Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
The finite element method solution of variable diffusion coefficient convection-diffusion equations
Aydin, Selçuk Han; ćiftçi, Canan
2012-08-01
Mathematical modeling of many physical and engineering problems is defined with convection-diffusion equation. Therefore, there are many analytic and numeric studies about convection-diffusion equation in literature. The finite element method is the most preferred numerical method in these studies since it can be applied to many problems easily. But, most of the studies in literature are about constant coefficient case of the convection-diffusion equation. In this study, the finite element formulation of the variable coefficient case of the convection-diffusion equation is given in both one and two dimensional cases. Accuracy of the obtained formulations are tested on some problems in one and two dimensions.
Dao-qi Yang; Jennifer Zhao
2003-01-01
An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems withstrongly discontinuous solutions, conormal derivatives, and coefficients. This algorithmiteratively solves small problems for each single phase with good accuracy and exchangeinformation at the interface to advance the iteration until convergence, following the ideaof Schwarz Alternating Methods. Error estimates are derived to show that this algorithmalways converges provided that relaxation parameters are suitably chosen. Numeric experiments with matching and non-matching grids at the interface from different phases areperformed to show the accuracy of the method for capturing discontinuities in the solutionsand coefficients. In contrast to standard numerical methods, the accuracy of our methoddoes not seem to deteriorate as the coefficient discontinuity increases.
Bo Li
2014-01-01
Full Text Available The lack of evaluation standard for safety coefficient based on finite element method (FEM limits the wide application of FEM in roller compacted concrete dam (RCCD. In this paper, the strength reserve factor (SRF method is adopted to simulate gradual failure and possible unstable modes of RCCD system. The entropy theory and catastrophe theory are used to obtain the ultimate bearing resistance and failure criterion of the RCCD. The most dangerous sliding plane for RCCD failure is found using the Latin hypercube sampling (LHS and auxiliary analysis of partial least squares regression (PLSR. Finally a method for determining the evaluation standard of RCCD safety coefficient based on FEM is put forward using least squares support vector machines (LSSVM and particle swarm optimization (PSO. The proposed method is applied to safety coefficient analysis of the Longtan RCCD in China. The calculation shows that RCCD failure is closely related to RCCD interface strength, and the Longtan RCCD is safe in the design condition. Considering RCCD failure characteristic and combining the advantages of several excellent algorithms, the proposed method determines the evaluation standard for safety coefficient of RCCD based on FEM for the first time and can be popularized to any RCCD.
大西, 泰史
2017-01-01
The purpose of this study is to perform to earth pressure coefficient calculation simulation using the Distinct Element Method (DEM). Earth pressure theory has been established since long ago and is still in use. Therefore, simulation based on Coulomb and Rankine's theory of earth pressure is carried out to confirm usability of DEM. As a result of the static earth pressure coefficient calculation simulation, good results were obtained. However, in the passive earth pressure coefficient calcul...
Two-level Schwartz methods for nonconforming finite elements and discontinuous coefficients
Sarkis, Marcus
1993-01-01
Two-level domain decomposition methods are developed for a simple nonconforming approximation of second order elliptic problems. A bound is established for the condition number of these iterative methods, which grows only logarithmically with the number of degrees of freedom in each subregion. This bound holds for two and three dimensions and is independent of jumps in the value of the coefficients.
Xie, Wenhao; Deng, Yong; Lian, Lichao; Yan, Dongmei; Yang, Xiaoquan; Luo, Qingming
2016-01-01
The functional information, the absorption and diffusion coefficients, as well as the structural information of biological tissues can be provided by the DOT(Diffuse Optical Tomograph)/MicroCT. In this paper, we use boundary element method to calculate the forward problem of DOT based on the structure prior given by the MicroCT, and then we reconstruct the absorption and diffusion coefficients of different biological tissues by the Levenberg-Marquardt algorithm. The method only needs surface meshing, reducing the complexity of calculation; in addition, it reconstructs a single value within an organ, which reduces the ill-posedness of the inverse problem to make reconstruction results have good noise stability. This indicates that the boundary element method-based reconstruction can serve as an new scheme for getting absorption and diffusion coefficients in DOT/MicroCT multimodality imaging.
Luo Chang
2006-01-01
In this work, system of parabolic equations with discontinuous coefficients is studied. The domain decomposition method modified by a characteristic finite element procedure is applied. A function is defined to approximate the fluxes on inner boundaries by using the solution at the previous level. Thus the parallelism is achieved. Convergence analysis and error estimate are also presented.
Mohd Zamri Jusoh
2013-06-01
Full Text Available The Direct Piercing Carved Wood Panel (DPCWP installed in Masjid Abidin, Kuala Terengganu, is one example that carries much aesthetic and artistic value. The use of DPCWP in earlier mosques was envisaged to improve the intelligibility of indoor speech because the perforated panels allow some of the sound energy to pass through. In this paper, the normal incidence sound absorption coefficient of DPCWP with Daun Sireh motif, which is a form of floral pattern, is discussed. The Daun Sireh motif was chosen and investigated for 30%, 35%, 40%, and 45% perforation ratios. The simulations were conducted using BEASY Acoustic Software based on the boundary element method. The simulation results were compared with measurements obtained by using the sound intensity technique. An accompanying discussion on both the numerical and the measurement tendencies of the sound absorption characteristics of the DPCWP is provided. The results show that the DPCWP with Daun Sireh motif can act as a good sound absorber.
Zampini, Stefano
2016-06-02
Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically established that are independent of the number of subdomains of the decomposition. The core of the methods resides in the design of a larger and partially discontinuous finite element space that allows for fast application of the preconditioner, where Cholesky factorizations of the subdomain finite element problems are additively combined with a coarse, global solver. Multilevel and highly-scalable algorithms can be obtained by replacing the coarse Cholesky solver with a coarse BDDC preconditioner. BDDC methods have the remarkable ability to control the condition number, since the coarse space of the preconditioner can be adaptively enriched at the cost of solving local eigenproblems. The proper identification of these eigenproblems extends the robustness of the methods to any heterogeneity in the distribution of the coefficients of the PDEs, not only when the coefficients jumps align with the subdomain boundaries or when the high contrast regions are confined to lie in the interior of the subdomains. The specific adaptive technique considered in this paper does not depend upon any interaction of discretization and partition; it relies purely on algebraic operations. Coarse space adaptation in BDDC methods has attractive algorithmic properties, since the technique enhances the concurrency and the arithmetic intensity of the preconditioning step of the sparse implicit solver with the aim of controlling the number of iterations of the Krylov method in a black-box fashion, thus reducing the number of global synchronization steps and matrix vector multiplications needed by the iterative solver; data movement and memory bound kernels in the solve phase can be thus limited at the expense of extra local ops during the setup of
L. Chen; P.L. Wang; P.N. Song; J.Y. Zhang
2007-01-01
With the technology support of virtual reality and ANSYS software, an example on the simulation of temperature distribution of casting system during the solidification process was provided, which took the latent heat of phase change, the conditions for convection, and the interface heat transfer coefficient into consideration. The result of ANSYS was found to agree well with the test data. This research offers an unorthodox way or "reverse method" of defining the relevant thermal physical coefficient.
Aberration coefficients of curved holographic optical elements
Verboven, P. E.; Lagasse, P. E.
1986-11-01
A general formula is derived that gives all aberration terms of holographic optical elements on substrates of any shape. The spherical substrate shape and the planar substrate shape are treated as important special cases. A numerical example illustrates the need of including higher-order aberrations.
quadratic spline finite element method
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Why the Method of Undetermined Coefficients Works.
Ross, Clay C., Jr.
1991-01-01
This note presents a simple theorem which explains why the method of undetermined coefficients works in finding a particular solution, both for differential equations and difference equations. (Author)
Why the Method of Undetermined Coefficients Works.
Ross, Clay C., Jr.
1991-01-01
This note presents a simple theorem which explains why the method of undetermined coefficients works in finding a particular solution, both for differential equations and difference equations. (Author)
Stochastic back analysis of permeability coefficient using generalized Bayesian method
Zheng Guilan; Wang Yuan; Wang Fei; Yang Jian
2008-01-01
Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method (SFEM) for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.
Torsion method for measuring piezooptic coefficients
Skab, I.; Smaga, I.; Savaryn, V.; Vasylkiv, Yu.; Vlokh, R. [Institute of Physical Optics, Lviv (Ukraine)
2011-01-15
We develop and describe analytically a torsion method for measuring piezooptic coefficients associated with shear stresses. It is shown that the method enables to increase significantly the accuracy of determination of piezooptic coefficients. The method and the appropriate apparatus are verified experimentally on the example of LiNbO{sub 3} crystals. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Stochastic back analysis of permeability coefficient using generalized Bayesian method
Gui-lan ZHENG
2008-09-01
Full Text Available Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method (SFEM for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.
Wet Friction-Elements Boundary Friction Mechanism and Friction Coefficient Prediction
WANG Yanzhong
2012-12-01
Full Text Available The friction mechanism for the boundary friction course of friction elements engagement was explicitly expressed. The boundary friction model was built up by the surface topography. The model contained the effect of boundary film, adhesion, plough and lubrication. Based on the model, a coefficient for weakening plough for the lubrication was proposed. The modified model could fit for the working condition of wet friction elements. The friction coefficient as a function curve of rotating speed could be finally obtained by the data k and s/sm. The method provides a well interpretation of friction condition and friction coefficient prediction and the agreement between theoretical and experimental friction coefficients is reasonably good.
Hall, Eric
2016-01-09
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.
Sandberg, Mattias
2015-01-07
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.
Calculation of Thermal Expansion Coefficients of Pure Elements and their Alloys
Abel, Phillip; Bozzolo, Guillermo; Huff, Dennis (Technical Monitor)
2002-01-01
A simple algorithm for computing the coefficient of thermal expansion of pure elements and their alloys, based on features of the binding energy curve, is introduced. The BFS method for alloys is used to determine the binding energy curves of intermetallic alloys and Ni-base superalloys.
The influence of aerodynamic coefficients on the elements of classic projectile paths
Damir D. Jerković
2011-04-01
Full Text Available The article deals with the results of the research on the influence of aerodynamic coefficient values on the trajectory elements and the stability parameters of classic axisymmetric projectiles. It presents the characteristic functions of aerodynamic coefficients with regard to aerodynamic parameters and the projectile body shape. The trajectory elements of the model of classic axisymmetric projectiles and the analyses of their changes were presented with respect to the aerodynamic coefficient values. Introduction Classic axisymmetric projectiles fly through atmosphere using muzzle velocity as initial energy resource, so the aerodynamic force and moment have the most significant influence on the motion of projectiles. The aerodynamic force and moment components represented as aerodynamic coefficients depend on motion velocity i. e. flow velocity, the flow features produced by projectile shape and position in the flow, and angular velocity (rate of the body. The functional dependence of aerodynamic coefficients on certain influential parameters, such as angle of attack and angular velocity components is expressed by the derivative of aerodynamic coefficients. The determination of aerodynamic coefficients and derivatives enables complete definition of the aerodynamic force and moment acting on the classic projectile. The projectile motion problem is considered in relation to defining the projectile stability parameters and the conditions under which the stability occurs. The comparative analyses of aerodynamic coefficient values obtained by numerical methods, semi empirical calculations and experimental research give preliminary evaluation of the quality of the determined values. The flight simulation of the motion of a classic axisymetric projectile, which has the shape defined by the aerodynamic coefficient values, enables the comparative analyses of the trajectory elements and stability characteristics. The model of the classic projectile
Yamashita, Osamu [Research and Development, Materials Science Co. Ltd., 5-5-44, Minamikasugaoka, Ibaraki, Osaka 567-0046 (Japan)
2009-09-15
The resultant Seebeck coefficient {alpha}{sub R}(T{sub z}) of a thermoelectric (TE) element was derived analytically from the temperature dependence of the intrinsic Seebeck coefficient {alpha}{sub I}(T{sub z}) by taking into account the Thomson effect, where T{sub z} is a temperature at z along a TE element. The analysis was performed by expanding {alpha}{sub I}(T{sub z}) in a power series in (T{sub z}-T), where T is a mean temperature. As a result, when {alpha}{sub I}(T{sub z}) has a convex curve exhibiting a local maximum at T{sub z}=T, {alpha}{sub R}(T{sub z}) is increased at the interfaces of a TE element, while when it has a concave curve giving a local minimum at T{sub z}=T, {alpha}{sub R}(T{sub z}) deteriorates there. If the p-type (Bi{sub 0.4}Sb{sub 0.6}){sub 2}Te{sub 3} with a local maximum of {alpha}{sub I}(T{sub z}) at T=390 K is employed for a TE element, {alpha}{sub R}(T{sub z})/{alpha}{sub I}(T) at both interfaces is increased up to 1.53 under the condition of T = 390 K and {delta}T=200 K. A similar enhancement in {alpha}{sub R}(T{sub z})/{alpha}{sub I}(T) appeared even in the n-type (Zr-Hf)NiSn half-Heusler. When {alpha}{sub I}(T{sub z}) varies nonlinearly with changes in T{sub z}, therefore, the TE figure of merit Z{sub R}(T{sub z})T{sub z} is found to be affected dramatically at the interfaces. The average resultants Z{sub AR}(T) estimated for the p-type Bi-Te and n-type half-Heusler compound reach great values of 1.46 and 1.26 times as large as their intrinsic Z(T), respectively. The experimental method to confirm such a phenomenon is also proposed here. The performance of a TE element is thus expected to be enhanced significantly not only by improving the intrinsic Z(T{sub z})T{sub z} but also by optimizing the T{sub z}-dependence of {alpha}{sub I}(T{sub z}). (author)
Caprio, M A; McCoy, A E; 10.1063/1.3445529
2010-01-01
It is shown that the method of infinitesimal generators ("Racah's method") can be broadly and systematically formulated as a method applicable to the calculation of reduced coupling coefficients for a generic subalgebra chain G>H, provided the reduced matrix elements of the generators of G and the recoupling coefficients of H are known. The calculation of SO(5)>SO(4) reduced coupling coefficients is considered as an example, and a procedure for transformation of reduced coupling coefficients between canonical and physical subalegebra chains is presented. The problem of calculating coupling coefficients for generic irreps of SO(5), reduced with respect to any of its subalgebra chains, is completely resolved by this approach.
Zhiguang Xiong; Chuanmiao Chen
2007-01-01
In this paper,n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u - uh = O(hn+2),n ≥ 2,at (n + 1)-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.
Review of analysis methods for rotating systems with periodic coefficients
Dugundji, J.; Wendell, J. H.
1981-01-01
Two of the more common procedures for analyzing the stability and forced response of equations with periodic coefficients are reviewed: the use of Floquet methods, and the use of multiblade coordinate and harmonic balance methods. The analysis procedures of these periodic coefficient systems are compared with those of the more familiar constant coefficient systems.
Some analysis methods for rotating systems with periodic coefficients
Dugundji, J.; Wendell, J. H.
1983-01-01
Two of the more common procedures for analyzing the stability and forced response of equations with periodic coefficients are reviewed: the use of Floquet methods, and the use of multiblade coordinate and harmonic balance methods. The analysis procedures of these periodic coefficient systems are compared with those of the more familiar constant coefficient systems. Previously announced in STAR as N82-23702
Transport Coefficients and nPI Methods
Carrington, M E
2011-01-01
Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation and suggests that one can calculate the next-to-leading contribution to transport coefficients from the 4-loop 4PI effective action. The integral equations have been derived for shear viscosity for a scalar theory with cubic and quartic interactions, with a non-vanishing field expectation value. We review these results, and explain how the calculation could be done at higher orders.
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
Kalchev, D
2012-04-02
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
Kalchev, D
2012-04-02
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the
RESEARCH METHODS OF LOCATIVE ELEMENT
SULAYMANOVA N.J.
2012-01-01
Full Text Available The article is devoted to the methods of investigation of locative elements. Sentence analysis with locative elements is taken according to the results of component analysis in the system of contradicting – opposition. More over the article is full of examples related to the description of various syntactic units.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles
Bi-Cheng Zhou
2015-12-01
Full Text Available Diffusion coefficients of alloying elements in Mg are critical for the development of new Mg alloys for lightweight applications. Here we present the data set of the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp Mg calculated from first-principles calculations based on density functional theory (DFT by combining transition state theory and an 8-frequency model. Benchmark for the DFT calculations and systematic comparison with experimental diffusion data are also presented. The data set refers to “Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study” by Zhou et al. [1].
Methods for Accurate Free Flight Measurement of Drag Coefficients
Courtney, Elya; Courtney, Michael
2015-01-01
This paper describes experimental methods for free flight measurement of drag coefficients to an accuracy of approximately 1%. There are two main methods of determining free flight drag coefficients, or equivalent ballistic coefficients: 1) measuring near and far velocities over a known distance and 2) measuring a near velocity and time of flight over a known distance. Atmospheric conditions must also be known and nearly constant over the flight path. A number of tradeoffs are important when designing experiments to accurately determine drag coefficients. The flight distance must be large enough so that the projectile's loss of velocity is significant compared with its initial velocity and much larger than the uncertainty in the near and/or far velocity measurements. On the other hand, since drag coefficients and ballistic coefficients both depend on velocity, the change in velocity over the flight path should be small enough that the average drag coefficient over the path (which is what is really determined)...
An Acoustic Method for Determining Ballistic Coefficients
Courtney, Michael
2007-01-01
This paper presents a method for using a PC soundcard, microphone and a chronograph to determine bullet BC with an accuracy of 6%. This is useful when a second chronograph is unavailable or when the projectile accuracy is insufficient to use a far chronograph.
LIMing-an; WANGZhong-min; GUOZhi-yong
2003-01-01
Based on a method of finite element model and combined with matrix theory,a method for solving differential equation with variable coefficients if proposed.With the method,it is easy to deal with the differential equations with variable coefficients.On most occasions and due to the nonuniformity nature,nonlinearity property can cause the equations of the kinds.Using the model,the satisfactory valuable results with only a few units can be obtained.
黎明安; 王忠民; 郭志勇
2003-01-01
Based on a method of finite element model and combined with matrix theory, a method for solving differential equation with variable coefficients is proposed. With the method, it is easy to deal with the differential equations with variable coefficients. On most occasions and due to the nonuniformity nature, nonlinearity property can cause the equations of the kinds. Using the model, the satisfactory valuable results with only a few units can be obtained.
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Selective Smoothed Finite Element Method
无
2007-01-01
The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.
Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
Teckentrup, A. L.; Scheichl, R.; Giles, M. B.; Ullmann, E
2012-01-01
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and that only have limited spatial regularity. We extend the finite element error analysis for this type of equation, carried out recently by Charrier, Scheichl and Teckentrup, to more difficult problems, posed on non--smooth domains and with discontinuities in t...
Peridynamic Multiscale Finite Element Methods
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Methods for measuring diffusion coefficients of radon in building materials
Cozmuta, [No Value; van der Graaf, ER
2001-01-01
Two methods for determining the Rn-222 diffusion coefficient in concrete are presented. Experimentally, the flush and adsorption technique to measure radon release rates underlines both methods. Theoretically, the first method was developed fur samples of cubical geometry. The radon diffusion
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
A neural network method to evaluate consolidation coefficient
无
2003-01-01
Many methods to calculate the consolidation coefficient of soil depend on judgment of testing curves of consolidation,and the calculation result is influenced by artificial factors. In this work, based on the main principle of back propagation neural network, a neural network model to determine the consolidation coefficient is established. The essence of the method is to simulate a serial of compression ratio and time factor curves because the neural network is able to process the nonlinear problems. It is demonstrated that this BP model has high precision and fast convergence. Such method avoids artificial influence factor successfully and is adapted to computer processing.
A new method of solving the coefficient inverse problem
2007-01-01
This paper is concerned with the new method for solving the coefficient inverse problem in the reproducing kernel space. It is different from the previous studies. This method gives accurate results and shows that it is valid by the numerical example.
Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation
V. Radhika
2016-01-01
Full Text Available Let R denote the family of functions f(z=z+∑n=2∞anzn of bounded boundary rotation so that Ref′(z>0 in the open unit disk U={z:z<1}. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions f∈R.
Garrido, J.; Casanovas, A.
2012-07-01
A new method for determining the Peltier coefficient of thermoelectric devices has been developed. The Peltier coefficient has been evaluated by measuring the temperature distribution along the junction of two dissimilar materials X and Y. The energy balance has been used to link the Peltier coefficient with the hot and cold temperatures of the metallic blocks of a thermoelectric module (TEM), thus enabling the evaluation of this coefficient. Data on the thermal conductance of the pellets are also needed. The experimental device used in this paper is a TEM composed of N = 71 couples of bismuth telluride, suitably doped to provide individual n and p elements. Using nominal values given by the manufacturer for the Seebeck coefficient of the TEM, the Onsager reciprocal relation has been confirmed.
Dynamic ADI methods for elliptic equations with gradient dependent coefficients
Doss, S.
