The INTERNODES Method for Non-conforming Discretizations of PDEs

INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into two or several disjoint subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interfaces, and the other for the Neumann trace. In this paper, in every subdomain the original problem is discretized by either the finite element method (FEM) or the spectral element method (SEM or hp-FEM), using a priori non-matching grids and piecewise polynomials of different degrees. Other discretization methods, however, can be used. INTERNODES can also be applied to heterogeneous or multiphysics problems, that is, problems that feature different differential operators inside adjacent subdomains. For instance, in this paper we apply the INTERNODES method to a Stokes- Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence with respect to the grid size and the polynomial degree.

Assessment of Potential Aerodrome Obstacles on Flight Safety Operations Using GIS: A Case of Murtala Mohammed International Airport, Lagos-Nigeria

The study focuses on the spatial analysis of the threat of potential Aerodrome obstacles on flight safety operations, in Murtala Mohammed Airport, Ikeja Lagos State. The study arises from the cases of flight safety in Nigerian airports which begins from the time passengers board the flight to the take-off time and location, the taxing of the plane and ends at the landing. The research employs GIS to model the 3D obstacles of the aerodrome, which demonstrated the ability in classifying the various threats on the aerodrome. The data acquired for this study ranging from primary data which included georeferencing of the obstacles that are found along the aerodrome with a Differential Global Positioning System (DGPS) to secondary data which included all base maps and satellite images. The spatial data conversion and manipulations were done using the ArcGIS 10.3.1 software. The 3D simulation of the obstacles was done in the ArcScene environment. To examine the spatial patterns of the obstacles around the aerodrome, the Average Nearest Neighbour Analysis (ANN) was used as statistical function from ArcGIS. The obstacles found within the MM2 aerodrome were grouped into the tolerant and non-tolerant ones. However, the finding shows that MM2 aerodrome conforms to ICAO standards and recommended practices. The study thus recommends strict daily monitoring of flight route to mark objects for foundation on the non-tolerance zones.

Laboratory Quality Audit in 25 Anti-Retroviral Therapy Facilities in North West of Nigeria

Introduction: A laboratory’s ability to consistently produce high-quality and reliable results hinges on adopting laboratory standards that guide daily practices to ensure steady quality improvement. Although assessment is an extremely rewarding exercise in health care quality improvement processes, it is always considered very time consuming and expensive in developing world settings. A quarterly internal audit was conducted in 25 FHI360 supported Antiretroviral Treatment laboratories in the North West of Nigeria which can surely provide reference for other countries. Methodology: A checklist adapted from the World Health Organization/African Regional Office laboratory accreditation checklist was used to quantitatively evaluate 7 quality essentials (QEs). A team composed of technical staff from FHI360, State Ministry of Health and facility laboratory heads, conducted the audits, developed and monitored intervention plans. Information obtained with the checklist was captured in excel, validated and imported into Grappa Prism software version 5.0 for analysis. Results: Most (92%) facilities were at secondary level with (8%) at tertiary level. The mean total score on all QEs across the facilities was 63.34 ± 9.77 in quarter (Q) 1, 68.8 ± 10.91 in Q2, 72.59 ± 8.02 in Q3 and 72.72 ± 9.16 in Q4 (p ≤ 0.0001). The most improved QE through Q1-Q4 was organization and personnel (32.2%), while signage/bench top reference had an 18.6% point decline. In ranking facilities based on differences of total scores between Q4 and Q1, Kachia General Hospital was the highest with 27 point increase. Considering the mean percentage score for all quarters per facility, 4 had ≥ 80%, 19 had between 60%-80% and 2 had <60%. The total non-conformities cited for QI-Q4 were 185, 100, 78 and 64 respectively with highest recorded in internal and external quality control and the least in facility and safety. Conclusion: We recorded some improvement in most QEs confirming the benefits of internal audits, reviews and follow-up. However, much more is needed in terms of technical assistance, capacity building, mentorship, and commitment at facility and state level to meet minimum acceptable laboratory quality standards.

