progress.Comment: 20 pages, 24 figure

Validation of a cyclic plasticity computational method using fatigue full-field deformation measurements

The evolution of crack tip displacement and strain fields during uniaxial, room temperature, low-cycle fatigue experiments of Nickel superalloy compact tension specimens was measured by a digital image correlation approach and was further used to validate a cyclic plasticity model and corresponding deformation calculations made by a finite elements methodology. The experimental results provided data trends for the opening displacements and near crack tip strains as function of cycles. A finite element model was developed to capture test conditions for a measured crack size. The model captures crack tip plasticity by using a constitutive model calibrated against stress-strain measurements performed on a round bar. Similar quantities were extracted from the model predictions to compare with the digital image correlation measurements for model validation purposes. This type of direct comparison demonstrated that the computational model was capable to adequately capture the crack opening displacements at various stages of the specimen's fatigue life, providing in this way a tool for quantitative cyclic plasticity model validation. In addition, this integrated experimental-computational approach provides a framework to accelerate our understanding related to interactions of fatigue test data and models, as well as ways to inform one another

EQUIPT: protocol of a comparative effectiveness research study evaluating cross-context transferability of economic evidence on tobacco control

This is an Open Access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial.This article has been made available through the Brunel Open Access Publishing Fund.Tobacco smoking claims 700 000 lives every year in Europe and the cost of tobacco smoking in the EU is estimated between €98 and €130 billion annually; direct medical care costs and indirect costs such as workday losses each represent half of this amount. Policymakers all across Europe are in need of bespoke information on the economic and wider returns of investing in evidence-based tobacco control, including smoking cessation agendas. EQUIPT is designed to test the transferability of one such economic evidence base-the English Tobacco Return on Investment (ROI) tool-to other EU member states

Роль общения в практике семейных медицинских сестёр

Center of Healthy for Youth, National College of Medicine and Pharmacy Neovita, Center for Continuing Medical Education for Medical and Pharmaceutical Secondary Staff, Congresul III al Medicilor de Familie din Republica Moldova, 17–18 mai, 2012, Chişinău, Republica Moldova, Conferinţa Naţională „Maladii bronhoobstructive la copii”, consacrată profesorului universitar, doctor habilitat Victor Gheţeul, 27 aprilie, Chişinău, Republica MoldovaCommunication in medicine should not be viewed as a common object, understood by itself. There is a difference between unconscious and intentional communication. The necessity to improve communication with the patient comes from the gaps that persist in the communication abilities of family nurses. All nurse-patient interactions are influenced by the expectations that both parties have.Общение в медицинской практике не должно трактоваться, как обычная составляющая практической деятельности. Существует четкая грань между обычным, в бытовом понятии, общением и общением профессиональным. Необходимость постоянного улучшения качественной составляющей общения с больными обусловлено, в первую очередь, теми недостатками, которые продолжают иметь место в общении между семейными медицинскими сестрами и больными. Взаимоотношения между медицинскими сестрами и пациентами регулируются, в конечном итоге, ожидаемыми результатами обеих сторон

Интерактивное обучение в процессе непрерывного медицинского образования семейных медицинских сестер

Center for Continuing Medical Education of Medical and Pharmaceutical Personnel with secundary education, Congresul III al Medicilor de Familie din Republica Moldova 17–18 mai, 2012, Chişinău, Republica MoldovaInteractive learning is not opposed to classical learning, but it is a new quality of the objectives pursued by the formation of personality. Active and creative work is based on the student aimed at his reflection on his identity, the learning needs and expectations by testing in accordance with the particular educational and cognitive possibilities, practical and intellectual and physical effort. Metacognition involves analyzing the degree of difficulty of learning tasks and strategies for achieving them effectively. Lifelong learning – a goal of postmodern education – must be interactive and creative in adopting strategies to seek involvement, conscious learning and interest in continuous improvement. Интерактивное обучение не противоречит классическому обучению, но это новое качество целей, способствующее формированию личности. Активная и творческая работа курсанта направлена на свое отражение как предмет изучения потребностей и ожиданий на тестирование в соответствии с определенными образовательными и познавательными возможностями, практических, умственных и физических усилий. Познание включает анализ степени трудности учебных задач и достижения эффективных стратегий. Непрерывное обучение – цель постмодернистского образования, интерактивная реклама и творческий подход в принятии стратегии добиваться участия, сознательного обучения и интерес к постоянному совершенствованию

GEOMETRIC PROCESSING OF VERY HIGH-RESOLUTION SATELLITE IMAGERY: QUALITY ASSESSMENT FOR 3D MAPPING NEEDS

In recent decades, the geospatial domain has benefitted from technological advances in sensors, methodologies, and processing tools to expand capabilities in mapping applications. Airborne techniques (LiDAR and aerial photogrammetry) generally provide most of the data used for this purpose. However, despite the relevant accuracy of these technologies and the high spatial resolution of airborne data, updates are not sufficiently regular due to significant flight costs and logistics. New possibilities to fill this information gap have emerged with the advent of Very High Resolution (VHR) optical satellite images in the early 2000s. In addition to the high temporal resolution of the cost-effective datasets and their sub-meter geometric resolutions, the synoptic coverage is an unprecedented opportunity for mapping remote areas, multi-temporal analyses, updating datasets and disaster management. For all these reasons, VHR satellite imagery is clearly a relevant study for National Mapping and Cadastral Agencies (NMCAs). This work, supported by EuroSDR, summarises a series of experimental analyses carried out over diverse landscapes to explore the potential of VHR imagery for large-scale mapping