1977-04-01
The dynamic alternating direction implicit (DADI) methods, previously introduced and applied to elliptic problems with linear and nonlinear coefficients (a(u)), are applied here to elliptic problems with nonlinear gradient-dependent coefficients (a(grad u)), such as the minimal surface equation, the capillary surface equation, and the magnetostatic equation. Certain improvements of these methods are developed, and they are extended to ''3-directional'' or ''3-dimensional'' situations. 28 figures, 6 tables.
A method for determination mass absorption coefficient of gamma rays by Compton scattering.
El Abd, A
2014-12-01
A method was proposed for determination mass absorption coefficient of gamma rays for compounds, alloys and mixtures. It is based on simulating interaction processes of gamma rays with target elements having atomic numbers from Z=1 to Z=92 using the MCSHAPE software. Intensities of Compton scattered gamma rays at saturation thicknesses and at a scattering angle of 90° were calculated for incident gamma rays of different energies. The obtained results showed that the intensity of Compton scattered gamma rays at saturations and mass absorption coefficients can be described by mathematical formulas. These were used to determine mass absorption coefficients for compound, alloys and mixtures with the knowledge of their Compton scattered intensities. The method was tested by calculating mass absorption coefficients for some compounds, alloys and mixtures. There is a good agreement between obtained results and calculated ones using WinXom software. The advantages and limitations of the method were discussed.
Method of securing filter elements
Brown, Erik P.; Haslam, Jeffery L.; Mitchell, Mark A.
2016-10-04
A filter securing system including a filter unit body housing; at least one tubular filter element positioned in the filter unit body housing, the tubular filter element having a closed top and an open bottom; a dimple in either the filter unit body housing or the top of the tubular filter element; and a socket in either the filter unit body housing or the top of the tubular filter element that receives the dimple in either the filter unit body housing or the top of the tubular filter element to secure the tubular filter element to the filter unit body housing.
Measurement of heat transfer coefficient using termoanemometry methods
Dančová P.
2014-03-01
Full Text Available This work deals with a measurement of heat transfer from a heated flat plate on which a synthetic jet impacts perpendicularly. Measurement of a heat transfer coefficient (HTC is carried out using the hot wire anemometry method with glue film probe Dantec 55M47. The paper brings also results of velocity profiles measurements and turbulence intensity calculations.
Jeong, Cheol-Ho; Ih, Jeong-Guon; Rindel, Jens Holger
2005-01-01
the measured surface impedance. However, it is not always possible to get the measured impedance data of the surface, so that a practical way of getting reflection characteristics is needed. Generally, in the architectural acoustics field, the absorption coefficients have been employed in the calculations......The phased beam tracing method (PBTM) is a technique which can calculate the pressure impulse response instead of energy impulse response, by taking the phase information into account. Inclusion of the phase information can extend the application of beam tracing technique to the mid frequency range...
Experimental Determination of Trace Element Partition Coefficients Between Zircon, Garnet and Melt
Taylor, R. J.; Harley, S. L.; Hinton, R. W.; Elphick, S.
2007-12-01
The problem of relating ages, as calculated by zircon U-Pb geochronology, to processes and hence geoological events is central to understanding mountain building and crustal evolution. Accurate P-T-t paths can only be produced if zircon growth can be linked to specific rock and mineral processes used to establish pressure and temperature values for metamorphic episodes. As a major metamorphic mineral in crustal events, garnet is widely used as a thermobarometric tool, and linking garnet growth to zircon formation could be used to refine the interpretation of U-Pb ages. Attempts to resolve this issue have focussed on REE partitioning between zircon and garnet, both of which strongly incorporate the HREE into their structure, and so it is possible there is a distinct REE partitioning signature which will highlight whether the two minerals have grown in equilibrium. There are two complementary methods to obtaining this information, empirical and experimental. Empirical methods of determining this signature using carefully selected rocks have proved troublesome, with a wide range of partitioning signatures found. This work has used experimental techniques to produce zircon-melt, garnet-melt and zircon-garnet-melt partition coefficients at a range of P-T conditions using synthetic materials. Zircon and garnet are grown in trace element equilibrium with a water-undersaturated granitic melt, which represents partial melts formed in the lower crust during anatexis. Temperature ranges from 850°C to 1000°C at a pressure of 5Kbar were produced using internally heated gas apparatus. Trace element concentrations were measured using SIMS analysis at the Ion Microprobe Facility at the University of Edinburgh. The experimental data produced will be applied to interpret chemical signatures in zircon in garnet-bearing metamorphic rocks, and will provide an objective basis for interpretation of the timing of growth or recrystallisation of zircon in many high-grade terrains.
Liu, Cong; Kolarik, Barbara; Gunnarsen, Lars; Zhang, Yinping
2015-10-20
Polychlorinated biphenyls (PCBs) have been found to be persistent in the environment and possibly harmful. Many buildings are characterized with high PCB concentrations. Knowledge about partitioning between primary sources and building materials is critical for exposure assessment and practical remediation of PCB contamination. This study develops a C-depth method to determine diffusion coefficient (D) and partition coefficient (K), two key parameters governing the partitioning process. For concrete, a primary material studied here, relative standard deviations of results among five data sets are 5%-22% for K and 42-66% for D. Compared with existing methods, C-depth method overcomes the inability to obtain unique estimation for nonlinear regression and does not require assumed correlations for D and K among congeners. Comparison with a more sophisticated two-term approach implies significant uncertainty for D, and smaller uncertainty for K. However, considering uncertainties associated with sampling and chemical analysis, and impact of environmental factors, the results are acceptable for engineering applications. This was supported by good agreement between model prediction and measurement. Sensitivity analysis indicated that effective diffusion distance, contacting time of materials with primary sources, and depth of measured concentrations are critical for determining D, and PCB concentration in primary sources is critical for K.
Roteta, M.; Baro, J.; Fernandez-Varea, J. M.; Salvat, F.
1994-07-01
The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within - 1%, in the energy range from 1 keV to 1 GeV. The complete source listing of the program PHOTAC is included. (Author) 14 refs.
Rare Earth Element Partition Coefficients from Enstatite/Melt Synthesis Experiments
Schwandt, Craig S.; McKay, Gordon A.
1997-01-01
Enstatite (En(80)Fs(19)Wo(01)) was synthesized from a hypersthene normative basaltic melt doped at the same time with La, Ce, Nd, Sm, Eu, Dy, Er, Yb and Lu. The rare earth element concentrations were measured in both the basaltic glass and the enstatite. Rare earth element concentrations in the glass were determined by electron microprobe analysis with uncertainties less than two percent relative. Rare earth element concentrations in enstatite were determined by secondary ion mass spectrometry with uncertainties less than five percent relative. The resulting rare earth element partition signature for enstatite is similar to previous calculated and composite low-Ca pigeonite signatures, but is better defined and differs in several details. The partition coefficients are consistent with crystal structural constraints.
A novel method for measuring polymer-water partition coefficients.
Zhu, Tengyi; Jafvert, Chad T; Fu, Dafang; Hu, Yue
2015-11-01
Low density polyethylene (LDPE) often is used as the sorbent material in passive sampling devices to estimate the average temporal chemical concentration in water bodies or sediment pore water. To calculate water phase chemical concentrations from LDPE concentrations accurately, it is necessary to know the LDPE-water partition coefficients (KPE-w) of the chemicals of interest. However, even moderately hydrophobic chemicals have large KPE-w values, making direct measurement experimentally difficult. In this study we evaluated a simple three phase system from which KPE-w can be determined easily and accurately. In the method, chemical equilibrium distribution between LDPE and a surfactant micelle pseudo-phase is measured, with the ratio of these concentrations equal to the LDPE-micelle partition coefficient (KPE-mic). By employing sufficient mass of polymer and surfactant (Brij 30), the mass of chemical in the water phase remains negligible, albeit in equilibrium. In parallel, the micelle-water partition coefficient (Kmic-w) is determined experimentally. KPE-w is the product of KPE-mic and Kmic-w. The method was applied to measure values of KPE-w for 17 polycyclic aromatic hydrocarbons, 37 polychlorinated biphenyls, and 9 polybrominated diphenylethers. These values were compared to literature values. Mass fraction-based chemical activity coefficients (γ) were determined in each phase and showed that for each chemical, the micelles and LDPE had nearly identical affinity.
Wassenburg, J. A.; Scholz, D.; Jochum, K. P.; Cheng, H.; Oster, J.; Immenhauser, A.; Richter, D. K.; Häger, T.; Jamieson, R. A.; Baldini, J. U. L.; Hoffmann, D.; Breitenbach, S. F. M.
2016-10-01
The processes that govern the incorporation of (trace) elements into speleothems can often be linked to environmental changes. Although element incorporation into speleothem calcite is now reasonably well understood, current knowledge regarding trace element variability in speleothem aragonite is very limited. Of particular interest is whether trace element distribution coefficients are above or below one in order to assess the extent to which prior aragonite precipitation has affected speleothem aragonite trace element records. This study uses nine calcite-to-aragonite transitions in seven speleothems from diverse environmental settings to derive the first quantitative estimates of the distribution coefficients for several elements in speleothem aragonite: DMg(Ar) = 9.7E-5 ± 9.01E-5, DBa(Ar) = 0.91 ± 0.88, DSr(Ar) = 1.38 ± 0.53, and DU(Ar) = 6.26 ± 4.54 (1σ SD). For one speleothem from western Germany, the distribution coefficients are generally higher, which is potentially related to the very low growth rates (negative correlation with growth rate when growth rate is below 20 μm/year. In summary, our results demonstrate that speleothem aragonite DMg(Ar) is below one, DU(Ar) is considerably above one, and DSr(Ar) is above one or close to unity. For DBa(Ar), reaching a similar conclusion is difficult due to the relatively high uncertainty. Enhanced prior aragonite precipitation will thus result in lower U and higher Mg concentrations in speleothem aragonite, although in many cases Mg in speleothem aragonite is most likely dominated by other processes. This result suggests that U concentrations in aragonitic stalagmites could serve as a very effective proxy for palaeo-rainfall.
Evaluating maximum likelihood estimation methods to determine the hurst coefficients
Kendziorski, C. M.; Bassingthwaighte, J. B.; Tonellato, P. J.
1999-12-01
A maximum likelihood estimation method implemented in S-PLUS ( S-MLE) to estimate the Hurst coefficient ( H) is evaluated. The Hurst coefficient, with 0.5long memory time series by quantifying the rate of decay of the autocorrelation function. S-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 2 10. A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 2 11.
On the definition of Burnett transport coefficients of the dense multi-element charged matter
Pavlov, G A
2003-01-01
To determine the Burnett transport coefficients of non-ideal multi-element charged matter the representations of conservation equations of matter as generalized Langevin equations are used. Mori's algorithm is revised to derive the equation of motion of a dynamical value operator of a system in the form of the generalized nonlinear Langevin equation. After transformation, using necessary variational derivatives, these equations are compared with the Burnett hydrodynamical conservation equations. In consequence, the response function expressions of transport coefficients corresponding to second-order derivatives of thermal disturbances are found in the long-wavelength and low-frequency limits. To establish a link between the results of the executed investigations and hydrodynamical problems the properties of the high derivative coefficients matrix of the set of conservation equations in the linearized Burnett approximation are discussed.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Facial Feature Extraction Method Based on Coefficients of Variances
Feng-Xi Song; David Zhang; Cai-Kou Chen; Jing-Yu Yang
2007-01-01
Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are two popular feature ex- traction techniques in statistical pattern recognition field. Due to small sample size problem LDA cannot be directly applied to appearance-based face recognition tasks. As a consequence, a lot of LDA-based facial feature extraction techniques are proposed to deal with the problem one after the other. Nullspace Method is one of the most effective methods among them. The Nullspace Method tries to find a set of discriminant vectors which maximize the between-class scatter in the null space of the within-class scatter matrix. The calculation of its discriminant vectors will involve performing singular value decomposition on a high-dimensional matrix. It is generally memory- and time-consuming. Borrowing the key idea in Nullspace method and the concept of coefficient of variance in statistical analysis we present a novel facial feature extraction method, i.e., Discriminant based on Coefficient of Variance (DCV) in this paper. Experimental results performed on the FERET and AR face image databases demonstrate that DCV is a promising technique in comparison with Eigenfaces, Nullspace Method, and other state-of-the-art facial feature extraction methods.
Measurement of the Ar diffusion coefficient in graphite at high temperature by the ISOL method
Eleon, C. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Jardin, P. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France)], E-mail: Jardin@ganil.fr; Thomas, J.C.; Saint-Laurent, M.-G.; Huet-Equilbec, C.; Alves Conde, R. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Angelique, J.C. [Laboratoire de Physique Subatomique et de Cosmologie, 38026 Grenoble (France); Laboratoire de Physique Corpusculaire, ISMRA, 14050 Caen (France); Boilley, D.; Cornell, J.; Dubois, M. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Franberg, H. [Paul Scherrer Institute, 5232 Villigen PSI (Switzerland); ISOLDE, CERN, 1211 Geneve 23 (Switzerland); Gaubert, G.; Jacquot, B. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Koester, U. [ISOLDE, CERN, 1211 Geneve 23 (Switzerland); Institut Laue Langevin, 38042 Grenoble (France); Leroy, R. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Maunoury, L. [Centre Interdisciplinaire de Recherche Ion Laser, 14070 Caen (France); Orr, N. [Laboratoire de Physique Corpusculaire, ISMRA, 14050 Caen (France); Pacquet, J.Y.; Pellemoine, F.; Stodel, C. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France)] (and others)
2008-10-15
This work has been carried out at GANIL within the ambit of the TARGISOL European collaboration which aims to study the relevant variables governing the release of radioactive elements from targets in an ISOL system. This work shows how it has been possible to extract diffusion coefficients for {sup 35}Ar atoms diffusing out of graphite targets from release time measurements by using an analytic description of the release times. The diffusion coefficients and efficiencies are presented and compared with results obtained using a 'continuous' method.
Hintz, C. J.; Shaw, T. J.; Chandler, G. T.; McCorkle, D. C.; Bernhard, J. M.; Blanks, J. K.
2006-12-01
Field studies have suggested that calcite saturation states (Ømega) near and below saturation alter trace element distribution coefficients in benthic foraminifera. Recent benthic foraminiferal culture experiments at the University of South Carolina investigated the response of trace element signatures to three different calcite saturation seawater environments by manipulating total alkalinity (TA). Starting with near-surface Gulf Stream water (Ømega = 3, TA=2380 μeq kg-1), two seawater reservoirs were titrated with HCl to lower their calcite saturation states (Ømega = 2, TA = 1910 μeq kg-1; Ømega = 1.1, TA = 1320 μeq kg-1). Mixed-species foraminiferal assemblages, with the calcite-specific fluorescent label calcein, were inoculated into 13 total culture chambers evenly distributed among the control and 2 treatment seawater reservoirs. These cultures were maintained at 7.2 ± 0.1 °C temperature and 36.6 ± 0.4 ‰ salinity for 8 months. Total alkalinity and dissolved inorganic carbon, measured biweekly, characterized the carbonate system and verified that the calcite saturation state remained stable over the culture duration. Trace element concentrations were also measured biweekly. Foraminiferal reproduction ( Bulimina marginata) was observed in each seawater chemistry. These individuals were utilized for trace element and stable isotope (data not presented here) analysis. Additionally, terminal chambers precipitated in alkalinity-adjusted cultures were identified by the absence of the pre-culture calcein label used on all inoculated foraminifera. These cultured chambers were separated by laser microdissection and analyzed for trace element content by isotope dilution inductively-coupled plasma mass spectrometry. We present the initial results of these trace element distribution coefficients measured in cultured benthic foraminifera from three different Ømega. This research was funded by National Science Foundation grants OCE-0351029 and OCE-0437366.
Coefficient of consolidation by end of arc method
Mohsen Abbaspout; Reza Porhoseini; Kazem Barkhordari; Ahmad Ghorbani
2015-01-01
One of the most important issues in geotechnical engineering is excess pore pressure caused by clay soil loading and consolidation. Regarding uncertainties and complexities, this issue has long been the subject of attention of many researchers. In this work, a one-dimensional consolidation apparatus was equipped in a way that pore water pressure and settlement could be continuously read and recorded during consolidation process under static loading. The end of primary consolidation was obtained using water pressure changes helping to present a new method for determining the end of primary consolidation and consolidation coefficient. This method was then compared with two classical theory methods of lg t and t . Using Terzaghi’s theory, the way of pore pressure dissipation for lg t, t and the new method was found and compared with experimental results. It is concluded that the new method has better results.
Improved transfer matrix methods for calculating quantum transmission coefficient.
Biswas, Debabrata; Kumar, Vishal
2014-07-01
Methods for calculating the transmission coefficient are proposed, all of which arise from improved nonreflecting WKB boundary conditions at the edge of the computational domain in one-dimensional geometries. In the first, the Schrödinger equation is solved numerically, while the second is a transfer matrix (TM) algorithm where the potential is approximated by steps, but with the first and last matrix modified to reflect the new boundary condition. Both methods give excellent results with first-order WKB boundary conditions. The third uses the transfer matrix method with third-order WKB boundary conditions. For the parabolic potential, the average error for the modified third-order TM method reduces by factor of 4100 over the unmodified TM method.
Wu Qiong; Li Shu-Suo; Ma Yue; Gong Sheng-Kai
2012-01-01
The diffusion coefficients of several alloying elements (Al,Mo,Co,Ta,Ru,W,Cr,Re) in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor (Do) and the activation energy (Q) of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order:DAl ＞ DCr ＞ DCo ＞ DTa ＞DMo ＞ DRu ＞ DW ＞ DRe.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair (E1).The value of E2-E1 (E2 is the solute diffusion energy) and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.
Tong Kang; Zheng-peng Wu; De-hao Yu
2004-01-01
In this paper, we investigate the finite element A - φ method to approximate the eddy current equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral eddy current region. Nonmatching finite element meshes on the interface are considered and optimal error estimates are obtained.
Finite element model for beef chilling using CFD-generated heat transfer coefficients
Pham, Q.T. [University of New South Wales, Sydney, NSW 2052 (Australia); Trujillo, F.J. [Food Science Australia, 11 Julius Avenue, North Ryde, NSW 2113 (Australia); McPhail, N. [Food Science Australia, P.O. Box 3312, Tingalpa DC, Brisbane, QLD 4173 (Australia)
2009-01-15
A combined model of the beef chilling process is presented, in which computational fluid dynamics (CFD) was used to estimate the local heat and mass transfer coefficients, assuming uniform surface temperatures, and a set of 2-D finite element grids was used to solve the heat transfer equation in the product, which has an elongated shape. Another set of 1-D grids was used to solve the water transport equation near the surface of the meat. The surface transfer coefficients were calculated for various combinations of air orientations and speeds, and summarised in a set of regression equations. The model was verified by existing and new data on heat load, temperatures, weight loss and surface water activity. (author)
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Linjun, Xie, E-mail: linjunx@zjut.edu.cn [College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014 (China); Guohong, Xue; Ming, Zhang [Shanghai Nuclear Engineering Research & Design Institute, Shanghai 200233 (China)
2016-08-01
friction coefficient f of the K1000 HDS are further calculated to be 0.336 by stress coefficient k{sub f}. It is very important that the research method of friction coefficient put forward by this paper for the first time. The method can provide an exact basis for HDS design and structure selection and can provide a guarantee for the safe operation of the reactor.
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
An element by element spectral element method for elastic wave modeling
LIN Weijun; WANG Xiuming; ZHANG Hailan
2006-01-01
The spectral element method which combines the advantages of spectral method with those of finite element method,provides an efficient tool in simulating elastic wave equation in complex medium. Based on weak form of elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order Lagrange interpolation, and integration over the element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element technique is introduced in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are presented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and spectral algorithms, this method can be used for complex models, including free surface boundaries and strong heterogeneity.
The solid-phase diffusion coefficient (Dm) and material-air partition coefficient (Kma) are key parameters for characterizing the sources and transport of semivolatile organic compounds (SVOCs) in the indoor environment. In this work, a new experimental method was developed to es...
Veksler, Ilya V.; Dorfman, Alexander M.; Danyushevsky, Leonid V.; Jakobsen, Jakob K.; Dingwell, Donald B.
2006-12-01
This study investigates partitioning of elements between immiscible aluminosilicate and borosilicate liquids using three synthetic mixtures doped with 32 trace elements. In order to get a good spatial separation of immiscible liquids, we employed a high-temperature centrifuge. Experiments were performed at 1,050-1,150°C, 1 atm, in sealed Fe and Pt containers. Quenched products were analysed by electron microprobe and LA ICP-MS. Nernst partition coefficients ( D’s) between the Fe-rich and Si-rich aluminosilicate immiscible liquids are the highest for Zn (3.3) and Fe (2.6) and the lowest for Rb and K (0.4-0.5). The plots of D values against ionic potential Z/r in all the compositions show a convex upward trend, which is typical also for element partitioning between immiscible silicate and salt melts. The results bear upon the speciation and structural position of elements in multicomponent silicate liquids. The ferrobasalt-rhyolite liquid immiscibility is observed in evolved basaltic magmas, and may play an important role in large gabbroic intrusions, such as Skaergaard, and during the generation of unusual lavas, such as ferropicrites.