A Multivariate Process Capability Index

Process capability indices have been widely used in the manufacturing industry,providing numerical measures on process precision,process accuracy,and process performance.Capability measures for processes with a single characteristic have been investigated extensively.However,capability measures for processes with multiple characteristics are comparatively neglected. In this paper,inspired by the approach and model of process capability index investigated by K.S.Chen et al.(2003) and A.B. Yeh et al.(1998),a note model of multivariate process capability index based on non-conformity is presented.As for this index, the data of each single characteristic don’t require satisfying normal distribution,of which its computing is simple and particioners will not fell too theoretical.At last the application analysis is made.

A comparative study of the ATC-40 recommended and numerically derived M-φ relationship

Nonlinear static analysis procedures are key tools in evaluating the performance of existing buildings and verifying the design of seismic retrofits in seismically active regions. In this procedure, nonlinear force-displacement or moment-curvature （M-φ） behavior needs to be defined. In the ATC-40 document, values of M-φ have been proposed to model elements in a nonlinear procedure. However, these values need to be investigated to determine if they are representative of actual values. In this paper, an attempt has been made to numerically derive M-φ curves to simulate actual performance. Then, these curves are compared with the ATC-40 recommended curves with respect to various parameters. The study indicated that ATC-40 suggested values are conservative in nature in most situations.

A PRACTICAL QUADRILATERAL MEMBRANE ELEMENT WITH DRILLING DEGREES OF FREEDOM

A simple, robust quadrilateral membrane element with drilling degrees of freedom is presented in this paper. This membrane element is based on Allman's approach, and derived from the constrained variational principle which enforces the equality of rotations obtained from the displacement field and independent rotation field by a penalty function. Examples show that the presented membrane element is fully compatible with typical beam element and plate element. And also, the non-conforming shape functions used in this element exhibits excellent performance over both regular and distorted meshes. Based on the presented membrane element, it is very convenient to construct the shear wall element of six degrees of freedom, which is often used in The analysis of general three-dimensional building structures.

Power and Personality

The term power is widespread in social and political theory. The polysemantic nature of the term power has led to a variety of definitions of this concept. The classical articulation of the definition of power/authority was given by the classics of sociology—Weber and Parsons. But classic articulation of power is defined in terms of relation-activity matrix of power, namely, authority. The paper conceptualizes power as the unity of power-kratia and power-arhiya and analyzes it from the point of view of functioning and development of society and personality. Such conception of power focuses on the ways in which personalities are constituted not only by power relations but are capable to change socio-cultural and economic conditions of their existence. So, power and freedom, resistance and transformation of power relations are complementary to one another.

滚动式内部审核不符合项数据分析与利用

本文说明了在滚动式内部审核中,不符合项数据对于评价组织体系运行情况和促进质量管理体系改进的关键作用 O并以某装备制造企业为实例,简要介绍了组织通过滚动式内部审核的不符合项进行数据分析和利用,识别组织质量管理体系存在的薄弱环节和风险,促进质量管理体系改进提升和有效保持的具体实现方法。

Eigenvalue approximation from below using non-conforming finite elements

This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,with emphasis on obtaining lower bounds. In addition,this article also contains some new materials for eigenvalue approximations of the Laplace operator,which include:1) the proof of the fact that the non-conforming Crouzeix-Raviart element approximates eigenvalues associated with smooth eigenfunctions from below;2) the proof of the fact that the non-conforming EQ rot1 element approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements;3) the explanation of the phenomena that numerical eigenvalues λ 1,h and λ 3,h of the non-conforming Q rot1 element approximate the true eigenvalues from below for the L-shaped domain. Finally,we list several unsolved problems.

Some Numerical Quadrature Schemes of a Non-conforming Quadrilateral Finite Element

Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional （2-D） and three dimensional （3-D） space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis.

Numerical Methods for Fluid-Structure Interaction—A Review

The interactions between incompressible fluid flows and immersed structures are nonlinearmulti-physics phenomena that have applications to a wide range of scientific and engineering disciplines.In this article,we review representative numericalmethods based on conforming and non-conformingmeshes that are currently available for computing fluid-structure interaction problems,with an emphasis on some of the recent developments in the field.A goal is to categorize the selected methods and assess their accuracy and efficiency.We discuss challenges faced by researchers in this field,and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions.

