NEW FICTITIOUS DOMAIN METHODS: FORMULATION AND ANALYSIS

2005 ◽  
Vol 15 (10) ◽  
pp. 1575-1594 ◽  
Author(s):  
IVO BABUŠKA ◽  
EUGENE G. PODNOS ◽  
GREGORY J. RODIN
Keyword(s):  
Model Problem ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Fictitious Domain ◽  
Element Mesh ◽  
Multiple Interfaces ◽  
Fictitious Domain Methods ◽  
The Cost

Two closely-related fictitious domain methods for solving problems involving multiple interfaces are introduced. Like other fictitious domain methods, the proposed methods simplify the task of finite element mesh generation and provide access to solvers that can take advantage of uniform structured grids. The proposed methods do not involve the Lagrange multipliers, which makes them quite different from existing fictitious domain methods. This difference leads to an advantageous form of the inf–sup condition, and allows one to avoid time-consuming integration over curvilinear surfaces. In principle, the proposed methods have the same rate of convergence as existing fictitious domain methods. Nevertheless it is shown that, at the cost of introducing additional unknowns, one can improve the quality of the solution near the interfaces. The methods are presented using a two-dimensional model problem formulated in the context of linearized theory of elasticity. The model problem is sufficient for presenting method details and mathematical foundations. Although the model problem is formulated in two dimensions and involves only one interface, there are no apparent conceptual difficulties to extending the methods to three dimensions and multiple interfaces. Further, it is possible to extend the methods to nonlinear problems involving multiple interfaces.

scholarly journals Access to Infertility Consultations “What Women Tell Us About it”?

2018 ◽  
Vol 15 (1) ◽  
pp. 75-83 ◽  
Author(s):  
Paula Remoaldo ◽  
Maria de Fátima da Silva Vieira Martins ◽  
Juliana Patrícia Alves Faria ◽  
Paula Veiga
Keyword(s):  
Public Health ◽  
Health Problem ◽  
Public Health Problem ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Cost Of Treatment ◽  
Short Period ◽  
Treatment Medication ◽  
The Cost

Background:Infertility has been considered as a serious public health problem. Nevertheless, it is still very difficult to assess the epidemiology of this individual and public health problem. On the other hand, promotion of access to infertility treatments must be treated as a priority to national and regional policies.Objective:The aim was to evaluate the perception of women concerning the barriers and access to infertility consultations.Methods:Socio cultural and economic access to infertility consultations is detached and three municipalities of the northwest of Portugal were chosen as an example of a peripheral country. A quantitative/qualitative study was done with 60 women.Results:Three dimensions were evaluated: geographic and structural and functional access, economic access and sociocultural access. The main barriers were mainly identified in the last two dimensions. The economic access was less well evaluated by women bearing the cost of treatment (medication, and concentration of costs in a short period) which is difficult to bear.Conclusion:This can justify a greater involvement of the Portuguese Government, by developing policies for the reimbursement of part of the costs. Also, some changes in structural and functional access must be done with special regard to the separation of the infertility consultations from the reproductive medicine section. The setting of the teams, with a follow-up by the same team of health professionals is also needed.

scholarly journals Data on Orientation to Happiness in Higher Education Institutions from Mexico and El Salvador

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos
Keyword(s):  
Higher Education ◽  
El Salvador ◽  
Latin American ◽  
Higher Education Institutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Stepwise Multiple Regression ◽  
Teacher Student ◽  
And Gender ◽  
Student’S T

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.

scholarly journals Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Konrad Simon ◽  
Jörn Behrens
Keyword(s):  
Nonlinear Problems ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Multiscale Methods ◽  
Galerkin Methods ◽  
Standard Methods ◽  
Multiscale Problems ◽  
Eulerian Method ◽  
Lower Order Terms ◽  
New Framework

AbstractWe introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the associated difficulties is a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

scholarly journals PARALLEL DELAUNAY REFINEMENT: ALGORITHMS AND ANALYSES

2007 ◽  
Vol 17 (01) ◽  
pp. 1-30 ◽  
Author(s):  
DANIEL A. SPIELMAN ◽  
SHANG-HUA TENG ◽  
ALPER ÜNGÖR
Keyword(s):  
Mesh Size ◽  
Constant Factor ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Delaunay Refinement ◽  
Steiner Points ◽  
Input Domain ◽  
Set Of Points ◽  
Refinement Algorithm

We present a parallel Delaunay refinement algorithm for generating well-shaped meshes in both two and three dimensions. Like its sequential counterparts, the parallel algorithm iteratively improves the quality of a mesh by inserting new points, the Steiner points, into the input domain while maintaining the Delaunay triangulation. The Steiner points are carefully chosen from a set of candidates that includes the circumcenters of poorly-shaped triangular elements. We introduce a notion of independence among possible Steiner points that can be inserted simultaneously during Delaunay refinements and show that such a set of independent points can be constructed efficiently and that the number of parallel iterations is O( log 2Δ), where Δ is the spread of the input — the ratio of the longest to the shortest pairwise distances among input features. In addition, we show that the parallel insertion of these set of points can be realized by sequential Delaunay refinement algorithms such as by Ruppert's algorithm in two dimensions and Shewchuk's algorithm in three dimensions. Therefore, our parallel Delaunay refinement algorithm provides the same shape quality and mesh-size guarantees as these sequential algorithms. For generating quasi-uniform meshes, such as those produced by Chew's algorithms, the number of parallel iterations is in fact O( log Δ). To the best of our knowledge, our algorithm is the first provably polylog(Δ) time parallel Delaunay-refinement algorithm that generates well-shaped meshes of size within a constant factor of the best possible.

scholarly journals Interaction between mean flow and turbulence in two dimensions

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160287 ◽  
Author(s):  
Gregory Falkovich
Keyword(s):  
Short Note ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Planar Domains ◽  
Developed Turbulence ◽  
Aspect Ratios ◽  
Simple Geometry ◽  
Turbulent Cascade

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end.

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