Yoshida, Kenichiro
2016-08-01
We derived the absorption coefficient ( μ a) and the reduced scattering coefficient ( μ s') using the edge-loss method (ELM) and the video reflectometry method (VRM), and compared the results. In a previous study, we developed the ELM to easily evaluate the lateral spread in the skin; the VRM is a conventional method. The ELM measures the translucency index, which is correlated with μ a and μ s'. To obtain a precise estimation of these parameters, we improved the treatment of a white standard and the surface reflection. For both skin phantoms and actual skin, the values for μ a and μ s' that we obtained using the ELM were similar to those obtained using the VRM, when μ a/ μ s' was less than or equal to 0.05 and the diffusion approximation was applicable. Under this condition, the spectral reflectivity is greater than 0.4. In this study, we considered wavelengths longer than 600 nm for Types III and IV of the Fitzpatrick scale. For skin, the repeatability errors of the parameters obtained with the ELM were smaller than those obtained with the VRM; this can be an advantage in field tests.
An improved optimal elemental method for updating finite element models
Duan Zhongdong(段忠东); Spencer B.F.; Yan Guirong(闫桂荣); Ou Jinping(欧进萍)
2004-01-01
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures,the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.Thc example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
Bretscher, M.M.
1984-01-01
Simple diffusion theory cannot be used to evaluate control rod worths in thermal neutron reactors because of the strongly absorbing character of the control material. However, reliable control rod worths can be obtained within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters. For thin slab absorbers the effective diffusion parameters can be expressed as functions of a suitably-defined pair of blackness coefficients. Methods for calculating these blackness coefficients in the P/sub 1/, P/sub 3/, and P/sub 5/ approximations, with and without scattering, are presented. For control elements whose geometry does not permit a thin slab treatment, other methods are needed for determining the effective diffusion parameters. One such method, based on reaction rate ratios, is discussed.
Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Schneider, C.; Wißbrock, F.
2017-08-01
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η = mc2 / mb2 ∼ 1 / 10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N = 2 , 4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3). We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); IHES, Bures-sur-Yvette (France)
2017-05-15
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m{sup 2}{sub c}/m{sup 2}{sub b}∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A{sup (3)}{sub gq}. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A{sub gg}. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Partial differential equations II elements of the modern theory equations with constant coefficients
Shubin, M
1994-01-01
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
Determination of the heat transfer coefficient from IRT measurement data using the Trefftz method
Maciejewska Beata
2016-01-01
Full Text Available The paper presents the method of heat transfer coefficient determination for boiling research during FC-72 flow in the minichannels, each 1.7 mm deep, 24 mm wide and 360 mm long. The heating element was the thin foil, enhanced on the side which comes into contact with fluid in the minichannels. Local values of the heat transfer coefficient were calculated from the Robin boundary condition. The foil temperature distribution and the derivative of the foil temperature were obtained by solving the two-dimensional inverse heat conduction problem, due to measurements obtained by IRT. Calculations was carried out by the method based on the approximation of the solution of the problem using a linear combination of Trefftz functions. The basic property of this functions is they satisfy the governing equation. Unknown coefficients of linear combination of Trefftz functions are calculated from the minimization of the functional that expresses the mean square error of the approximate solution on the boundary. The results presented as IR thermographs, two-phase flow structure images and the heat transfer coefficient as a function of the distance from the channel inlet, were analyzed.
Li, Yang; Xia, Peng-Fei; Ma, Xiao; Fan, Qin; Zhao, Lei; Wang, Ya-Li; Liu, Xiong
2013-08-01
To investigate the utilization of fuzzy matter-element model in evaluating the quality of Angelica sinensis. The quality of Angelica sinensis from different habitats was evaluated by determining six main compositions contained in the samples with fuzzy matter-element model based on variation coefficient weight. Angelica sinensis collected from 22 hatitats were divided into three ranges based on the values of approach degrees. Fuzzy matter-element model based on variation coefficient weight can judge the quality of Angelica sinensis objectively and feasibly.
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
On Hybrid and mixed finite element methods
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
Introducing the Boundary Element Method with MATLAB
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Introducing the Boundary Element Method with MATLAB
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Evaluation of the Reflection Coefficient of Microstrip Elements for Reflectarray Antennas
Rengarajan, Sembiam
2011-01-01
Basis functions were studied and identified that provide efficient and accurate solutions for the induced patch currents and the reflection phase in microstrip reflect arrays. The integral equation of an infinite array of microstrip elements in the form of patches or crossed dipoles excited by a uniform plane wave is solved by the method-of-moments. Efficient choices of entire domain basis functions that yield accurate results have been described.
Boundary element-free method for elastodynamics
CHENG; Yumin; PENG; Miaojuan
2005-01-01
The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.
Standard test method for distribution coefficients of inorganic species by the batch method
American Society for Testing and Materials. Philadelphia
2010-01-01
1.1 This test method covers the determination of distribution coefficients of chemical species to quantify uptake onto solid materials by a batch sorption technique. It is a laboratory method primarily intended to assess sorption of dissolved ionic species subject to migration through pores and interstices of site specific geomedia. It may also be applied to other materials such as manufactured adsorption media and construction materials. Application of the results to long-term field behavior is not addressed in this method. Distribution coefficients for radionuclides in selected geomedia are commonly determined for the purpose of assessing potential migratory behavior of contaminants in the subsurface of contaminated sites and waste disposal facilities. This test method is also applicable to studies for parametric studies of the variables and mechanisms which contribute to the measured distribution coefficient. 1.2 The values stated in SI units are to be regarded as standard. No other units of measurement a...
Ayatollahi, Majid R.; Moazzami, Mostafa
2017-03-01
The digital image correlation (DIC) method is used to obtain the coefficients of higher-order terms in the Williams expansion in a compact tension (CT) specimens made of polymethyl methacrylate (PMMA). The displacement field is determined by the correlation between reference image (i.e., before deformation) and deformed image. The part of displacements resulting from rigid body motion and rotation is eliminated from the displacement field. For a large number of points in the vicinity of the crack tip, an over-determined set of simultaneous linear equations is collected, and by using the fundamental concepts of the least-squares method, the coefficients of the Williams expansion are calculated for pure mode I conditions. The experimental results are then compared with the numerical results calculated by finite element method (FEM). Very good agreement is shown to exist between the DIC and FE results confirming the effectiveness of the DIC technique in obtaining the coefficients of higher order terms of Williams series expansion from the displacement field around the crack tip.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Accelerated Matrix Element Method with Parallel Computing
Schouten, Doug; Stelzer, Bernd
2014-01-01
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current collider experiments. However, the computational complexity of this method for final states with many particles and degrees of freedom sets it at a disadvantage compared to supervised classification methods such as decision trees, k nearest-neighbour, or neural networks. This note presents a concrete implementation of the matrix element technique using graphics processing units. Due to the intrinsic parallelizability of multidimensional integration, dramatic speedups can be readily achieved, which makes the matrix element technique viable for general usage at collider experiments.
Method of classification of integumentary landscape elements
Voloshyn, V. I.; Bushuyev, Ye. I.; Parshina, O. I.; Fedorov, O. P.
We develop the method for the determination of technology for creation of thematic map of landscape elements of the territory of Ukraine using remotely sensed data. The purpose of our investigation is maximum formalization and accessibility of the method for many users.
Spectral/hp element methods for CFD
Karniadakis, George Em
1999-01-01
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.
F.P. Wenzl; G. Langer; J. Nicolics; P. Fulmek; C. Sommer; S. Schweitzer; W. Nemitz; P. Hartmann; P. Pachler; H. Hoschopf; F. Schrank
2014-01-01
Besides their direct impact on the respective correlated color temperature, the extinction coefficient and the quantum effi-ciency of the phosphor also have tremendous impact on the thermal load of the color conversion elements of phosphor converted LEDs under operation. Because of the low thermal conductivity of the silicone matrix in which the phosphor particles are typically embedded, the by far highest temperatures within the LED assembly are reached within the color conversion element. Based on a combined optical and thermal simulation procedure we show that in particular a larger value for the extinction coefficient might have a beneficial impact on the resulting thermal load.
Kriging-Based Finite Element Method: Element-By-Element Kriging Interpolation
W. Kanok-Nukulchai
2009-01-01
Full Text Available An enhancement of the finite element method with Kriging shape functions (K-FEM was recently proposed. In this method, the field variables of a boundary value problem are approximated using ‘element-by-element’ piecewise Kriging interpolation (el-KI. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.
A new simple multidomain fast multipole boundary element method
Huang, S.; Liu, Y. J.
2016-09-01
A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.
40 CFR 799.6755 - TSCA partition coefficient (n-octanol/water), shake flask method.
2010-07-01
... organometallic compounds. (4) Alternative methods. High-pressure liquid chromatography (HPLC) methods described... coefficient by high pressure liquid chromatography. Journal of Medicinal Chemistry 19:615 (1976). (6)...
Stochastic method for modeling of the rarefied gas transport coefficients
Rudyak, V. Ya; Lezhnev, E. V.
2016-08-01
In this paper, we propose an algorithm for computation of the transport coefficients of rarefied gas, which is based on stochastic modeling of phase trajectories considered molecular system. The hard spheres potential is used. The number of operations is proportional to the number of used molecules. Naturally in this algorithm the conservation laws are performed. The efficiency of the algorithm is demonstrated by the calculation of the viscosity and diffusion coefficients of several noble gases (argon, neon, xenon, krypton). It was shown that the algorithm accuracy of the order of 1-2% can be obtained by using a relatively small number of molecules. The accuracy dependence on the number of used molecules, statistics (number of the used phase trajectories) and calculation time was analyzed.
Efficient partial element calculation and the extension to cylindrical elements for the PEEC method
Muesing, A.; Kolar, J. W.
2008-07-01
For various electrical interconnect and electromagnetic compatibility (EMC) problems, the Partial Element Equivalent Circuit (PEEC) method has proven to be a valid and fast solution method of the electrical field integral equation in the time as well as the frequency domain. Therefore, PEEC has become a multipurpose full-wave simulation method, especially suited for the solution of combined circuit and EM problems, as found on printed circuit board layouts, power electronics devices or EMC filters. Recent research introduced various extensions to the basic PEEC approach, for example a non-orthogonal cell geometry formulation. This work presents a fast, flexible and accurate computational method for determining the matrix entries of partial inductances and the coefficients of potential for general non-orthogonal PEEC cell geometries. The presented computation method utilizes analytical filament formulas to reduce the integration order and therefore to reduce computation time. The validity, accuracy and speed of the proposed method is compared with a standard integration routine on example cell geometries where the numeric results of the new method show improved accuracy, coming along with reduced computation time. Furthermore, this work shows an extension to cylindrical elements which is consistent with classical PEEC models, using the proposed integration routines for the partial element calculations. (author)
Wen-zhi ZHANG; Pei-yan HUANG
2014-01-01
Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob-lems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma-trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
Perfetti, Christopher M [ORNL; Martin, William R [University of Michigan; Rearden, Bradley T [ORNL; Williams, Mark L [ORNL
2012-01-01
Three methods for calculating continuous-energy eigenvalue sensitivity coefficients were developed and implemented into the SHIFT Monte Carlo code within the Scale code package. The methods were used for several simple test problems and were evaluated in terms of speed, accuracy, efficiency, and memory requirements. A promising new method for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was developed and produced accurate sensitivity coefficients with figures of merit that were several orders of magnitude larger than those from existing methods.
A method for monitoring nuclear absorption coefficients of aviation fuels
Sprinkle, Danny R.; Shen, Chih-Ping
1989-01-01
A technique for monitoring variability in the nuclear absorption characteristics of aviation fuels has been developed. It is based on a highly collimated low energy gamma radiation source and a sodium iodide counter. The source and the counter assembly are separated by a geometrically well-defined test fuel cell. A computer program for determining the mass attenuation coefficient of the test fuel sample, based on the data acquired for a preset counting period, has been developed and tested on several types of aviation fuel.
CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT
Chun-jia Bi; Dan-hui Hong
2005-01-01
In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optimal complexity.
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
A new method for detemining the Angstrom turbidity coefficient from broad-band filter measurements.
Utrillas Esteban, Mª Pilar; Pedrós Esteban, Roberto; Martínez Lozano, José Antonio; Tena Sangüesa, Fernando
2000-01-01
In this work, a new method for determining Ångström turbidity coefficients is presented. This method is based on broadband filter irradiance measurements. By combining measurements obtained with different filters it is possible to obtain a single value of the turbidity coefficient representative of the whole measurement range of the pyrheliometer. The results provided by this new method are compared with the original Ångström method and turbidity coefficient values derived by spectroradiometr...
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS
Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon
2002-01-01
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
A new in-situ method to determine the apparent gas diffusion coefficient of soils
Laemmel, Thomas; Paulus, Sinikka; Schack-Kirchner, Helmer; Maier, Martin
2015-04-01
Soil aeration is an important factor for the biological activity in the soil and soil respiration. Generally, gas exchange between soil and atmosphere is assumed to be governed by diffusion and Fick's Law is used to describe the fluxes in the soil. The "apparent soil gas diffusion coefficient" represents the proportional factor between the flux and the gas concentration gradient in the soil and reflects the ability of the soil to "transport passively" gases through the soil. One common way to determine this coefficient is to take core samples in the field and determine it in the lab. Unfortunately this method is destructive and needs laborious field work and can only reflect a small fraction of the whole soil. As a consequence insecurity about the resulting effective diffusivity on the profile scale must remain. We developed a new in-situ method using new gas sampling device, tracer gas and inverse soil gas modelling. The gas sampling device contains several sampling depths and can be easily installed into vertical holes of an auger, which allows for fast installation of the system. At the lower end of the device inert tracer gas is injected continuously. The tracer gas diffuses into the surrounding soil. The resulting distribution of the tracer gas concentrations is used to deduce the diffusivity profile of the soil. For Finite Element Modeling of the gas sampling device/soil system the program COMSOL is used. We will present the results of a field campaign comparing the new in-situ method with lab measurements on soil cores. The new sampling pole has several interesting advantages: it can be used in-situ and over a long time; so it allows following modifications of diffusion coefficients in interaction with rain but also vegetation cycle and wind.
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T. [University of Southern Queensland, Toowoomba, QLD (Australia); Graham, A.L. [Los Alamos National Lab., NM (United States)
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
Multiphase Transformer Modelling using Finite Element Method
Nor Azizah Mohd Yusoff
2015-03-01
Full Text Available In the year of 1970 saw the starting invention of the five-phase motor as the milestone in advanced electric motor. Through the years, there are many researchers, which passionately worked towards developing for multiphase drive system. They developed a static transformation system to obtain a multiphase supply from the available three-phase supply. This idea gives an influence for further development in electric machines as an example; an efficient solution for bulk power transfer. This paper highlighted the detail descriptions that lead to five-phase supply with fixed voltage and frequency by using Finite-Element Method (FEM. Identifying of specification on a real transformer had been done before applied into software modeling. Therefore, Finite-Element Method provides clearly understandable in terms of visualize the geometry modeling, connection scheme and output waveform.
Feng, Dai; Svetnik, Vladimir; Coimbra, Alexandre; Baumgartner, Richard
2014-01-01
The intraclass correlation coefficient (ICC) with fixed raters or, equivalently, the concordance correlation coefficient (CCC) for continuous outcomes is a widely accepted aggregate index of agreement in settings with small number of raters. Quantifying the precision of the CCC by constructing its confidence interval (CI) is important in early drug development applications, in particular in qualification of biomarker platforms. In recent years, there have been several new methods proposed for construction of CIs for the CCC, but their comprehensive comparison has not been attempted. The methods consisted of the delta method and jackknifing with and without Fisher's Z-transformation, respectively, and Bayesian methods with vague priors. In this study, we carried out a simulation study, with data simulated from multivariate normal as well as heavier tailed distribution (t-distribution with 5 degrees of freedom), to compare the state-of-the-art methods for assigning CI to the CCC. When the data are normally distributed, the jackknifing with Fisher's Z-transformation (JZ) tended to provide superior coverage and the difference between it and the closest competitor, the Bayesian method with the Jeffreys prior was in general minimal. For the nonnormal data, the jackknife methods, especially the JZ method, provided the coverage probabilities closest to the nominal in contrast to the others which yielded overly liberal coverage. Approaches based upon the delta method and Bayesian method with conjugate prior generally provided slightly narrower intervals and larger lower bounds than others, though this was offset by their poor coverage. Finally, we illustrated the utility of the CIs for the CCC in an example of a wake after sleep onset (WASO) biomarker, which is frequently used in clinical sleep studies of drugs for treatment of insomnia.
UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS
Xiaoping Xie; Jinchao Xu; Guangri Xue
2008-01-01
In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy's law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods are based on the original weak formulations of Darcy-Stokes-Brinkman equations. In the first method we consider the existing Stokes elements. We show that a stable Stokes element is also uniformly stable with respect to the coefficients and the jumps of Darcy-Stokes-Brinkman equations if and only if the discretely divergence-free velocity implies almost everywhere divergence-free one. In the second method we construct uniformly stable elements by modifying some well-known H(div)-conforming elements. We give some new 2D and 3D elements in a unified way. In the last method we modify the original weak formulation of Darcy-Stokes-Brinkman equations with a stabilization term. We show that all traditional stable Stokes elements are uniformly stable with respect to the coefficients and their jumps under this new formulation.
Boundary element method for internal axisymmetric flow
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
Boundary element methods for electrical engineers
POLJAK, D
2005-01-01
In the last couple of decades the Boundary Element Method (BEM) has become a well-established technique that is widely used for solving various problems in electrical engineering and electromagnetics. Although there are many excellent research papers published in the relevant literature that describe various BEM applications in electrical engineering and electromagnetics, there has been a lack of suitable textbooks and monographs on the subject. This book presents BEM in a simple fashion in order to help the beginner to understand the very basic principles of the method. It initially derives B
Iterative methods for mixed finite element equations
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
A two-level stochastic collocation method for semilinear elliptic equations with random coefficients
Chen, Luoping; Zheng, Bin; Lin, Guang; Voulgarakis, Nikolaos
2017-05-01
In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse mesh $\\mathcal{T}_H$ with a low level stochastic collocation (corresponding to the polynomial space $\\mathcal{P}_{P}$) and solve linearized equations on a fine mesh $\\mathcal{T}_h$ using high level stochastic collocation (corresponding to the polynomial space $\\mathcal{P}_p$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $\\mathcal{T}_h$ and $\\mathcal{P}_p$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.
Faria, Marco Tulio C.
This paper presents a finite element procedure specially devised to analyze the misalignment effects on the behavior of spiral groove gas face seals operating at high speeds. In this study, the seal stationary face is slightly misaligned and the flexibly mounted face is perfectly aligned. Predictions of some steady-state and dynamic performance characteristics versus misalignment angle are presented for spirally grooved gas seals operating under stringent conditions. Curves of dynamic force coefficients versus the static misalignment angle of the seal face indicate that the seal misalignment affects considerably the dynamic response of gas lubricated face seals. At high speeds, the static seal misalignment not only results in increased stiffness coefficients but also leads to negative damping coefficients, which may be a sign of the seal susceptibility to excessive angular motions.
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Water quality evaluation based on improved fuzzy matter-element method
Dongjun Liu; Zhihong Zou
2012-01-01
For natural water,method of water quality evaluation based on improved fuzzy matter-element evaluation method is presented.Two important parts are improved,the weights determining and fuzzy membership functions.The coefficient of variation of each indicator is used to determine the weight instead of traditional calculating superscales method.On the other hand,fuzzy matter-elements are constructed,and normal membership degrees are used instead of traditional trapezoidal ones.The composite fuzzy matter-elements with associated coefficient are constructed through associated transformation.The levels of natural water quality are determined according to the principle of maximum correlation.The improved fuzzy matter-element evaluation method is applied to evaluate water quality of the Luokou mainstream estuary at the first ten weeks in 2011 with the coefficient of variation method determining the weights.Water quality of Luokou mainstream estuary is dropping from level Ⅰ to level Ⅱ.The results of the improved evaluation method are basically the same as the official water quality.The variation coefficient method can reduce the workload,and overcome the adverse effects from abnormal values,compared with the traditional calculating superscales method.The results of improved fuzzy matterelement evaluation method are more credible than the ones of the traditional evaluation method.The improved evaluation method can use information of monitoring data more scientifically and comprehensively,and broaden a new evaluation method for water quality assessment.
Limits to the use of angular coefficients determined by the Polysk method
Goman, V. G.; Krivosheev, V. E.
The Polyak 'taut threads' method for determining angular coefficients in heat exchange by radiation is considered. A relation is derived for determining the angular coefficient in a system of plane parallel bodies of finite dimensions, and the accuracy of the taut threads method for solving this problem is assessed.
A simple method of determination of partition coefficient for biologically active molecules.
Sersen, F
1995-02-01
A simple method is presented for the determination of partition coefficient of an effector between water environment and biological material, based on concentration-dependent effects. The method allows the determination of partition coefficients for biological objects such as algae, bacteria and other microorganisms.