Discontinuous Galerkin Methods for Isogeometric Analysis for Elliptic Equations on Surfaces

We propose a method that combines isogeometric analysis(IGA)with the discontinuous Galerkin(DG)method for solving elliptic equations on 3-dimensional(3D)surfaces consisting of multiple patches.DG ideology is adopted across the patch interfaces to glue the multiple patches,while the traditional IGA,which is very suitable for solving partial differential equations(PDEs)on(3D)surfaces,is employed within each patch.Our method takes advantage of both IGA and the DG method.Firstly,the time-consuming steps in mesh generation process in traditional finite element analysis(FEA)are no longer necessary and refinements,including h-refinement and p-refinement which both maintain the original geometry,can be easily performed by knot insertion and order-elevation(Farin,in Curves and surfaces for CAGD,2002).Secondly,our method can easily handle the cases with non-conforming patches and different degrees across the patches.Moreover,due to the geometric flexibility of IGA basis functions,especially the use of multiple patches,we can get more accurate modeling of more complex surfaces.Thus,the geometrical error is significantly reduced and it is,in particular,eliminated for all conic sections.Finally,this method can be easily formulated and implemented.We generally describe the problem and then present our primal formulation.A new ideology,which directly makes use of the approximation property of the NURBS basis functions on the parametric domain rather than that of the IGA functions on the physical domain(the former is easier to get),is adopted when we perform the theoretical analysis including the boundedness and stability of the primal form,and the error analysis under both the DG norm and the L2 norm.The result of the error analysis shows that our scheme achieves the optimal convergence rate with respect to both the DG norm and the L2 norm.Numerical examples are presented to verify the theoretical result and gauge the good performance of our method.

METHOD OF NONCONFORMING MIXED FINITE ELEMENTFOR SECOND ORDER ELLIPTIC PROBLEMSMETHOD OF NONCONFORMING MIXED FINITE ELEMENTFOR SECOND ORDER ELLIPTIC PROBLEM

In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.

A Family of Methods of the DG-Morley Type for Polyharmonic Equations

Discontinuous Galerkin methods as a solution technique of second order elliptic problems,have been increasingly exploited by several authors in the past ten years.It is generally claimed the alledged attractive geometrical flexibility of these methods,although they involve considerable increase of computational effort,as compared to continuous methods.This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic m-harmonic equations in a bounded domain of R^(n),for n=2 or n=3,with m≥n+1,as a valid and reasonable alternative to classical finite elements,or even to boundary element methods.

A Hybrid FETD-FDTD Method with Nonconforming Meshes

A quasi non-overlapping hybrid scheme that combines the finite-difference time-domain(FDTD)method and the finite-element time-domain(FETD)method with nonconforming meshes is developed for time-domain solutions of Maxwell’s equations.The FETD method uses mixed-order basis functions for electric and magnetic fields,while the FDTD method uses the traditional Yee’s grid;the two methods are joined by a buffer zone with the FETD method and the discontinuous Galerkin method is used for the domain decomposition in the FETD subdomains.The main features of this technique is that it allows non-conforming meshes and an arbitrary numbers of FETD and FDTD subdomains.The hybrid method is completely stable for the time steps up to the stability limit for the FDTD method and FETD method.Numerical results demonstrate the validity of this technique.

Marker-Based,3-D Adaptive Cartesian Grid Method for Multiphase Flow Around Irregular Geometries

Computational simulations of multiphase flow are challenging because many practical applications require adequate resolution of not only interfacial physics associated with moving boundaries with possible topological changes,but also around three-dimensional,irregular solid geometries.In this paper,we highlight recent efforts made in simulating multiphase fluid dynamics around complex geometries,based on an Eulerian-Lagrangian framework.The approach uses two independent but related grid layouts to track the interfacial and solid boundary conditions,and is capable of capturing interfacial as well as multiphase dynamics.In particular,the stationary Cartesian grid with time dependent,local adaptive refinement is utilized to handle the computation of the transport equations,while the interface shape and movement are treated by marker-based triangulated surface meshes which freely move and interact with the Cartesian grid.The markers are also used to identify the location of solid boundaries and enforce the no-slip condition there.Issues related to the contact line treatment,topological changes of multiphase fronts during merger or breakup of objects,and necessary data structures and solution techniques are also highlighted.Selected test cases including spacecraft fuel tank flow management and liquid plug flow dynamics are presented.