An atmospheric electrical method to determine the eddy diffusion coefficient
M N Kulkarni; A K Kamra
2010-02-01
The ion–aerosol balance equations are solved to get the profiles of atmospheric electric parameters over the ground surface in an aerosol-rich environment under the conditions of surface radioactivity. Combining the earlier results for low aerosol concentrations and the present results for high aerosol concentrations, a relation is obtained between the average value of atmospheric electric space charge in the lowest ∼2m, the surface electric field and eddy diffusivity/aerosol concentration. The values of eddy diffusivity estimated from this method using some earlier measurements of space charge and surface electric field are in reasonably good agreement with those calculated from other standard methods using meteorological or electrical variables.
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
A COLLOCATION METHOD FOR THE CONDUCTIVITY PROBLEM WITH DISCONTINUOUS COEFFICIENT
无
2005-01-01
In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the γ is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.
Perfetti, C.; Martin, W. [Univ. of Michigan, Dept. of Nuclear Engineering and Radiological Sciences, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109-2104 (United States); Rearden, B.; Williams, M. [Oak Ridge National Laboratory, Reactor and Nuclear Systems Div., Bldg. 5700, P.O. Box 2008, Oak Ridge, TN 37831-6170 (United States)
2012-07-01
Three methods for calculating continuous-energy eigenvalue sensitivity coefficients were developed and implemented into the Shift Monte Carlo code within the SCALE code package. The methods were used for two small-scale test problems and were evaluated in terms of speed, accuracy, efficiency, and memory requirements. A promising new method for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was developed and produced accurate sensitivity coefficients with figures of merit that were several orders of magnitude larger than those from existing methods. (authors)
Improved method for calculating neoclassical transport coefficients in the banana regime
Taguchi, M., E-mail: taguchi.masayoshi@nihon-u.ac.jp [College of Industrial Technology, Nihon University, Narashino 275-8576 (Japan)
2014-05-15
The conventional neoclassical moment method in the banana regime is improved by increasing the accuracy of approximation to the linearized Fokker-Planck collision operator. This improved method is formulated for a multiple ion plasma in general tokamak equilibria. The explicit computation in a model magnetic field shows that the neoclassical transport coefficients can be accurately calculated in the full range of aspect ratio by the improved method. The some neoclassical transport coefficients for the intermediate aspect ratio are found to appreciably deviate from those obtained by the conventional moment method. The differences between the transport coefficients with these two methods are up to about 20%.
Numerical Improvement of The Three-dimensional Boundary Element Method
Ortiz-Aleman, C.; Gil-Zepeda, A.; SÃ¡nchez-Sesma, F. J.; Luzon-Martinez, F.
2001-12-01
Boundary element methods have been applied to calculate the seismic response of various types of geological structures. Dimensionality reduction and a relatively easy fulfillment of radiation conditions at infinity are recognized advantages over domain approaches. Indirect Boundary Element Method (IBEM) formulations give rise to large systems of equations, and the considerable amount of operations required for solving them suggest the possibility of getting some benefit from exploitation of sparsity patterns. In this article, a brief study on the structure of the linear systems derived from the IBEM method is carried out. Applicability of a matrix static condensation algorithm to the inversion of the IBEM coefficient matrix is explored, in order to optimize the numerical burden of such method. Seismic response of a 3-D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzon (1995), was computed and comparisons on time consumption and memory allocation are established. An alternative way to deal with those linear systems is the use of threshold criteria for the truncation of the coefficient matrix, which implies the solution of sparse approximations instead of the original full IBEM systems (Ortiz-Aleman et al., 1998). Performance of this optimized approach is evaluated on its application to the case of a three-dimensional alluvial basin with irregular shape. Transfer functions were calculated for the frequency range from 0 to 1.25 Hz. Inversion of linear systems by using this algorithm lead to significant saving on computer time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
Manzini, Gianmarco [Los Alamos National Laboratory
2012-07-13
We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Irving, A. J.; Frey, F. A.
1984-01-01
Rare earth and other trace element abundances are determined in megacrysts of clinopyroxene, orthopyroxene, amphibole, mica, anorthoclase, apatite and zircon, as well as their host basalts, in an effort to gather data on mineral/melt trace element partitioning during the high pressure petrogenesis of basic rocks. Phase equilibria, major element partitioning and isotopic ratio considerations indicate that while most of the pyroxene and amphibole megacrysts may have been in equilibrium with their host magmas at high pressures, mica, anorthoclase, apatite, and zircon megacrysts are unlikely to have formed in equilibrium with their host basalts. It is instead concluded that they were precipitated from more evolved magmas, and have been mixed into their present hosts.
Prediction of residual stress using explicit finite element method
W.A. Siswanto
2015-12-01
Full Text Available This paper presents the residual stress behaviour under various values of friction coefficients and scratching displacement amplitudes. The investigation is based on numerical solution using explicit finite element method in quasi-static condition. Two different aeroengine materials, i.e. Super CMV (Cr-Mo-V and Titanium alloys (Ti-6Al-4V, are examined. The usage of FEM analysis in plate under normal contact is validated with Hertzian theoretical solution in terms of contact pressure distributions. The residual stress distributions along with normal and shear stresses on elastic and plastic regimes of the materials are studied for a simple cylinder-on-flat contact configuration model subjected to normal loading, scratching and followed by unloading. The investigated friction coefficients are 0.3, 0.6 and 0.9, while scratching displacement amplitudes are 0.05 mm, 0.10 mm and 0.20 mm respectively. It is found that friction coefficient of 0.6 results in higher residual stress for both materials. Meanwhile, the predicted residual stress is proportional to the scratching displacement amplitude, higher displacement amplitude, resulting in higher residual stress. It is found that less residual stress is predicted on Super CMV material compared to Ti-6Al-4V material because of its high yield stress and ultimate strength. Super CMV material with friction coefficient of 0.3 and scratching displacement amplitude of 0.10 mm is recommended to be used in contact engineering applications due to its minimum possibility of fatigue.
Kumblad, Linda; Bradshaw, Clare (Dept. of Systems Ecology, Stockholm Univ. (Sweden))
2008-08-15
In this study the elemental composition of biota, water and sediment from a shallow bay in the Forsmark region have been determined. The report presents data for 48 different elements (Al, As, Ba, Br, C, Ca, Cd, Ce, Cl, Co, Cr, Cs, Cu, Dy, Er, Eu, F, Fe, Gd, Hg, Ho, I, K, Li, Lu, Mg, Mn, N, Na, Nd, Ni, P, Pb, Pr, Ra, Rb, S, Se, Si, Sm, Tb, Th, Ti, Tm, V, Yb, Zn, Zr) in all major functional groups of the coastal ecosystem (phytoplankton, zooplankton, benthic microalgae, macroalgae, macrophytes, benthic herbivores, benthic filter feeders, benthic detrivores, planktivorous fish, benthic omnivorous fish, carnivorous fish, dissolved and particulate matter in the water and the sediment) during spring 2005. The overall aim of the study is to contribute to a better understanding of ecological properties and processes that govern uptake and transfer of trace elements, heavy-metals, radionuclides and other non-essential elements/contaminants in coastal environments of the Baltic Sea. In addition, the data was collected to provide site-specific Bioconcentration Factors (BCF), Biomagnification Factors (BMF), partitioning coefficients (K{sub d}) and element ratios (relative to carbon) for use in ongoing SKB safety assessments. All these values, as well as the element concentration data from which they are derived, are presented here. As such, this is mainly a data report, although initial interpretations of the data also are presented and discussed. Reported data include element concentrations, CNP-stoichiometry, and multivariate data analysis. Elemental concentrations varied greatly between organisms and environmental components, depending on the function of the elements, and the habitat, ecosystem function, trophic level and morphology (taxonomy) of the organisms. The results show for instance that food intake and metabolism strongly influence the elemental composition of organisms. The three macrophytes had quite similar elemental composition (despite their taxonomic
Study on gas permeability coefficient measurement of coal seam by radial flow method
Zhang, Shuchuan
2017-08-01
For the accurate measurement of the coal seam permeability coefficient, the application range of the coal seam permeability coefficient was studied under various gas flow conditions with the guidance of the coal seam gas flow theory. Adopting the radial flow method, the measurement and calculation of the permeability coefficient of the coal seam C13-1 in Xinji No.1 Coal Mine shows that the permeability coefficient of the original coal seam C13-1 is less than 0.1, and the coal seam is difficult to extract.
Terui, Akira
2010-01-01
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to polynomials with the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transfered to a constrained minimization problem, then solved with a so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. While our original method is designed for polynomials with the real coefficients, we extend it to accept polynomials with the complex coefficients in this paper.
Membrane finite element method for simulating fluid flow in porous medium
Mei-li ZHAN; Wen-jie ZHANG; Jin-chang SHENG; Jian-hui LI; Shu-yuan HE
2009-01-01
A new membrane finite element method for modeling fluid flow in a porous medium is presented in order to quickly and accurately simulate the geo-membrane fabric used in civil engineering. It is based on discontinuous finite element theory, and can be easily coupled with the normal Galerkin finite element method. Based on the saturated seepage equation, the element coefficient matrix of the membrane element method is derived, and a geometric transform relation for the membrane element between a global coordinate system and a local coordinate system is obtained. A method for the determination of the fluid flux conductivity of the membrane element is presented. This method provides a basis for determining discontinuous parameters in discontinuous finite element theory. An anti-seepage problem regarding the foundation of a building is analyzed by coupling the membrane finite element method with the normal Galerkin finite element method. The analysis results demonstrate the utility and superiority of the membrane finite element method in fluid flow analysis of a porous medium.
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...... convergence of the postbuckling coefficients. (C) 1998 John Wiley & Sons, Ltd....
Test Simulation using Finite Element Method
Ali, M B; Abdullah, S; Nuawi, M Z; Ariffin, A K, E-mail: abgbas@yahoo.com [Department of Mechanical and Materials Engineering, Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia 43600 Bangi, Selangor (Malaysia)
2011-02-15
The dynamic responses of the standard Charpy impact machine are experimentally studied using the relevant data acquisition system, for the purpose of obtaining the impact response. For this reason, the numerical analysis by means of the finite element method has been used for experiment findings. Modelling of the charpy test was performed in order to obtain strain in the striker during the test. Two types of standard charpy specimens fabricated from different materials, i.e. aluminium 6061 and low carbon steel 1050, were used for the impact simulation testing. The related parameters on between different materials, energy absorbed, strain signal, power spectrum density (PSD) and the relationship between those parameters was finally correlated and discussed.
Slip and Slide Method of Factoring Trinomials with Integer Coefficients over the Integers
Donnell, William A.
2012-01-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…
Low-Cost Design of an FIR Filter by Using a Coefficient Mapping Method
Ming-Chih Chen
2013-01-01
Full Text Available This work presents a novel coefficient mapping method to reduce the area cost of the finite impulse response (FIR filter design, especially for optimizing its coefficients. Being capable of reducing the area cost and improving the filter performance, the proposed mapping method consists of four steps: quantization of coefficients, import of parameters, constitution of prime coefficients with parameters, and constitution of residual coefficients with prime coefficients. Effectiveness of the proposed coefficient mapping method is verified by selecting the 48-tap filter of IS-95 code division multiple access (CDMA standard as the benchmark. Experimental results indicate that the proposed design with canonical signed digit (CSD coefficients can operate at 86 MHz with an area of 241,813 um2, leading to a throughput rate of 1,382 Mbps. Its ratio of throughput/area is 5,715 Kbps/um2, yielding a higher performance than that of previous designs. In summary, the proposed design reduces 5.7% of the total filter area, shortens 25.7% of the critical path delay, and improves 14.8% of the throughput/area by a value over that of the best design reported before.
Simona Elena Dragomirescu
2014-07-01
Full Text Available One of the most important stages in the budget drafting process is the sales forecasting. As a matter of fact, the sales affect the whole activity of a company, their variation being considered the main risk factor for the performance and the financial position of the company. Sales forecasting starts with analyzing the turnover over a longer period of time. It includes all the studies and calculations made in order to determine the potential market to which the company can get access, as well as the part of it that the company is estimated to cover. There are several methods for planning the amount of sales, each company being able to choose one or more such methods. All the sales forecasting methods have advantages and disadvantages; however, in practice it was proved that most large companies use a combination of several methods. However, when there are seasonal variations each year, the seasonal coefficient method is used in order to forecast the sales. The exemplification of this method is done on the level of an production industrial company.
ZHAO Hong; TAN Hongbo; AN Junying; XU Haiting
2004-01-01
The finite element method (FEM) is applied to analyze sound characteristics of the viscoelastic coatings containing doubly periodic cavities immersed in water or adhered to steel plate between water and air. The reflection coefficients and transmission coefficients are obtained for the coatings with spherical, cylindrical or conic cavities in above two conditions.Moreover, the vibration modes of the coatings are analyzed. Numerical results show that the cavities have great impact on the sound characteristics at low frequency.
无
2002-01-01
It is a problem to be solved that the experimental selectivity coefficients of ion selective electrodes (ISEs) depend on the activity.This paper studied the new method of determining selectivity coefficients.A mixed ion response equation,which was similar to Nicolsky-Eisenman (N-E) equation recommended by IUPAC,was proposed.The equation includes the practical response slope of ISEs to the primary ion and the interfering ion.The selectivity coefficient was defined by the equation instead of the N-E equation.The experimental part of the method is similar to that based on the N-E equation.The values of selectivity coefficients obtained with this method do not depend on the activity whether the electrodes exhibit the Nernst response or non-Nernst response.The feasibility of the new method is illustrated experimentally.
The Nakhla parent melt: REE partition coefficients and clues to major element composition
Mckay, G.; Le, L.; Wagstaff, J.
1993-01-01
Nakhla is one of the SNC meteorites, generally believed to be of Martian origin. It is a medium-grained augite-olivine cumulate with a variolitic groundmass of sodic plagioclase, alkali feldspar, and Fe-rich pyroxenes and olivine. One of the major tasks in deciphering Nakhla's petrogenesis is determining the composition of its parent melt. Gaining an understanding of the composition and petrogenesis of this parent melt may help unravel Nakhla's relationship to the other SNCs, and provide clues to Martian petrogenesis in general. Our experimental partitioning studies provide new information that helps constrain both the major and trace element composition of the Nakhla parent melt.
Li, Min; Zhou, Tong; Song, Yanan
2016-07-01
A grain size characterization method based on energy attenuation coefficient spectrum and support vector regression (SVR) is proposed. First, the spectra of the first and second back-wall echoes are cut into several frequency bands to calculate the energy attenuation coefficient spectrum. Second, the frequency band that is sensitive to grain size variation is determined. Finally, a statistical model between the energy attenuation coefficient in the sensitive frequency band and average grain size is established through SVR. Experimental verification is conducted on austenitic stainless steel. The average relative error of the predicted grain size is 5.65%, which is better than that of conventional methods.
A Simple and Accurate Method for Calculating the Gaussian Beam Expansion Coefficients
LIU Wei; YANG Jun
2010-01-01
@@ The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique.The key problem of this technique is how to determine the coefficients of Gaussian functions.We present a simple and accurate optimization method to calculate the Gaussian beam expansion Coefficients.Half of the coefficients are obtained by solving linear equations.The other half are derived from the Fourier series expansion.Wave field simulation results demonstrate the validity of the new method.
Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method
Bahadir A. R.
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Study on the testing methods of friction coefficient in metal sheet deep drawing
2001-01-01
A more suitable method is introduced about testing friction coefficient on deep drawingcondition. It is pointed out that many ways to mesture friction coefficient. However, if a study of thefriction and lubrication in sheet metal deep drawing process is made, the testing method recom-mended in this paper should be used. As it is identical with the actual working condition accordingto its testing principle and state of stress.
Shumanova M.V.
2015-03-01
Full Text Available The process fish salting has been studied by the method of photon correlation spectroscopy; the distribution of salt concentration in the solution and herring flesh with skin has been found, diffusion coefficients and salt concentrations used for creating a mathematical model of the salting technology have been worked out; the possibility of determination by this method the coefficient of dynamic viscosity of solutions and different media (minced meat etc. has been considered
Application of finite-element-methods in food processing
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
A new fast direct solver for the boundary element method
Huang, S.; Liu, Y. J.
2017-04-01
A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.
A new method for simultaneous measurement of Seebeck coefficient and resistivity
He, Xu; Yang, Junyou; Jiang, Qinghui; Luo, Yubo; Zhang, Dan; Zhou, Zhiwei; Ren, Yangyang; Li, Xin; Xin, Jiwu; Hou, Jingdi
2016-12-01
A new method has been proposed and verified to measure the Seebeck coefficient and electrical resistivity of a sample in the paper. Different from the conventional method for Seebeck coefficient and resistivity measurement, the new method adopts a four-point configuration to measure both the Seebeck coefficient and resistivity. It can well identify the inhomogeneity of the sample by simply comparing the four Seebeck coefficients of different probe combinations, and it is more accurate and appropriate to take the average value of the four Seebeck coefficients as the measured result of the Seebeck coefficient of the sample than that measured by the two-point method. Furthermore, the four-point configuration makes it also very convenient to measure the resistivity by using the Van der Pauw method. The validity of this method has been verified with both the constantan alloy and p-type Bi2Te3 semiconductor samples, and the measurement results are in good agreement with those obtained by commercial available equipment.
Maciejewska Beata
2012-04-01
Full Text Available The paper presents the FEM method for determination of boiling heat transfer coefficient in cooling liquid flow in a rectangular minichannel with asymmetric heating. Experimental research has focused on the transition from single phase forced convection to nucleate boiling, i.e. the zone of boiling incipience. The “boiling front” location has been determined from the temperature distribution of the heated wall obtained from liquid crystal thermography. The main part of the test section has been a minichannel of pre-set depth from 0.7 to 2.0 mm, of different spatial orientations. Local values of heat transfer coefficient have been determined following the solution of the two-dimensional inverse heat transfer problem. This problem has been solved with the use of Trefftz functions. Trefftz functions have been used to construct base functions in the finite element method (FEMT.
无
2006-01-01
Based on the model structure of the influence coefficient method analyzed in depth by matrix theory,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing. It also presened the new ridge regression method for solving correction masses according to the Tikhonov regularization theory, and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.
On the methods for determining the transverse dispersion coefficient in river mixing
Baek, Kyong Oh; Seo, Il Won
2016-04-01
In this study, the strengths and weaknesses of existing methods for determining the dispersion coefficient in the two-dimensional river mixing model were assessed based on hydraulic and tracer data sets acquired from experiments conducted on either laboratory channels or natural rivers. From the results of this study, it can be concluded that, when the longitudinal dispersion coefficient as well as the transverse dispersion coefficients must be determined in the transient concentration situation, the two-dimensional routing procedures, 2D RP and 2D STRP, can be employed to calculate dispersion coefficients among the observation methods. For the steady concentration situation, the STRP can be applied to calculate the transverse dispersion coefficient. When the tracer data are not available, either theoretical or empirical equations by the estimation method can be used to calculate the dispersion coefficient using the geometric and hydraulic data sets. Application of the theoretical and empirical equations to the laboratory channel showed that equations by Baek and Seo [[3], 2011] predicted reasonable values while equations by Fischer [23] and Boxwall and Guymer (2003) overestimated by factors of ten to one hundred. Among existing empirical equations, those by Jeon et al. [28] and Baek and Seo [6] gave the agreeable values of the transverse dispersion coefficient for most cases of natural rivers. Further, the theoretical equation by Baek and Seo [5] has the potential to be broadly applied to both laboratory and natural channels.
Pourmand, Ali; Dauphas, Nicolas
2010-05-15
Batch equilibration experiments are conducted to measure the distribution coefficients (K(d)) of a large number of elements in nitric, nitric plus hydrofluoric, and hydrochloric acids on Eichrom TODGA extraction chromatography resin. The K(d)s are used to devise a multi-element extraction scheme for high-precision elemental and isotopic analyses of Ca, Hf, Lu, Th and U in geological materials, using high-purity lithium metaborate (LiBO(2)) flux fusion that allows rapid digestion of even the most refractory materials. The fusion melt, dissolved in nitric acid, is directly loaded to a TODGA cartridge on a vacuum chamber for elemental separation. An Ln-Spec cartridge is used in tandem with TODGA for Lu purification. The entire procedure, from flux digestion to preparation for isotopic analysis, can be completed in a day. The accuracy of the proposed technique is tested by measuring the concentrations of Ca (standard bracketing), Hf, Lu, Th and U (isotope dilution), and the isotopic composition of Hf in geostandards (USNM3529, BCR-2, BHVO-1, AGV-1 and AGV-2). All measurements are in excellent agreement with recommended literature values, demonstrating the effectiveness of the proposed analytical procedure and the versatility of TODGA resin.
LIANG Xinhua; ZHU Ping; LIN Zhongqin; ZHANG Yan
2007-01-01
A lightweight automotive prototype using alter- native materials and gauge thickness is studied by a numeri- cal method. The noise, vibration, and harshness (NVH) performance is the main target of this study. In the range of 1-150 Hz, the frequency response function (FRF) of the body structure is calculated by a finite element method (FEM) to get the dynamic behavior of the auto-body structure. The pressure response of the interior acoustic domain is solved by a boundary element method (BEM). To find the most contrib- uting panel to the inner sound pressure, the panel acoustic contribution analysis (PACA) is performed. Finally, the most contributing panel is located and the resulting structural optimization is found to be more efficient.
Nykolay Hristov Dyulgerov
2013-12-01
Full Text Available The aim of the present study was to generate information on interrelationships of some important productivity elements, direct and indirect effects of these characters on fruit yield of 1 plant in coriander. The study was conducted in the Institute of Agriculture - Karnobat, during the period 2006-2008 and included 81 coriander accessions. Phenotypic correlations of fruit weight per plant were highly significant and positive with number of branches per plant, number of umbels per plant, number of fruits per 1 umbel, fruit weight per umbel and 1000-fruits weight. Maximum direct contribution to fruit weight per plant was made by 1000-fruits weight, followed by fruit weight per umbel and number of umbels per plant. Therefore, these traits can be used as selection criteria to increase plant yield in coriander.
Enhanced patch test of finite element methods
CHEN; Wanji
2006-01-01
Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.
A method for making an alkaline element
Obi, F.; Takada, K.
1983-05-11
A mixture of asphalt with polybutene is applied to the contacting surfaces of the body top and the hermetically sealing stuffing. After assembly the element is heated to a temperature which exceeds the softening point of the mixture. The edge of the body is rolled in. The element has high reliability.
无
2000-01-01
The present study aims at developing a new method-Random M icrostructure Finite Element Method (RMFEM)for the effective properties of composite materials . In this method, a random microstructure model is used to simulate the microstructure of the real composite materials. The physical fields in such a randm microstructure model under specified boundary and initial conditions are analyzed by finite element method. The effective properties of composite materials can be obtained from the analysis results. As verification, some effective properties of composite materials, such as elastic module,thermal expansion coefficient, thermal conductivity and elastoplastic properties, are investigated by random microstructure finite element method. The numerical results are given together with the experimental data. It i- revealed that the random microstructure finite element method is a very valid method for the determination of the effective properties of composite materials.
New numerical analysis method in computational mechanics: composite element method
无
2000-01-01
A new type of FEM, called CEM (composite element method), is proposed to solve the static and dynamic problems of engineering structures with high accuracy and efficiency. The core of this method is to define two sets of coordinate systems for DOF's description after discretizing the structure, i.e. the nodal coordinate system UFEM(ξ) for employing the conventional FEM, and the field coordinate system UCT(ξ) for utilizing classical theory. Then, coupling these two sets of functional expressions could obtain the composite displacement field U(ξ) of CEM. The computations of the stiffness and mass matrices can follow the conventional procedure of FEM. Since the CEM inherents some good properties of the conventional FEM and classical analytical method, it has the powerful versatility to various complex geometric shapes and excellent approximation. Many examples are presented to demonstrate the ability of CEM.
New numerical analysis method in computational mechanics: composite element method
曾攀
2000-01-01
A new type of FEM, called CEM (composite element method), is proposed to solve the static and dynamic problems of engineering structures with high accuracy and efficiency. The core of this method is to define two sets of coordinate systems for DOF’ s description after discretizing the structure, i.e. the nodal coordinate system UFEM(ζ) for employing the conventional FEM, and the field coordinate system UCT(ζ) for utilizing classical theory. Then, coupling these two sets of functional expressions could obtain the composite displacement field U(ζ) of CEM. The computations of the stiffness and mass matrices can follow the conventional procedure of FEM. Since the CEM inherents some good properties of the conventional FEM and classical analytical method, it has the powerful versatility to various complex geometric shapes and excellent approximation. Many examples are presented to demonstrate the ability of CEM.
Method and system for processing optical elements using magnetorheological finishing
Menapace, Joseph Arthur; Schaffers, Kathleen Irene; Bayramian, Andrew James; Molander, William A
2012-09-18
A method of finishing an optical element includes mounting the optical element in an optical mount having a plurality of fiducials overlapping with the optical element and obtaining a first metrology map for the optical element and the plurality of fiducials. The method also includes obtaining a second metrology map for the optical element without the plurality of fiducials, forming a difference map between the first metrology map and the second metrology map, and aligning the first metrology map and the second metrology map. The method further includes placing mathematical fiducials onto the second metrology map using the difference map to form a third metrology map and associating the third metrology map to the optical element. Moreover, the method includes mounting the optical element in the fixture in an MRF tool, positioning the optical element in the fixture; removing the plurality of fiducials, and finishing the optical element.
Variations in the light extinction coefficient of elemental carbon in the Indian outflow
Andersson, August; Sheesley, Rebecca J.; Krusâ, Martin; Kirillova, Elena; Budhavant, Krishnakant; Rao, P. S. P.; Praveen, P. S.; Gustafsson, Örjan
2010-05-01
High wintertime concentrations of black carbon aerosols (BCA) over South Asia and the northern Indian Ocean are thought to have a large impact on the regional climate. Direct absorption of sunlight by BCAs causes heating of the atmosphere and cooling at the surface. To quantify such effects it is important to characterize a number of different properties of the aerosols. Here we report the concentrations of the organic carbon (OC) and elemental carbon (EC) as well as absorptive properties of these aerosols. Samples were collected during a continuous 14-month campaign Dec 2008 - Mar 2009 at Sinaghad in Western India and on Hanimaadhoo, the Northernmost Island in the Maldives. This data set suggests that the absorptive properties of the BCAs are variable, sometimes by a factor of 4 compared to the mean. This observation adds to the complexity of calculating the radiative forcing for BCAs, reinforcing previous observations that parameters such as internal mixing and knowledge about the sources need to be taken into account.
Application of the Clustering Method in Molecular Dynamics Simulation of the Diffusion Coefficient
无
2008-01-01
Using molecular dynamics (MD) simulation, the diffusion of oxygen, methane, ammonia and carbon dioxide in water was simulated in the canonical NVT ensemble, and the diffusion coefficient was analyzed by the clustering method. By comparing to the conventional method (using the Einstein model) and the differentiation-interval variation method, we found that the results obtained by the clustering method used in this study are more close to the experimental values. This method proved to be more reasonable than the other two methods.
Tatulli, Eric
2013-04-01
This paper studies the effects on Zernike coefficients of aperture scaling, translation, and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes an analytical method for computing the matrix that enables the building of transformed Zernike coefficients from the original ones. The technique is based on the properties of Zernike polynomials and Fourier transform, and, in the case of a full aperture without central obstruction, the coefficients of the matrix are given in terms of integrals of Bessel functions. The integral formulas are exact and do not depend on any specific ordering of the polynomials.
On the Diffusion Coefficient of Two-step Method for LWR analysis
Lee, Deokjung; Choi, Sooyoung [UNIST, Ulsan (Korea, Republic of); Smith, Kord S. [Massachusetts Institute of Technology, Cambridge (United States)
2015-10-15
The few-group constants including diffusion coefficients are generated from the assembly calculation results. Once the assembly calculation is done, the cross sections (XSs) are spatially homogenized, and a critical spectrum calculation is performed in order to take into account the neutron leakages of the lattice. The diffusion coefficient is also generated through the critical spectrum calculation. Three different methods of the critical spectrum calculation such as B1 method, P1 method, and fundamental mode (FM) calculation method are considered in this paper. The diffusion coefficients can also be affected by transport approximations for the transport XS calculation which is used in the assembly transport lattice calculation in order to account for the anisotropic scattering effects. The outflow transport approximation and the inflow transport approximation are investigated in this paper. The accuracy of the few group data especially the diffusion coefficients has been studied to optimize the combination of the transport correction methods and the critical spectrum calculation methods using the UNIST lattice physics code STREAM. The combination of the inflow transport approximation and the FM method is shown to provide the highest accuracy in the LWR core calculations. The methodologies to calculate the diffusion coefficients have been reviewed, and the performances of them have been investigated with a LWR core problem. The combination of the inflow transport approximation and the fundamental mode critical spectrum calculation shows the smallest errors in terms of assembly power distribution.
Pourmand, A.; Dauphas, N.
2008-03-01
Distribution coefficients for 60 elements on TODGA resin are presented along with a robust single-column protocol for separation of HSFE, lanthanides and actinides in meteorites and terrestrial rocks for high-precision isotope analysis.
Xia, Yi-Ming
2015-01-01
A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a multireolution finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The rational MRA enables the implementation of the multiresolution Mindlin plate element method to be more rational and efficient than that of the conventional monoresolution or o...
A method for making a dry element
Abe, T.; Isikhara, K.; Kimura, T.; Momose, K.; Sakata, Y.
1983-08-11
The agglomerate is coated along the lateral surface by a separator and is enclosed in a zinc cylinder which serves as the anode. A separating plate is installed in the upper part of the agglomerate between the agglomerate and the anode. A current outlead is attached to the anode. The element is inserted into a body, pressing the plate into the agglomerate with a punch which has a recess. A guide cylinder is used for precise installation of the element. The space between the plate and the body in the upper part of the element is filled with wax or another substance. Short circuiting (KZ) between the current outlead and the agglomerate is prevented in the element.
An automatic fractional coefficient setting method of FODPSO for hyperspectral image segmentation
Xie, Weiying; Li, Yunsong
2015-05-01
In this paper, an automatic fractional coefficient setting method of fractional-order Darwinian particle swarm optimization (FODPSO) is proposed for hyperspectral image segmentation. The spectrum has been already taken into consideration by integrating various types of band selection algorithms, firstly. We provide a short overview of the hyperspectral image to select an appropriate set of bands by combining supervised, semi-supervised and unsupervised band selection algorithms. Some approaches are not limited in regards to their spectral dimension, but are limited with respect to their spatial dimension owing to low spatial resolution. The addition of spatial information will be focused on improving the performance of hyperspectral image segmentation for later fusion or classification. Many researchers have advocated that a large fractional coefficient should be in the exploration state while a small fractional coefficient should be in the exploitation, which does not mean the coefficient purely decrease with time. Due to such reasons, we propose an adaptive FODPSO by setting the fractional coefficient adaptively for the application of final hyperspectral image segmentation. In fact, the paper introduces an evolutionary factor to automatically control the fractional coefficient by using a sigmoid function. Therefore, fractional coefficient with large value will benefit the global search in the exploration state. Conversely, when the fractional coefficient has a small value, the exploitation state is detected. Hence, it can avoid optimization process get trapped into the local optima. Ultimately, the experimental segmentation results prove the validity and efficiency of our proposed automatic fractional coefficient setting method of FODPSO compared with traditional PSO, DPSO and FODPSO.
Novel high-performance element in the electromagnetic finite-element method--node-edge element
Sheng Xinqing; Peng Zhen
2008-01-01
It is known in the computational electromagnetics (CEM) that the node element has a relative well-conditioned matrix,but suffers from the spurious solution problem; whereas the edge element has no spurious solutions,but usually produces an ill-conditioned matrix.Particularly,when the mesh is over dense,the iterative solution of the matrix equation from edge element converges very slowly.Based on the node element and edge element,a node-edge element is presented,which has no spurious solutions and better-conditioned matrix.Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.
Diffusion coefficients for LMFBR cells calculated with MOC and Monte Carlo methods
Rooijen, W.F.G. van, E-mail: rooijen@u-fukui.ac.j [Research Institute of Nuclear Energy, University of Fukui, Bunkyo 3-9-1, Fukui-shi, Fukui-ken 910-8507 (Japan); Chiba, G., E-mail: chiba.go@jaea.go.j [Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195 (Japan)
2011-01-15
The present work discusses the calculation of the diffusion coefficient of a lattice of hexagonal cells, with both 'sodium present' and 'sodium absent' conditions. Calculations are performed in the framework of lattice theory (also known as fundamental mode approximation). Unlike the classical approaches, our heterogeneous leakage model allows the calculation of diffusion coefficients under all conditions, even if planar voids are present in the lattice. Equations resulting from this model are solved using the method of characteristics (MOC). Independent confirmation of the MOC result comes from Monte Carlo calculations, in which the diffusion coefficient is obtained without any of the assumptions of lattice theory. It is shown by comparison to the Monte Carlo results that the MOC solution yields correct values of the diffusion coefficient under all conditions, even in cases where the classic calculation of the diffusion coefficient fails. This work is a first step in the development of a robust method to calculate the diffusion coefficient of lattice cells. Adoption into production codes will require more development and validation of the method.
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
Yun-qing Huang; Shi Shu; Xi-jun Yu
2006-01-01
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
Primoff, Ernest S.
This paper concerns two features of a project on the assessment of job potential: the J-Coefficient, and the J-Scale. The J-Coefficient is a means of determining the validity of a test for a position on the basis of (1) the Beta Weights for predicting test scores from a set of elements and (2) estimates of importance of each element in the…
Hilario, Eric C; Stern, Alan; Wang, Charlie H; Vargas, Yenny W; Morgan, Charles J; Swartz, Trevor E; Patapoff, Thomas W
2017-01-01
Concentration determination is an important method of protein characterization required in the development of protein therapeutics. There are many known methods for determining the concentration of a protein solution, but the easiest to implement in a manufacturing setting is absorption spectroscopy in the ultraviolet region. For typical proteins composed of the standard amino acids, absorption at wavelengths near 280 nm is due to the three amino acid chromophores tryptophan, tyrosine, and phenylalanine in addition to a contribution from disulfide bonds. According to the Beer-Lambert law, absorbance is proportional to concentration and path length, with the proportionality constant being the extinction coefficient. Typically the extinction coefficient of proteins is experimentally determined by measuring a solution absorbance then experimentally determining the concentration, a measurement with some inherent variability depending on the method used. In this study, extinction coefficients were calculated based on the measured absorbance of model compounds of the four amino acid chromophores. These calculated values for an unfolded protein were then compared with an experimental concentration determination based on enzymatic digestion of proteins. The experimentally determined extinction coefficient for the native proteins was consistently found to be 1.05 times the calculated value for the unfolded proteins for a wide range of proteins with good accuracy and precision under well-controlled experimental conditions. The value of 1.05 times the calculated value was termed the predicted extinction coefficient. Statistical analysis shows that the differences between predicted and experimentally determined coefficients are scattered randomly, indicating no systematic bias between the values among the proteins measured. The predicted extinction coefficient was found to be accurate and not subject to the inherent variability of experimental methods. We propose the use of a
Adaptive finite element-element-free Galerkin coupling method for bulk metal forming processes
Lei-chao LIU; Xiang-huai DONG; Cong-xin LI
2009-01-01
An adaptive finite element-element-free Galerkin (FE-EFG) coupling method is proposed and developed for the numerical simulation of bulk metal forming processes. This approach is able to adaptively convert distorted FE elements to EFG domain in analysis. A new scheme to implement adaptive conversion and coupling is presented. The coupling method takes both advantages of finite element method (FEM) and meshless methods. It is capable of handling large deformations with no need of remeshing procedures, while it is computationally more efficient than those full meshless methods. The effectiveness of the proposed method is demonstrated with the numerical simulations of the bulk metal forming processes including forging and extrusion.
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Jiang, Lijian
2010-08-01
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
A method of quaternion typification of Clifford algebra elements
Shirokov, Dmitry
2008-01-01
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method of analysis of commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebra elements.
The Matrix Element Method and Vector-Like Quark Searches
Morrison, Benjamin
2016-01-01
In my time at the CERN summer student program, I worked on applying the matrix element method to vector-like quark identification. I worked in the ATLAS University of Geneva group under Dr. Olaf Nackenhorst. I developed automated plotting tools with ROOT, a script for implementing and optimizing generated matrix element calculation code, and kinematic transforms for the matrix element method.
Kai, Bo; Li, Runze; Zou, Hui
2011-02-01
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we further develop a semiparametric composite quantile regression procedure. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the estimators achieve the best convergence rate. Moreover, we show that the proposed method is much more efficient than the least-squares-based method for many non-normal errors and that it only loses a small amount of efficiency for normal errors. In addition, it is shown that the loss in efficiency is at most 11.1% for estimating varying coefficient functions and is no greater than 13.6% for estimating parametric components. To achieve sparsity with high-dimensional covariates, we propose adaptive penalization methods for variable selection in the semiparametric varying-coefficient partially linear model and prove that the methods possess the oracle property. Extensive Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. Finally, we apply the new methods to analyze the plasma beta-carotene level data.
A new multiresolution finite element method based on a multiresolution quadrilateral plate element
Xia, YiMing
2014-01-01
A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape function. The basic node shape function is constructed by extending shape function around a specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node quadrilateral plate element and method is a monoresolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is fully determined by the RL, not by th...
Vibration Analysis of Plates by MLS-Element Method
Zhou, L.; Xiang, Y.
2010-05-01
This paper presents a novel numerical method, the moving least square element (MLS-element) method for the free vibration analysis of plates based on the Mindlin shear deformable plate theory. In the MLS-element method, a plate can be first divided into multiple elements which are connected through selected nodal points on the interfaces of the elements. An element can be of any shape and the size of the element varies dependent on the problem at hand. The shape functions of the element for the transverse displacement and the rotations are derived based on the MLS interpolation technique. The convergence and accuracy of the method can be controlled by either increasing the number of elements or by increasing the number of MLS interpolation points within elements. Two selected examples for vibration of a simply supported square Mindlin plate and a clamped L-shaped Mindlin plate are studied to illustrate the versatility and accuracy of the proposed method. It shows that the proposed method is highly accurate and flexible for the vibration analysis of plate problems. The method can be further developed to bridge the existing meshless method and the powerful finite element method in dealing with various engineering computational problems, such as large deformation and crack propagation in solid mechanics.
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
Based on a new intermediate transformation, a variable-coefficient hyperbola function method is proposed.Being concise and straightforward, it is applied to the (2+1)-dimensional variable-coefficient Broer Kaup system. As a result, several new families of exact soliton-like solutions are obtained, besides the travelling wave. When imposing some conditions on them, the new exact solitary wave solutions of the (2+1)-dimensional Broer-Kaup system are given. The method can be applied to other variable-coefficient nonlinear evolution equations in mathematical physics.
Variational iteration method for solving partial differential equations with variable coefficients
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt)], E-mail: ahaali_49@yahoo.com; Raslan, K.R. [Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)], E-mail: kamal_raslan@yahoo.com
2009-05-15
An extremely simple and elementary but rigorous derivation of exact solutions of partial differential equations in different dimensions with variable coefficients is given using the variational iteration method. The efficiency of the considered method is illustrated by some examples. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.
GE Jian-Ya; WANG Rui-Min; DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schr(o)dinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.
An Improved DC Recovery Method from AC Coefficients of DCT-Transformed Images
Li, Shujun; Saupe, Dietmar; Kuo, C -C Jay
2010-01-01
Motivated by the work of Uehara et al. [1], an improved method to recover DC coefficients from AC coefficients of DCT-transformed images is investigated in this work, which finds applications in cryptanalysis of selective multimedia encryption. The proposed under/over-flow rate minimization (FRM) method employs an optimization process to get a statistically more accurate estimation of unknown DC coefficients, thus achieving a better recovery performance. It was shown by experimental results based on 200 test images that the proposed DC recovery method significantly improves the quality of most recovered images in terms of the PSNR values and several state-of-the-art objective image quality assessment (IQA) metrics such as SSIM and MS-SSIM.
A review of flexibility-based finite element method for beam-column elements
LI Shuang; ZHAI Changhai; XIE Lili
2009-01-01
For material nonlinear problem, elements derived with the flexibility-based method are more accurate than classical elements derived with the stiffness-based method. A review of the current state of the art of the flexibility-based finite element method is provided to enhance the robustness of structure analysis. The research on beam-column elements is the mainstream in the research on flexibility-based finite element method at present. The original development of flexibility-based finite element method is reviewed, and the further development of this method is then presented in several specific aspects, such as geometrically nonlinear analysis and dynamic analysis. The further research needed to be carried out in the future is finally discussed.
Hydraulic fracturing with distinct element method
Pruiksma, J.P.; Bezuijen, A.
2002-01-01
In this report, hydraulic fracturing is investigated using the distinct element code PFC2D from Itasca. Special routines were written to be able to model hydraulic fracturing. These include adding fluid flow to PFC2D and updating the fluid flow domains when fractures appear. A brief description of t
Parallel computation with the spectral element method
Ma, Hong
1995-12-01
Spectral element models for the shallow water equations and the Navier-Stokes equations have been successfully implemented on a data parallel supercomputer, the Connection Machine model CM-5. The nonstaggered grid formulations for both models are described, which are shown to be especially efficient in data parallel computing environment.
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Analysis of bender element test interpretation using the discrete element method
O’Donovan, J.; O’Sullivan, C.; Marketos, G.; Muir Wood, D.
2015-01-01
While bender element testing is now well-established as a laboratory technique to determine soil stiffness, a robust technique to interpret the data remains elusive. A discrete element method (DEM) model of a face-centred cubic packing of uniform spheres was created to simulate bender element tests
On Some Versions of the Element Agglomeration AMGe Method
Lashuk, I; Vassilevski, P
2007-08-09
The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate element based AMG method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom (dofs) is based on solving large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V-cycle utilizing simple interpolation matrices and nested conjugate gradient (CG) based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods.
NON SPURIOUS SPECTRAL-LIKE ELEMENT METHODS FOR MAXWELL'S EQUATIONS
Gary Cohen; Marc Duruflé
2007-01-01
In this paper, we give the state of the art for the so called "mixed spectral elements" for Maxwell's equations. Several families of elements, such as edge elements and discontinuous Galerkin methods (DGM) are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is a novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
The extended auxiliary equation method for the KdV equation with variable coefficients
Shi Lan-Fang; Chen Cai-Sheng; Zhou Xian-Chun
2011-01-01
This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients.As a result,solitary wave solutions,trigonometric function solutions,rational function solutions,Jacobi elliptic doubly periodic wave solutions,and nonsymmetrical kink solution are obtained.It is shown that the extended auxiliary equation method,with the help of a computer symbolic computation system,is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.
YANG Sheng; ZHANG Zhi; SHI Peng-fei
2006-01-01
Feature subset selection is a fundamental problem of data mining. The mutual information of feature subset is a measure for feature subset containing class feature information. A hashing mechanism is proposed to calculate the mutual information of feature subset. The feature relevancy is defined by mutual information. Redundancy-synergy coefficient, a novel redundancy and synergy measure for features to describe the class feature, is defined. In terms of information maximization rule, a bidirectional heuristic feature subset selection method based on mutual information and redundancy-synergy coefficient is presented. This study' s experiments show the good performance of the new method.
Camporesi, Roberto
2011-06-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.
Pimienta, Lucas; Fortin, Jérôme; Guéguen, Yves
2017-04-01
Over the last decades, a large understanding has been gained on the elastic properties of rocks. Rocks are, however, porous materials, which properties depend on both response of the bulk material and of the pores. Because in that case both the applied external pressure and the fluid pressure play a role, different poroelasticity coefficients exist. While theoretical relations exist, measuring precisely those different coefficients remains an experimental challenge. Accounting for the different experimental complexities, a new methodology is designed that allows attaining accurately a large set of compressibility and poroelasticity coefficients in porous and permeable rocks. This new method relies on the use of forced confining or pore fluid pressure oscillations. In total, seven independent coefficients have been measured using three different boundary conditions. Because the usual theories predict only four independent coefficients, this overdetermined set of data can be checked against existing thermodynamic relations. Measurements have been performed on a Bentheim sandstone under, water- and glycerine-saturated conditions for different values of confining and pore fluid pressure. Consistently with the poroelasticity theory, the effect of the fluid bulk modulus is observed under undrained conditions but not under drained ones. Using thermodynamic relations, (i) the unjacketed, quartz, and skeleton (Zimmerman's relation) bulk moduli fit, (ii) the drained and undrained properties fit, and (iii) it is directly inferred from the measurements that the pore skeleton compressibility Cϕ is expected to be constant with pressure and to be exceedingly near the bulk skeleton Cs and mineral Cm compressibility coefficients.
Tao JIN; Jian-ping HONG; Hao ZHENG; Ke TANG; Zhi-hua GAN
2009-01-01
Inverse heat conduction method (IHCM)is one of the most effective approaches to obtaining the boiling heat transfer coefficient from measured results.This paper focuses on its application in cryogenic boiling heat transfer.Experiments were conducted on the heattransfer of a stainless steel block in a liquid nitrogen bath.with the assumption of a ID conduction condition to realize fast acquisition of the temperature of the test points inside the block.With the inverse-heat conduction theory and the explicit finite difference model,a solving program was developed to calculate the heat flux and the boiling heat transfer coefficient of a stainless steel block in liquid nitrogen bath based on the temperature acquisition data.Considering the oscillating data and some unsmooth transition points in the inverse-heat-conduction calculation result of the heat-transfer coefficient,a two-step data-fitting procedure was proposed to obtain the expression for the boiling heat transfer coefficients.The coefficient was then verified for accuracy by a comparison between the simulation results using this expression and the verifying experimental results of a stainless steel block.The maximum error with a revised segment fitting iS around 6%.which verifies the feasibility of using IHCM to measure the boiling heat transfer coefficient in liquid nitrogen bath.
GUZELBEY Ibrahim H.; KANBER Bahattin; AKPOLAT Abdullah
2004-01-01
In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.
Analysis of Dynamic Modeling Method Based on Boundary Element
Xu-Sheng Gan
2013-07-01
Full Text Available The aim of this study was to study an improved dynamic modeling method based on a Boundary Element Method (BEM. The dynamic model was composed of the elements such as the beam element, plate element, joint element, lumped mass and spring element by the BEM. An improved dynamic model of a machine structure was established based on plate-beam element system mainly. As a result, the dynamic characteristics of a machine structure were analyzed and the comparison of computational results and experimental’s showed the modeling method was effective. The analyses indicate that the introduced method inaugurates a good way for analyzing dynamic characteristics of a machine structure efficiently.
Convergence of adaptive finite element methods for eigenvalue problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2008-01-01
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
Finite element method for thermal analysis of concentrating solar receivers
Shtrakov, Stanko; Stoilov, Anton
2006-01-01
Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great number of numerical experiments is carried out. Illustrative numerical results are given for an array...
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
Equality of Medical Health Resource Allocation in China Based on the Gini Coefficient Method.
Jian Jin
2015-04-01
Full Text Available The Chinese government is trying to achieve the goal of "universal access to basic health care services". However, the inequality of the distribution of health care resources across the country is the biggest obstacle. This paper aims to explore these inequalities and the extent to which the method of analysis influences the perception.The indicators of health care resource distribution studied consisted of the number of health care institutions, the number of beds in health care institutions and the number of medical personnel. Data were obtained from the China Statistical Yearbook 2014. The extent of equality was assessed using the Lorenz Curve and Gini Coefficient Method.Health care resource distribution in China demonstrates inequalities. The demographic Gini Coefficients based on the Lorenz Curves for the distribution of health care institutions, beds in health care institutions and medical personnel are 0.190, 0.070 and 0.070 respectively, while the corresponding Coefficients based on geographical areas are 0.616, 0.639 and 0.650.The equality of China's demographically assessed distribution of health care resources is greater than that of its geographically measured distribution. Coefficients expressed by population imply there is ready access to healthcare in all regions, whilst the Coefficients by geographical area apparently indicate inequality. This is the result of the sparsity of population.
Choi, Myung Soo; Yang, Kyong Uk [Chonnam National University, Yeosu (Korea, Republic of); Kondou, Takahiro [Kyushu University, Fukuoka (Japan); Bonkobara, Yasuhiro [University of Miyazaki, Miyazaki (Japan)
2016-03-15
We developed a method for analyzing the free vibration of a structure regarded as a distributed system, by combining the Wittrick-Williams algorithm and the transfer dynamic stiffness coefficient method. A computational algorithm was formulated for analyzing the free vibration of a straight-line beam regarded as a distributed system, to explain the concept of the developed method. To verify the effectiveness of the developed method, the natural frequencies of straight-line beams were computed using the finite element method, transfer matrix method, transfer dynamic stiffness coefficient method, the exact solution, and the developed method. By comparing the computational results of the developed method with those of the other methods, we confirmed that the developed method exhibited superior performance over the other methods in terms of computational accuracy, cost and user convenience.
Knott, J.R.; Sarna-Wojcicki, A. M.; Montanez, I.P.; Wan, E.
2007-01-01
Volcanic glass samples from the same volcanic center (intra-source) often have a similar major-element composition. Thus, it can be difficult to distinguish between individual tephra layers, particularly when using similarity coefficients calculated from electron microprobe major-element measurements. Minor/trace element concentrations in glass can be determined by solution inductively coupled plasma mass spectrometry (S-ICP-MS), but have not been shown as suitable for use in large tephrochronologic databases. Here, we present minor/trace-element concentrations measured by S-ICP-MS and compare these data by similarity coefficients, the method commonly used in large databases. Trial samples from the Bishop Tuff, the upper and lower tuffs of Glass Mountain and the tuffs of Mesquite Spring suites from eastern California, USA, which have an indistinguishable major-element composition, were analyzed using S-ICP-MS. The resulting minor/trace element similarity coefficients clearly separated the suites of tephra layers and, in most cases, individual tephra layers within each suite. Comparisons with previous instrumental neutron activation analysis (INAA) elemental measurements were marginally successful. This is important step toward quantitative correlation in large tephrochronologic databases to achieve definitive identification of volcanic glass samples and for high-resolution age determinations. ?? 2007 Elsevier Ltd and INQUA.
NEW ALGORITHM OF COUPLING ELEMENT-FREE GALERKIN WITH FINITE ELEMENT METHOD
ZHAO Guang-ming; SONG Shun-cheng
2005-01-01
Through the construction of a new ramp function, the element-free Galerkin method and finite element coupling method were applied to the whole field, and was made fit for the structure of element nodes within the interface regions, both satisfying the essential boundary conditions and deploying meshless nodes and finite elements in a convenient and flexible way, which can meet the requirements of computation for complicated field. The comparison between the results of the present study and the corresponding analytical solutions shows this method is feasible and effective.
Raykov, Tenko; Marcoulides, George A.
2015-01-01
A direct approach to point and interval estimation of Cronbach's coefficient alpha for multiple component measuring instruments is outlined. The procedure is based on a latent variable modeling application with widely circulated software. As a by-product, using sample data the method permits ascertaining whether the population discrepancy…
Camporesi, Roberto
2011-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…
Trial equation method for solving the generalized Fisher equation with variable coefficients
Triki, Houria [Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba (Algeria); Wazwaz, Abdul-Majid, E-mail: wazwaz@sxu.edu [Department of Mathematics, Saint Xavier University, Chicago, IL 60655 (United States)
2016-03-22
We investigate a generalized Fisher equation with temporally varying coefficients, describing the dynamics of a field in inhomogeneous media. A class of exact soliton solutions of this equation is presented, and some of which are derived for the first time. The trial equation method is applied to obtain these soliton solutions. The constraint conditions for the existence of these solutions are also exhibited.
Raykov, Tenko; Marcoulides, George A.
2015-01-01
A direct approach to point and interval estimation of Cronbach's coefficient alpha for multiple component measuring instruments is outlined. The procedure is based on a latent variable modeling application with widely circulated software. As a by-product, using sample data the method permits ascertaining whether the population discrepancy…
Camporesi, Roberto
2011-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…
ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD
1998-01-01
The estimate model for a nonlinear system of squeeze-film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed.
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
An H1-Galerkin Expanded Mixed Element Method for Semi-linear Hyperbolic Wave Equation
WANG Jin-feng; LIU Yang; LI Hong; HE Siriguleng
2013-01-01
An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations.By using the mixed formulation,we can get the optimal approximation for three variables:the scalar unknown,its gradient and its flux(coefficient times the gradient),simultaneously.We also prove the existence and uniqueness of semi-discrete solution.Finally,we obtain some numerical results to illustrate the efficiency of the method.
A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals
Dietzen, F. J.; Nordmann, R.
1989-01-01
A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.
Hooper, Russell; Toose, E.M.; Macosko, Christopher W.; Derby, Jeffrey J.
2001-01-01
A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are
Aleš Mráček
2010-02-01
Full Text Available The amorphous polymer film swelling in a liquid solvent below the glass transition temperature was characterized by a few kinetic parameters (especially the mutual diffusion coefficient of swelling and its mean value obtained by interference of monochromatic light in the wedge arrangement. This interferometric method allows one to determine the concentration field in the swollen surface layer and consequently to compute the concentration-dependent diffusion coefficient. A software system developed at the Department of Physics and Material Engineering at TBU in Zlin has been used for the evaluation of the main kinetic parameters of the swelling process. The software can be used for the on-line analyses of interferograms during the swelling process. The main application outputs are the computation of the concentration profile, the concentration gradient, the mutual diffusion coefficient of the swelling by the solvent and its mean value.
Measurement of the Thermal-Conductivity Coefficient of Nanofluids by the Hot-Wire Method
Minakov, A. V.; Rudyak, V. Ya.; Guzei, D. V.; Pryazhnikov, M. I.; Lobasov, A. S.
2015-01-01
In this work, the authors present results of adaptation and testing of the hot-wire method for determination for the thermal-conductivity coefficient of nanofluids. A mathematical model of heat transfer with allowance for free convection has been constructed to elucidate the parameters of an experimental setup and the range of its applicability. The experimental procedure has been tested on measurements of the thermal conductivities of water and ethylene glycol. The thermal-conductivity coefficient of a nanofluid has been measured at room temperature. The nanofluid under study was prepared on the basis of ethylene glycol and alumina nanoparticles. The concentrations of the nanoparticles ranged from 0.5% to 2% by volume. Good agreement has been obtained between the measured values of the thermal-conductivity coefficient and the data of other authors.
Wu, Wen; Wu, Zhouhu; Song, Zhiwen
2017-07-01
Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.
Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids
Scheichl, Robert [Univ. of Bath (United Kingdom). Dept. of Mathematical Sciences; Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2012-06-21
We generalize the analysis of classical multigrid and two-level overlapping Schwarz methods for 2nd order elliptic boundary value problems to problems with large discontinuities in the coefficients that are not resolved by the coarse grids or the subdomain partition. The theoretical results provide a recipe for designing hierarchies of standard piecewise linear coarse spaces such that the multigrid convergence rate and the condition number of the Schwarz preconditioned system do not depend on the coefficient variation or on any mesh parameters. One assumption we have to make is that the coarse grids are sufficiently fine in the vicinity of cross points or where regions with large diffusion coefficients are separated by a narrow region where the coefficient is small. We do not need to align them with possible discontinuities in the coefficients. The proofs make use of novel stable splittings based on weighted quasi-interpolants and weighted Poincaré-type inequalities. Finally, numerical experiments are included that illustrate the sharpness of the theoretical bounds and the necessity of the technical assumptions.
Lotfollah Saghaie
2003-08-01
Full Text Available The partition coefficients (Kpart , in octanol/water system of a range of bidentate ligands containing the 3-hydroxypyridin-4-one moiety were determined using shake flask and automated continuous flow methods (filter probe method. The shake flask method was used for extremely hydrophilic or hydrophobic compounds with a Kpart values greater than 100 and less than 0.01. For other ligands which possess moderate lipophilicity (Kpart values between 0.01-100 the filter probe method was used. Also the partition coefficient of four ligands with moderate lipophilicity was determined by shake flask method in order to check comparability of these two methods. While the shake flask method was able to determine either extremely hydrophilic or hydrophobic compounds efficiently, the filter probe method was unable to measure such Kpart values. Although, determination of the Kpart values of all compounds is possible with the classical shake-flask method, the procedure is time consuming. In contrast, the filter probe method offers many advantages over the traditional shake-flask method in terms of speed, efficiency of separation and degree of automation. The shake-flask method is the method of choice for determination of partition coefficients of extremely hydrophilic and hydrophobic ligands.
Kucza, Witold, E-mail: witek@agh.edu.pl
2013-07-25
Graphical abstract: -- Highlights: •Former random walk approach for FIA simulations has been improved. •Random walk and uniform dispersion models have been used for FIA simulations. •Diffusivities have been optimized by genetic and the Levenberg–Marquardt methods. •Both approaches have given similar results in agreement with experimental ones. -- Abstract: Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg–Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches.
A fast collocation method for a variable-coefficient nonlocal diffusion model
Wang, Che; Wang, Hong
2017-02-01
We develop a fast collocation scheme for a variable-coefficient nonlocal diffusion model, for which a numerical discretization would yield a dense stiffness matrix. The development of the fast method is achieved by carefully handling the variable coefficients appearing inside the singular integral operator and exploiting the structure of the dense stiffness matrix. The resulting fast method reduces the computational work from O (N3) required by a commonly used direct solver to O (Nlog N) per iteration and the memory requirement from O (N2) to O (N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O (N2) to O (N). Numerical results are presented to show the utility of the fast method.
Investigation on tribology behavior of lubricants using the coefficient of friction test method
2001-01-01
This test method is used to determine the property of lubricants by measure the pa-rameters such as the coefficient of friction, wear value and seizure load on the Four Ball Wear TestMachine. Experiments were conducted using ASTM D5183-95 Standard Test Method (StandardTest Method For Determination Of The Coefficient of Friction of Lubricants Using the Four BallWear Test Machine) to measure the friction reducing ability , antiwear property and ex-treme-pressure property of different type of lubricants, the additives are also been studied at thesame time. From the test result, this test method can distinguish not only the property of differenttype of lubricants rapidly, sensitively and effectively but also can reflect the friction reducingability , antiwear property and extreme-pressure property of various additive formula.
Finite element methods in resistivity logging
Lovell, J. R.
1993-09-01
Resistivity measurements are used in geophysical logging to help determine hydrocarbon reserves. The derivation of formation parameters from resistivity measurements is a complicated nonlinear procedure often requiring additional geological information. This requires an excellent understanding of tool physics, both to design new tools and interpret the measurements of existing tools. The Laterolog measurements in particular are difficult to interpret because the response is very nonlinear as a function of electrical conductivity, unlike Induction measurements. Forward modeling of the Laterolog is almost invariably done with finite element codes which require the inversion of large sparse matrices. Modern techniques can be used to accelerate this inversion. Moreover, an understanding of the tool physics can help refine these numerical techniques.
Method for acquiring part load distribution coefficient of air conditioning system
丁勇; 李百战; 谭颖
2009-01-01
This paper presents a method to acquire runtime distribution ratio of building air conditioning system under part load condition (part load coefficient of system) through practical energy consumption data. By utilizing monthly energy consumption data of the entire year as the analysis object,this paper identifies data distribution,verifies distribution characteristics and analyzes distribution probability density for the issue of running time distribution ratio of air conditioning system in part load zones in the whole operation period,thus providing a basic calculation basis for an overall analysis of energy efficiency of air conditioning system. In view of the general survey of public building energy consumption carried by the government of Chongqing,this paper takes the governmental office building as an example,the part load ratio coefficient corresponding to practical running of air conditioning system of governmental office building in Chongqing is obtained by utilizing the above probability analysis and the solving method of probability density function. By utilizing the ratio coefficient obtained using this method,the part load coefficient with any running ratio of air conditioning system can be obtained according to the requirement of analysis,which can be used in any load ratio for analyzing running energy efficiency of air conditioning system.
Determination of the activity coefficient of neodymium in liquid aluminium by potentiometric methods
De Cordoba, G. [HLW/DFN/DE, CIEMAT, Avda. Complutense 22, Madrid 28040 (Spain)], E-mail: g.cordoba@ciemat.es; Laplace, A.; Conocar, O.; Lacquement, J. [DEN/DRCP/SCPS/LPP, CEA, Site de Marcoule. Bat. 399, BP 17171, 30207 Bagnols sur Ceze (France); Caravaca, C. [HLW/DFN/DE, CIEMAT, Avda. Complutense 22, Madrid 28040 (Spain)
2008-12-30
The activity coefficient of neodymium in liquid aluminium phase has been determined potentiometrically in the temperature range of 973-1073 K. To the author's knowledge, no data on this parameter has been published yet. Three different electrochemical methods have been tested: the cyclic voltammetry technique, the coulometric additions method and the direct use of an Al-Nd alloy. In addition, an experimental set-up has been designed which allows working with small amounts of solvent (30 g). The molten eutectic mixture CaCl{sub 2}-NaCl (52-48 mol%) has been selected as the electrolyte. From the results obtained, the variation of the activity coefficient of Nd in Al(l) as a function of the temperature can be expressed as follows: log {gamma}{sub Nd(Al)} = 9.81 - 17134/T(K), in the range 973-1073 K. It has been found a good agreement between the activity coefficient values obtained from the different methods tested. Hence, it can be stated that either of the techniques used allows determining reliable values for the activity coefficient.
Energy method for Stability of 1st Order CE with Variable Coefficients
LIU Ming
2011-01-01
It is well known that the Convection--diffusion e- quations arise in the fields of fluid mechanics and has been con- sidered extensively. The solving for these initial boundary value problems includes upwind difference scheme, Las- Friedrichs and Lax-- Wendroff difference schemes etc.. Methods such as Matrix method, the Hirt Heuristic Method and Fourier Method can be used to research the stability of the difference schemes. In the paper, using the 1st order convection equation（CE） with var- iable- coefficients as an example, the author gets the corre- sponding Lax--Wendroff difference scheme first, then Energy Method has been used to analyze the stability of the scheme.
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method
1989-08-01
jACCESSION NO. 11. TITLE (Include Security Classification) (UNCLASSIFIED) ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS FOR THE TRANSFER MATRIX METHOD 12...SECURITY CLASSIFICATION OF THIS PAGE AFIT/CI "OVERPRINT" iii ABSTRACT Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method. (August...analysts in indus- try . ’ . ," Accesiu:, For NTIS CR,4i Fi FilC TA,: [3 0. fi A-1 B I ., ,.................. ,., ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS
Hongwu Zhang
2011-08-01
Full Text Available In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.
Application of Exp-function method for nonlinear evolution equations with variable coefficients
El-Wakil, S.A.; Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Faculty of Education for Girls, Physics Department, King Kahlid University, Bisha, Kingdom Saudi Arabia (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com
2007-09-10
In this Letter, the Exp-function method with the aid of symbolic computational system Maple is used to obtain generalized solitary solutions and periodic solutions of a generalized Zakharov-Kuznetsov equation with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.
A New Variable-Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations
Fanwei Meng
2013-01-01
Full Text Available We propose a new variable-coefficient Riccati subequation method to establish new exact solutions for nonlinear differential-difference equations. For illustrating the validity of this method, we apply it to the discrete (2 + 1-dimensional Toda lattice equation. As a result, some new and generalized traveling wave solutions including hyperbolic function solutions, trigonometric function solutions, and rational function solutions are obtained.
无
2011-01-01
[Objective] The aim was to study the driving forces of rocky desertification in Guizhou Province. [Method] Based on GIS and RS technology, the main driving forces of rocky desertification in Guizhou Province were analyzed by means of correlation analysis and variation coefficient method, and then the distribution of rocky desertification in Guizhou Province was assessed synthetically. [Result] The main driving forces of rocky desertification in Guizhou Province were vegetation cover, rainfall, peasant incom...
Finite Element Method for Analysis of Material Properties
Rauhe, Jens Christian
description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using...
Annotations on the virtual element method for second-order elliptic problems
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-03
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks (also free on the internet) are available. Eventually, this document is intended to evolve into a tutorial introduction to the VEM (but this is really a long-term goal).
Efficient Finite Element Methods for Transient Analysis of Shells.
1985-04-01
Triangular Shell Element with Improved Membrane Interpolation," Communications in Applied Numerical Methods , in press 1985. Results of this work were...in Applied Numerical Methods , to appear. G.R. Cowper, G.M. Lindberg and M.D. Olson (1970), "A Shallow Shell Finite Element of Triangular Shape," Int. J
SPECTRAL FINITE ELEMENT METHOD FOR A UNSTEADY TRANSPORT EQUATION
MeiLiquan
1999-01-01
In this paper,a new numerical method,the coupling method of spherical harmonic function spectral and finite elements,for a unsteady transport equation is dlscussed,and the error analysis of this scheme is proved.
Ganta, D.; Dale, E. B.; Rezac, J. P.; Rosenberger, A. T.
2011-08-01
A novel optical method has been developed for the measurement of thermal accommodation coefficients in the temperature-jump regime. The temperature dependence of the resonant frequency of a fused-silica microresonator's whispering-gallery mode is used to measure the rate at which the microresonator comes into thermal equilibrium with the ambient gas. The thermal relaxation time is related to the thermal conductivity of the gas under some simplifying assumptions and measuring this time as a function of gas pressure determines the thermal accommodation coefficient. Using a low-power tunable diode laser of wavelength around 1570 nm to probe a microsphere's whispering-gallery mode through tapered-fiber coupling, we have measured the accommodation coefficients of air, helium, and nitrogen on fused silica at room temperature. In addition, by applying thin-film coatings to the microsphere's surface, we have demonstrated that accommodation coefficients can be measured for various gases on a wide range of modified surfaces using this method.
A method for the determination of the coefficient of rolling friction using cycloidal pendulum
Ciornei, M. C.; Alaci, S.; Ciornei, F. C.; Romanu, I. C.
2017-08-01
The paper presents a method for experimental finding of coefficient of rolling friction appropriate for biomedical applications based on the theory of cycloidal pendulum. When a mobile circle rolls over a fixed straight line, the points from the circle describe trajectories called normal cycloids. To materialize this model, it is sufficient that a small region from boundary surfaces of a moving rigid body is spherical. Assuming pure rolling motion, the equation of motion of the cycloidal pendulum is obtained - an ordinary nonlinear differential equation. The experimental device is composed by two interconnected balls rolling over the material to be studied. The inertial characteristics of the pendulum can be adjusted via weights placed on a rod. A laser spot oscillates together to the pendulum and provides the amplitude of oscillations. After finding the experimental parameters necessary in differential equation of motion, it can be integrated using the Runge-Kutta of fourth order method. The equation was integrated for several materials and found values of rolling friction coefficients. Two main conclusions are drawn: the coefficient of rolling friction influenced significantly the amplitude of oscillation but the effect upon the period of oscillation is practically imperceptible. A methodology is proposed for finding the rolling friction coefficient and the pure rolling condition is verified.
Comparison of boundary element and finite element methods in spur gear root stress analysis
Sun, H.; Mavriplis, D.; Huston, R. L.; Oswald, F. B.
1989-01-01
The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.
Determination of contact parameters for discrete element method simulations of granular systems
无
2008-01-01
Both linear-spring-dashpot (LSD) and non-linear Hertzian-spring-dnshpot (HSD) contact models are commonly used for the calculation of contact forces in Discrete Element Method (DEM) simulations of granular systems.Despite the popularity of these models, determination of suitable values for the contact parameters of the simulated particles such as stiffness, damping coefficient, coefficient of restitution, and simulation time step,is not altogether obvious.In this work the relationships between these contact parameters for a model system where a particle impacts on a flat base are examined.Recommendations are made concerning the determination of these contact parameters for use in DEM simulations.
CONVERGENCE OF ADAPTIVE EDGE ELEMENT METHODS FOR THE 3D EDDY CURRENTS EQUATIONS
R.H.W. Hoppe; J. Sch(o)berl
2009-01-01
We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy cur-rents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.
Ovchintsev Mikhail Petrovich
2014-04-01
Full Text Available This paper considers the problem of optimal recovery of bounded analytic functions. Namely, the values of these functions are determined at the point from their values at n given points lying in the unit circle. At first, we recall the necessary basic concepts: error of approximation by some method (which is a complex function of n complex variables, the best approximation method. Some theorems from the works of K.U. Osipenko are discussed: on the existence of a best linear approximation method and on calculating the error of best recovery method. After that we write out the formula for finding the error of best approximation method of bounded analytic functions in a unit circle. The lemma of conformal invariance of optimal recovery problem of these functions follows. We prove that under conformal mapping of the unit circle onto itself the error of the best approximation method before mapping coincides with the error of the best approximation method after mapping. It is also proved that a linear best method after conformal mapping coincides with the linear best restore method before this mapping (wherein the problem of optimal recovery after mapping is considered on the images of n given points lying in the original unit circle. Finally, we consider the problem of optimal recovery of bounded analytic functions in a circle in special case when the given points coincide with the vertices of a regular n-gon, and the point itself coincides with its center (which coincides with the origin. We prove that all the coefficients of the best linear method in this case are identical (wherein we apply the lemma of conformal invariance of optimal recovery problem of bounded analytic functions. The formulas for calculating these coefficients are given (for this purpose we write out an integral. The result is the smart, simple formulas for calculating the coefficients of the best linear approximation method for this particular case.
Equivariant preconditioners for boundary element methods
Tausch, J. [Colorado State Univ., Fort Collins, CO (United States)
1994-12-31
In this paper the author proposes and discusses two preconditioners for boundary integral equations on domains which are nearly symmetric. The preconditioners under consideration are equivariant, that is, they commute with a group of permutation matrices. Numerical experiments demonstrate their efficiency for the GMRES method.
Transforming Mean and Osculating Elements Using Numerical Methods
Ely, Todd A.
2010-01-01
Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order
A multigrid solution method for mixed hybrid finite elements
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
QIU Daohong
2014-08-01
Full Text Available Collapse is one of the most common accidents in underground constructions. Risk evaluation is the method of measuring the risk of chamber collapse. To ensure the safety of construction, a risk evaluation model of tunnel collapse based on an efficacy coefficient method and geological prediction was put forward. Based on the comprehensive analysis of collapse factors, five main factors including rock uniaxial compressive strength, surrounding rock integrated coefficient, state of discontinuous structural planes, the angle between tunnel axis and major structural plane and underground water were chosen as the risk evaluation indices of tunnel collapse. The evaluation indices were quantitatively described by using TSP203 system and core-drilling to establish the risk early warning model of tunnel collapse based on the basic principle of the efficacy coefficient method. The model established in this research was applied in the collapse risk recognition of Kiaochow Bay subsea tunnel in Qingdao, China. The results showed that the collapse risk recognition method presents higher prediction accuracy and provided a new idea for the risk prediction of tunnel collapse.
Kumar, Sudhir; Srinivasan, P; Sharma, S D
2010-06-01
A cylindrical graphite ionization chamber of sensitive volume 1002.4 cm(3) was designed and fabricated at Bhabha Atomic Research Centre (BARC) for use as a reference dosimeter to measure the strength of high dose rate (HDR) (192)Ir brachytherapy sources. The air kerma calibration coefficient (N(K)) of this ionization chamber was estimated analytically using Burlin general cavity theory and by the Monte Carlo method. In the analytical method, calibration coefficients were calculated for each spectral line of an HDR (192)Ir source and the weighted mean was taken as N(K). In the Monte Carlo method, the geometry of the measurement setup and physics related input data of the HDR (192)Ir source and the surrounding material were simulated using the Monte Carlo N-particle code. The total photon energy fluence was used to arrive at the reference air kerma rate (RAKR) using mass energy absorption coefficients. The energy deposition rates were used to simulate the value of charge rate in the ionization chamber and N(K) was determined. The Monte Carlo calculated N(K) agreed within 1.77 % of that obtained using the analytical method. The experimentally determined RAKR of HDR (192)Ir sources, using this reference ionization chamber by applying the analytically estimated N(K), was found to be in agreement with the vendor quoted RAKR within 1.43%.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
A finite-volume numerical method to calculate fluid forces and rotordynamic coefficients in seals
Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.
1992-01-01
A numerical method to calculate rotordynamic coefficients of seals is presented. The flow in a seal is solved by using a finite-volume formulation of the full Navier-Stokes equations with appropriate turbulence models. The seal rotor is perturbed along a diameter such that the position of the rotor is a sinusoidal function of time. The resulting flow domain changes with time, and the time-dependent flow in the seal is solved using a space conserving moving grid formulation. The time-varying fluid pressure reaction forces are then linked with the rotor center displacement, velocity and acceleration to yield the rotordynamic coefficients. Results for an annular seal are presented, and compared with experimental data and other more simplified numerical methods.
A. A. Pozhalostin
2015-01-01
Full Text Available The paper considers a problem of small axisymmetric oscillations of two-layer liquid with a foam-based separator. The separator is supposed to be rigid and non-deformable, liquid flow through the separator is modeled as a stream with a certain linear-viscous resistance. The liquid is assumed to be ideal and incompressible, its stream being potential. The paper presents experimental and analytical method for finding such a drag coefficient.The work [1] considered the problem of oscillations of a two-layer liquid divided by nondeforming permeable separator where, taking into consideration the interaction between liquid and separator, a reduced drag coefficient is introduced, which is expected to be determined experimentally, thereby generalizing the results of works [4] and [5] in case of moving two-layer liquid through a resistance. The work [6] investigated the motion of ideal incompressible and non-stratified liquid together with the elastic bottom. The work [7] studied a stability of the free liquid surface in low gravity. The paper [8] examined free axially symmetric oscillations of a two-layer liquid with an impermeable separator.Analytical dependence for the drag coefficient obtained in the paper [1] contains the frequency values of free harmonic oscillation system with no resistance (with a missing delimiter and the damping coefficient for the system with resistance (with a separator available. These values can be obtained experimentally if the tank model oscillations with a separator and without it are excited and the natural frequencies of these oscillations are determined. The model under consideration can be used to analyze dynamic interaction between liquid and phase separator of the upper stage or launch vehicle stage and provide ground experimental method for the starting systems from the gravity-free state and low gravity one.The article shows the relationship of the analytic dependence of the damping coefficient at symmetric
ClogP(alk): a method for predicting alkane/water partition coefficient.
Kenny, Peter W; Montanari, Carlos A; Prokopczyk, Igor M
2013-05-01
Alkane/water partition coefficients (P(alk)) are less familiar to the molecular design community than their 1-octanol/water equivalents and access to both data and prediction tools is much more limited. A method for predicting alkane/water partition coefficient from molecular structure is introduced. The basis for the ClogP(alk) model is the strong (R² = 0.987) relationship between alkane/water partition coefficient and molecular surface area (MSA) that was observed for saturated hydrocarbons. The model treats a molecule as a perturbation of a saturated hydrocarbon molecule with the same MSA and uses increments defined for functional groups to quantify the extent to which logP(alk) is perturbed by the introduction each functional group. Interactions between functional groups, such as intramolecular hydrogen bonds are also parameterized within a perturbation framework. The functional groups and interactions between them are specified substructurally in a transparent and reproducible manner using SMARTS notation. The ClogP(alk) model was parameterized using data measured for structurally prototypical compounds that dominate the literature on alkane/water partition coefficients and then validated using an external test set of 100 alkane/water logP measurements, the majority of which were for drugs.
Ji-ting Qu
2013-01-01
Full Text Available A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.
Hesameddini, Esmail; Rahimi, Azam
2015-05-01
In this article, we propose a new approach for solving fractional partial differential equations with variable coefficients, which is very effective and can also be applied to other types of differential equations. The main advantage of the method lies in its flexibility for obtaining the approximate solutions of time fractional and space fractional equations. The fractional derivatives are described based on the Caputo sense. Our method contains an iterative formula that can provide rapidly convergent successive approximations of the exact solution if such a closed form solution exists. Several examples are given, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.
无
2000-01-01
@@1 INTRODUCTION Due to its short experimental time, little sample needed, suitable for broad temperature range, inverse gas chromatography (IGC) has been widely used to measure variety of properties of polymer systems, such as the intinite diluted activity coefficients of solvent in polymer, the glass transition temperature of polymer and the surface properties of polymer[1-5], etc. Those data have been used to develop the group contribution method for the prediction of thermodynamic proper-ties of polymer solution[6].
Effects of Linear Induction Motor Parameters in Its Optimum Design Based on Finite Element Method
Mehrdad JafarBoland; AbdolAmir Nekoubin
2009-01-01
Effective parameters in performance of linear induction motors such as air gap, number of poles and the thickness of secondary must be selected and optimized to increase power coefficients and motor performance significantly. In this paper a double sided linear induction motor in different conditions is designed and next by finite element method analyzed. Then for comparing analytical model and numerical model a linear motor using Matlab software is simulated in different condition. It is cle...
Method for Calculating the Optical Diffuse Reflection Coefficient for the Ocular Fundus
Lisenko, S. A.; Kugeiko, M. M.
2016-07-01
We have developed a method for calculating the optical diffuse reflection coefficient for the ocular fundus, taking into account multiple scattering of light in its layers (retina, epithelium, choroid) and multiple refl ection of light between layers. The method is based on the formulas for optical "combination" of the layers of the medium, in which the optical parameters of the layers (absorption and scattering coefficients) are replaced by some effective values, different for cases of directional and diffuse illumination of the layer. Coefficients relating the effective optical parameters of the layers and the actual values were established based on the results of a Monte Carlo numerical simulation of radiation transport in the medium. We estimate the uncertainties in retrieval of the structural and morphological parameters for the fundus from its diffuse reflectance spectrum using our method. We show that the simulated spectra correspond to the experimental data and that the estimates of the fundus parameters obtained as a result of solving the inverse problem are reasonable.
Element Free Lattice Boltzmann Method for Fluid-Flow Problems
Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)
2007-10-15
The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.
Walker, E.; Glover, P. W. J.; Ruel, J.
2014-02-01
High-quality streaming potential coupling coefficient measurements have been carried out using a newly designed cell with both a steady state methodology and a new pressure transient approach. The pressure transient approach has shown itself to be particularly good at providing high-quality streaming potential coefficient measurements as each transient increase or decrease allows thousands of measurements to be made at different pressures to which a good linear regression can be fitted. Nevertheless, the transient method can be up to 5 times as fast as the conventional measurement approaches because data from all flow rates are taken in the same transient measurement rather than separately. Test measurements have been made on samples of Berea and Boise sandstone as a function of salinity (approximately 18 salinities between 10-5 mol/dm3 and 2 mol/dm3). The data have also been inverted to obtain the zeta potential. The streaming potential coefficient becomes greater (more negative) for fluids with lower salinities, which is consistent with existing measurements. Our measurements are also consistent with the high-salinity streaming potential coefficient measurements made by Vinogradov et al. (2010). Both the streaming potential coefficient and the zeta potential have also been modeled using the theoretical approach of Glover (2012). This modeling allows the microstructural, electrochemical, and fluid properties of the saturated rock to be taken into account in order to provide a relationship that is unique to each particular rock sample. In all cases, we found that the experimental data were a good match to the theoretical model.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Axisymmetric nonconforming element method and its convergence analysis
陈万吉; 高岩
1997-01-01
By virtue of the weighted Sobolev space theory, three convergence tests of the axisymmetric non-conforming element method are established. They consist of the generalized patch test, the F-E-M test and a test which could be used conveniently, called the strong patch test (SPT). In the light of SPT, a class of axisymmetric nonconforming elements is established.
A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS
Tian-xiao Zhou; Xiao-ping Xie
2003-01-01
In this paper, a combined hybrid method is applied to finite element discretization ofplate bending problems. It is shown that the resultant schemes are stabilized, i.e., theconvergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this, two new series of plate elements are proposed.
Forward seismic modeling with the use of boundary element method
Xuejun, L.
1991-01-01
Boundary element method for wave equation boundary value problem involves three steps: the boundary value problem of wave equations is converted into the boundary value problem of Helmholtz's equations by performing the one-dimensional Fourier transform of time variable, the new boundary value problem is converted into an integral equation by using Green's formula; and the integral equation is solved using boundary element method, and the required numerical solution is obtained by using inverse Fourier transform. This paper analyzes the theoretical formulas and application of the method. This method can be applied to forward and inverse seismic problems. In solving integral equation using boundary element method, the adoption of interval truncation division results in less element knots, less internal storage, faster operation and more accurate computation.
Thermal Analysis of Thin Plates Using the Finite Element Method
Er, G. K.; Iu, V. P.; Liu, X. L.
2010-05-01
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.
Sterling, N C
2011-01-01
We present total and final-state resolved charge transfer (CT) rate coefficients for low-charge Ge, Se, Br, Kr, Rb, and Xe ions reacting with neutral hydrogen over the temperature range 10^2--10^6 K. Each of these elements has been detected in ionized astrophysical nebulae, particularly planetary nebulae. CT rate coefficients are a key ingredient for the ionization equilibrium solutions needed to determine total elemental abundances from those of the observed ions. A multi-channel Landau Zener approach was used to compute rate coefficients for projectile ions with charges q=2-5, and for singly-charged ions the Demkov approximation was utilized. Our results for five-times ionized species are lower limits, due to the incompleteness of level energies in the NIST database. In addition, we computed rate coefficients for charge transfer ionization reactions between the neutral species of the above six elements and ionized hydrogen. The resulting total and state-resolved CT rate coefficients are tabulated and availa...
Seo, Na Jin; Armstrong, Thomas J; Drinkaus, Philip
2009-01-01
This study compares two methods for estimating static friction coefficients for skin. In the first method, referred to as the 'tilt method', a hand supporting a flat object is tilted until the object slides. The friction coefficient is estimated as the tangent of the angle of the object at the slip. The second method estimates the friction coefficient as the pull force required to begin moving a flat object over the surface of the hand, divided by object weight. Both methods were used to estimate friction coefficients for 12 subjects and three materials (cardboard, aluminium, rubber) against a flat hand and against fingertips. No differences in static friction coefficients were found between the two methods, except for that of rubber, where friction coefficient was 11% greater for the tilt method. As with previous studies, the friction coefficients varied with contact force and contact area. Static friction coefficient data are needed for analysis and design of objects that are grasped or manipulated with the hand. The tilt method described in this study can easily be used by ergonomic practitioners to estimate static friction coefficients in the field in a timely manner.
Vahidi, B.; Ghaffarzadeh, N.; Hosseinian, S.H. [Dept. of Electrical Engineering, Amirkabir University of Technology, Tehran (Iran)
2010-09-15
In this paper a new method based on discrete wavelet transform and correlation coefficient is presented for digital differential protection. The algorithm includes offline and online operations. In offline operation, discrete wavelet transform is used to decompose typical three-phase differential currents for inrush current. Then an index is defined and computed. The index is based on the sum of the energy of detail coefficients at level 5 of three-phase differential currents at each half cycle. The online operation consists of capturing the three-phase differential currents using 10 kHz sampling rate, decomposing it by db1. Finally, the inrush current and internal fault is detected based on correlation coefficients of the computed index of pre-stored typical inrush current and a recorded indistinct signal. The effectiveness of the approach is tested using numerous inrush and internal fault currents. Simulations are used to confirm the aptness and the capability of the proposed method to discriminate inrush current from internal fault. (author)
Finite Element Method for Analysis of Material Properties
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...
Rate coefficients of open shell molecules and radicals: $R$-matrix method
JASMEET SINGH; K L BALUJA; GAGANDEEP LONGIANY
2017-05-01
The open shell molecules with even number of electrons have $\\pi^2$ or $\\pi^{2}_{g}$ ground-state electronic configuration. Several homonuclear diatomic molecules like $\\rm{O_2, S_2, B_2}$ have $\\pi^{2}_{g}$ ground state in the $D_{\\infty h}$ point group and heteronuclear diatomic radicals like PH, NH, SO have $\\pi^2$ ground state in the $C_{\\infty v}$ point group. We have computed and presented here the rate coefficient of these open shell molecules $\\rm{(O_2, S_2, B_2)}$ and radicals (PH, NH,SO) from the results of our previous studies using a well-established $\\it {ab-initio}$ formalism: the $R$-matrix method. The rate coefficients for elastic and electron-excited processes are studied over a wide electron temperature range.
Shiva, Amir Houshang; Teasdale, Peter R., E-mail: p.teasdale@griffith.edu.au; Bennett, William W.; Welsh, David T.
2015-08-12
A systematic comparison of the diffusion coefficients of cations (Al, Cd, Co, Cu, Mn, Ni, Pb, Zn) and oxyanions (Al, As, Mo, Sb, V, W) in open (ODL) and restricted (RDL) diffusive layers used by the DGT technique was undertaken. Diffusion coefficients were measured using both the diffusion cell (D{sub cell}) method at pH 4.00 and the DGT time-series (D{sub DGT}) method at pH 4.01 and 7.04 (pH 8.30 was used instead of 7.04 for Al) using the Chelex-Metsorb mixed binding layer. The performance of Chelex-Metsorb as a new DGT binding layer for Al uptake was also evaluated for the first time. Reasonable agreement was observed between D{sub cell} and D{sub DGT} measurements for both ODL and RDL, except for V and W. The ratios of D{sub cell}/D{sub DGT} for V of 0.44 and 0.39, and for W of 0.66 and 0.63 with ODL and RDL respectively, were much lower due to the formation of a high proportion of polyoxometalate species at the higher concentrations required with the D{sub cell} measurements. This is the first time that D values have been reported for several oxyanions using RDL. Except for Al at pH 8.30 with ODL, all D{sub DGT} measurements were retarded relative to diffusion coefficients in water (D{sub W}) for both diffusive hydrogels. Diffusion in RDL was further retarded compared with ODL, for all elements (0.66–0.78) with both methods. However, the degree of retardation observed changed for cations and anions at each pH. At pH 7.04 cations had a slightly higher D{sub DGT} and oxyanions had a slightly lower D{sub DGT} than at pH 4.01 for both ODL and RDL. It is proposed that this is due to partial formation of acrylic acid functional groups (pK{sub a} ≈4.5), which would be fully deprotonated at pH 7.04 (negative) and mostly protonated at pH 4.01 (neutral). As Al changes from being cationic at pH 4.01 to anionic at pH 8.30 the results were more complex. - Highlights: • Determining elemental diffusion coefficients in open and restricted diffusive gels. • The DGT
Finite Element Model Updating Using Response Surface Method
Marwala, Tshilidzi
2007-01-01
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated parameters of the finite element model were calculated using genetic algorithm by optimizing the surface response equation. The proposed method was compared to the existing methods that use simulated annealing or genetic algorithm together with a full finite element model for finite element model updating. The proposed method was tested on an unsymmetri-cal H-shaped structure. It was observed that the proposed method gave the updated natural frequen-cies and mode shapes that were of the same order of accuracy as those given by simulated annealing and genetic algorithm. Furthermore, it was observed that the response surface method achieved these results at a computational speed that was more than 2.5 times as fast as the genetic algorithm and a full finite element model and 24 ti...
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Test-field method for mean-field coefficients with MHD background
Rheinhardt, M
2010-01-01
Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electr...
Experimental apparatus for measuring heat transfer coefficients by the Wilson plot method
Fernandez-Seara, Jose [Area de Maquinas y Motores Termicos, Escuela Superior de Ingenieros Industriales, Campus Lagoas-Marcosende, No 9, 36200 Vigo (Spain); UhIa, Francisco Jose [Area de Maquinas y Motores Termicos, Escuela Superior de Ingenieros Industriales, Campus Lagoas-Marcosende, No 9, 36200 Vigo (Spain); Sieres, Jaime [Area de Maquinas y Motores Termicos, Escuela Superior de Ingenieros Industriales, Campus Lagoas-Marcosende, No 9, 36200 Vigo (Spain); Campo, Antonio [Mechanical Engineering Department, University of Vermont, Burlington, VT 05405 (United States)
2005-05-01
The Wilson plot is a technique to estimate the film coefficients in several types of heat transfer processes and to obtain general heat transfer correlations. This method is an outstanding tool in practical applications and in laboratory research activities that involve analysis of heat exchangers. Moreover, the application of this method is simple enough to be taught in laboratory practices for students at university and doctoral level of physics and engineering. Therefore, an experimental apparatus has been designed and built in our laboratory that allows the students to carry out experiments based on the application of the Wilson plot method. In this note, the principles of the method are explained, the experimental apparatus is described and representative results of the experimental data taken from the apparatus and the application of the Wilson plot method are shown. (note)
Johannes E. Hunink
2017-02-01
Full Text Available The parameterization of crop coefficients (kc is critical for determining a water balance. We used satellite-based and literature-based methods to derive kc values for a distributed hydrologic model. We evaluated the impact of different kc parametrization methods on the water balance and simulated hydrologic response at the basin and sub-basin scale. The hydrological model SPHY was calibrated and validated for a period of 15 years for the upper Segura basin (~2500 km2 in Spain, which is characterized by a wide range of terrain, soil, and ecosystem conditions. The model was then applied, using six kc parameterization methods, to determine their spatial and temporal impacts on actual evapotranspiration, streamflow, and soil moisture. The parameterization methods used include: (i Normalized Difference Vegetation Index (NDVI observations from MODIS; (ii seasonally-averaged NDVI patterns, cell-based and landuse-based; and (iii literature-based tabular values per land use type. The analysis shows that the influence of different kc parametrization methods on basin-level streamflow is relatively small and constant throughout the year, but it has a bigger effect on seasonal evapotranspiration and soil moisture. In the autumn especially, deviations can go up to about 15% of monthly streamflow. At smaller, sub-basin scale, deviations from the NDVI-based reference run can be more than 30%. Overall, the study shows that modeling of future hydrological changes can be improved by using remote sensing information for the parameterization of crop coefficients.
Least-squares finite-element lattice Boltzmann method.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2004-06-01
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G.; Rogers, John A.; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2009-11-24
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G.; Rogers, John A.; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2017-09-19
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G; Rogers, John A; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2013-05-14
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G [Champaign, IL; Rogers, John A [Champaign, IL; Menard, Etienne [Durham, NC; Lee, Keon Jae [Daejeon, KR; Khang, Dahl-Young [Urbana, IL; Sun, Yugang [Champaign, IL; Meitl, Matthew [Raleigh, NC; Zhu, Zhengtao [Urbana, IL
2011-07-19
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G [Champaign, IL; Rogers, John A [Champaign, IL; Menard, Etienne [Urbana, IL; Lee, Keon Jae [Savoy, IL; Khang, Dahl-Young [Urbana, IL; Sun, Yugang [Champaign, IL; Meitl, Matthew [Champaign, IL; Zhu, Zhengtao [Urbana, IL
2009-11-24
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G; Rogers, John A; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2014-03-04
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Experimental Optimization Methods for Multi-Element Airfoils
Landman, Drew; Britcher, Colin P.
1996-01-01
A modern three element airfoil model with a remotely activated flap was used to investigate optimum flap testing position using an automated optimization algorithm in wind tunnel tests. Detailed results for lift coefficient versus flap vertical and horizontal position are presented for two angles of attack: 8 and 14 degrees. An on-line first order optimizer is demonstrated which automatically seeks the optimum lift as a function of flap position. Future work with off-line optimization techniques is introduced and aerodynamic hysteresis effects due to flap movement with flow on are discussed.
Research of Stamp Forming Simulation Based on Finite Element Method
SU Xaio-ping; XU Lian
2008-01-01
We point out that the finite element method offers a greta functional improvement for analyzing the stamp forming process of an automobile panel. Using the finite element theory and the simulation method of sheet stamping forming, the element model of sheet forming is built based on software HyperMesh,and the simulation of the product's sheet forming process is analyzed based on software Dynaform. A series of simulation results are obtained. It is clear that the simulation results from the theoretical basis for the product's die design and are useful for selecting process parameters.
Hong-jun BAO
2011-03-01
Full Text Available A real-time channel flood forecast model was developed to simulate channel flow in plain rivers based on the dynamic wave theory. Taking into consideration channel shape differences along the channel, a roughness updating technique was developed using the Kalman filter method to update Manning’s roughness coefficient at each time step of the calculation processes. Channel shapes were simplified as rectangles, triangles, and parabolas, and the relationships between hydraulic radius and water depth were developed for plain rivers. Based on the relationship between the Froude number and the inertia terms of the momentum equation in the Saint-Venant equations, the relationship between Manning’s roughness coefficient and water depth was obtained. Using the channel of the Huaihe River from Wangjiaba to Lutaizi stations as a case, to test the performance and rationality of the present flood routing model, the original hydraulic model was compared with the developed model. Results show that the stage hydrographs calculated by the developed flood routing model with the updated Manning’s roughness coefficient have a good agreement with the observed stage hydrographs. This model performs better than the original hydraulic model.
Josué Imbert‐González
2014-08-01
Full Text Available La transferencia de calor incrementada por métodos pasivos se emplea en diversosintercambiadores de calor de alta efectividad. El objetivo del trabajo presentado fue la evaluación del estado de las investigaciones en el campo de la transferencia de calor mejorada en espacios anulares, a partir del empleo de elementos turbulizadores helicoidales como técnicas pasivas. La revisión se centró en el empleo de láminas helicoidales y espirales, la obtención de ecuaciones de correlación del coeficiente de transferencia de calor incrementado, el coeficiente de fricción y la evaluación que se realiza de este proceso por parte de diferentes autores. El análisis crítico permitió realizar valoraciones integradas y recomendar sobre los aspectos que podrían ser analizados en el futuro en esta temática.Palabras claves: transferencia de calor incrementada, láminas helicoidales, espirales, espacios anulares, métodos pasivos._______________________________________________________________________________AbstractThe transfer enhancement by passive methods is used in several heat exchanger of high effectiveness. The objective of the presented work was the evaluation of the state of the investigations in heat transfer enhancement in annular spaces, from the employment of elements helical. The revision was centered in the employment of twisted tape and wire coil in spiral, the equations of correlation obtained of the coefficient of transfer of increased heat, the coefficient of friction and the evaluation that was carried out of this process on the part of different authors. From the critical analysis of the published results, the authors recommend on the topics that can be analyzed in the future in this area.Key words: heat transfer enhancement, twisted tape, helical springs, annular spaces, passive methods.
Streamline upwind finite element method for conjugate heat transfer problems
Niphon Wansophark; Atipong Malatip; Pramote Dechaumphai; Yunming Chen
2005-01-01
This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components,the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.
Shiva, Amir Houshang; Teasdale, Peter R; Bennett, William W; Welsh, David T
2015-08-12
A systematic comparison of the diffusion coefficients of cations (Al, Cd, Co, Cu, Mn, Ni, Pb, Zn) and oxyanions (Al, As, Mo, Sb, V, W) in open (ODL) and restricted (RDL) diffusive layers used by the DGT technique was undertaken. Diffusion coefficients were measured using both the diffusion cell (Dcell) method at pH 4.00 and the DGT time-series (D(DGT)) method at pH 4.01 and 7.04 (pH 8.30 was used instead of 7.04 for Al) using the Chelex-Metsorb mixed binding layer. The performance of Chelex-Metsorb as a new DGT binding layer for Al uptake was also evaluated for the first time. Reasonable agreement was observed between D(cell) and D(DGT) measurements for both ODL and RDL, except for V and W. The ratios of D(cell)/D(DGT) for V of 0.44 and 0.39, and for W of 0.66 and 0.63 with ODL and RDL respectively, were much lower due to the formation of a high proportion of polyoxometalate species at the higher concentrations required with the D(cell) measurements. This is the first time that D values have been reported for several oxyanions using RDL. Except for Al at pH 8.30 with ODL, all D(DGT) measurements were retarded relative to diffusion coefficients in water (DW) for both diffusive hydrogels. Diffusion in RDL was further retarded compared with ODL, for all elements (0.66-0.78) with both methods. However, the degree of retardation observed changed for cations and anions at each pH. At pH 7.04 cations had a slightly higher D(DGT) and oxyanions had a slightly lower D(DGT) than at pH 4.01 for both ODL and RDL. It is proposed that this is due to partial formation of acrylic acid functional groups (pKa ≈4.5), which would be fully deprotonated at pH 7.04 (negative) and mostly protonated at pH 4.01 (neutral). As Al changes from being cationic at pH 4.01 to anionic at pH 8.30 the results were more complex.
From the Index Numers’ Method to the Method Of Coefficient Of Elasticity
Gheorghe Săvoiu
2013-08-01
Full Text Available Using the simple method of index numbers, and synthesizing the originality of his excellent statistical thinking by definition, this article identifies and presents an inimitable shortcut from Index – Numbers’ method to elasticity method. A final remark underlines the beauty and the rigour of this scientific demarche specific for the statistical thinking. This paper is a real homage addressed to Professor M. C. Demetrescu, and to his remarkable PhD thesis, printed approximately half a century ago, one of the best statistic and economic book about population demand.
Sarakorn, Weerachai
2017-04-01
In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.
Aydin, E. D.; Katsimichas, S.; de Oliveira, C. R. E.
2005-10-01
In this paper, the finite-element-spherical harmonics (FE-PN) method is applied to the solution of transient Boltzmann transport equation. Firstly, transport and diffusion calculations are obtained for homogeneous and inhomogeneous circular regions. Results are compared in order to show the effects of different absorption coefficient values on the propagation of photons. Significant differences between two theories are shown to occur especially in cases when the absorption is increased. Secondly, to validate the FE-PN method, results from this method are compared with Monte Carlo calculations for different cases. Comparisons show good agreements between FE-transport and Monte Carlo solutions and demonstrate the correctness of the results obtained.
Righter, K.; Pando, K.; Danielson, L. R.; Humayun, M.; Righter, M.; Lapen, T.; Boujibar, A.
2016-01-01
Earth's core contains approximately 10 percent light elements that are likely a combination of S, C, Si, and O, with Si possibly being the most abundant. Si dissolved into Fe liquids can have a large effect on the magnitude of the activity coefficient of siderophile elements (SE) in Fe liquids, and thus the partitioning behavior of those elements between core and mantle. The effect of Si can be small such as for Ni and Co, or large such as for Mo, Ge, Sb, As. The effect of Si on many siderophile elements is unknown yet could be an important, and as yet unquantified, influence on the core-mantle partitioning of SE. Here we report new experiments designed to quantify the effect of Si on the partitioning of P, Au, Pd, and many other SE between metal and silicate melt. The results will be applied to Earth, for which we have excellent constraints on the mantle siderophile element concentrations.
The Matrix Element Method at Next-to-Leading Order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-01-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...
Impact of post-processing methods on apparent diffusion coefficient values.
Zeilinger, Martin Georg; Lell, Michael; Baltzer, Pascal Andreas Thomas; Dörfler, Arnd; Uder, Michael; Dietzel, Matthias
2017-03-01
The apparent diffusion coefficient (ADC) is increasingly used as a quantitative biomarker in oncological imaging. ADC calculation is based on raw diffusion-weighted imaging (DWI) data, and multiple post-processing methods (PPMs) have been proposed for this purpose. We investigated whether PPM has an impact on final ADC values. Sixty-five lesions scanned with a standardized whole-body DWI-protocol at 3 T served as input data (EPI-DWI, b-values: 50, 400 and 800 s/mm(2)). Using exactly the same ROI coordinates, four different PPM (ADC_1-ADC_4) were executed to calculate corresponding ADC values, given as [10(-3) mm(2)/s] of each lesion. Statistical analysis was performed to intra-individually compare ADC values stratified by PPM (Wilcoxon signed-rank tests: α = 1 %; descriptive statistics; relative difference/∆; coefficient of variation/CV). Stratified by PPM, mean ADCs ranged from 1.136-1.206 *10(-3) mm(2)/s (∆ = 7.0 %). Variances between PPM were pronounced in the upper range of ADC values (maximum: 2.540-2.763 10(-3) mm(2)/s, ∆ = 8 %). Pairwise comparisons identified significant differences between all PPM (P ≤ 0.003; mean CV = 7.2 %) and reached 0.137 *10(-3) mm(2)/s within the 25th-75th percentile. Altering the PPM had a significant impact on the ADC value. This should be considered if ADC values from different post-processing methods are compared in patient studies. • Post-processing methods significantly influenced ADC values. • The mean coefficient of ADC variation due to PPM was 7.2 %. • To achieve reproducible ADC values, standardization of post-processing is recommended.
A Simple Method for Determining the Temperature Coefficient of Voltaic Cell Voltage
Saieed, Alfred E.; Davies, Keith M.
1996-10-01
Although use of the Nernst equation to illustrate the dependence of cell potential on half-cell concentrations is routinely covered in first-year college chemistry and high school AP chemistry classes, the temperature dependence of cell voltages is rarely encountered outside of the undergraduate physical chemistry laboratory. Even there, its coverage is somewhat limited because of the cost and sophistication of the instrumentation required. This article describes a relatively simple method for preparing voltaic cells, and through their temperature coefficient, _Eo/_T, it explores relationships between DeltaGo, DeltaHo and DeltaSo for the cell reactions involved.
Optimization of method a load cell calibration for the measurement of coefficient of friction
Castro, R. M.; Pereira, M.; Sousa, A. R.; Curi, E. I. M.; Izidoro, C. L.; Correa, L. C.
2016-07-01
The instrumentation of equipment for mechanical testing is used to optimize the time to deliver a result, besides minimizing errors associated with manual measurements. Given this context, this work aims to present a calibration method for a load cell to determine the measurement results of force and friction coefficient, developed from on rotary pin-on-disk tribometer. The results indicate that the procedure provides measurements reliable for the tribological phenomena, resulting in with proximity the values provided by the ASTM G99-04.
The matrix element method at next-to-leading order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-11-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory, for electro-weak final states. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of unweighted next-to-leading order events. As examples of the application of our next-to-leading order matrix element method we consider the measurement of the mass of the Z boson and also the search for the Higgs boson in the four lepton channel.
A multigrid method for variable coefficient Maxwell's equations
Jones, J E; Lee, B
2004-05-13
This paper presents a multigrid method for solving variable coefficient Maxwell's equations. The novelty in this method is the use of interpolation operators that do not produce multilevel commutativity complexes that lead to multilevel exactness. Rather, the effects of multilevel exactness are built into the level equations themselves--on the finest level using a discrete T-V formulation, and on the coarser grids through the Galerkin coarsening procedure of a T-V formulation. These built-in structures permit the levelwise use of an effective hybrid smoother on the curl-free near-nullspace components, and these structures permit the development of interpolation operators for handling the curl-free and divergence-free error components separately, with the resulting block diagonal interpolation operator not satisfying multilevel commutativity but having good approximation properties for both of these error components. Applying operator-dependent interpolation for each of these error components leads to an effective multigrid scheme for variable coefficient Maxwell's equations, where multilevel commutativity-based methods can degrade. Numerical results are presented to verify the effectiveness of this new scheme.
Kuo, Frances
2016-01-05
In this talk I will provide a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. Such PDE problems occur in the area of uncertainty quantification. In recent years many papers have been written on this topic using a variety of methods. QMC methods are relatively new to this application area. I will consider different models for the randomness (uniform versus lognormal) and contrast different QMC algorithms (single-level versus multilevel, first order versus higher order, deterministic versus randomized). I will give a summary of the QMC error analysis and proof techniques in a unified view, and provide a practical guide to the software for constructing QMC points tailored to the PDE problems.
Hano, Mitsuo; Hotta, Masashi
A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.
Modelling of Granular Materials Using the Discrete Element Method
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression...... of the grains. This is true even of the resilient (or reversible) deformations. It is also interesting because the Discrete Element Method models resilient and plastic deformations as well as failure in a single process.The paper describes two types of calculations. One on a small sample of angular elements...... subjected to a pulsating (repeated) biaxial loading and another of a larger sample of circular element subjected to a plate load. Both cases are two dimensional, i.e. plane strain.The repeated biaxial loading showed a large increase in plastic strain for the first load pulse at a given load level...
Experimental validation of boundary element methods for noise prediction
Seybert, A. F.; Oswald, Fred B.
1992-01-01
Experimental validation of methods to predict radiated noise is presented. A combined finite element and boundary element model was used to predict the vibration and noise of a rectangular box excited by a mechanical shaker. The predicted noise was compared to sound power measured by the acoustic intensity method. Inaccuracies in the finite element model shifted the resonance frequencies by about 5 percent. The predicted and measured sound power levels agree within about 2.5 dB. In a second experiment, measured vibration data was used with a boundary element model to predict noise radiation from the top of an operating gearbox. The predicted and measured sound power for the gearbox agree within about 3 dB.
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
Wheeler, Mary F.
2011-01-01
In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...3-D steady-state seepage analysis of permeability of the cutoff walls was varied from 10 to Cerrillos Dam near Ponce , Puerto Rico, for the U.S.-6 10...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element
The Mortar Element Method with Lagrange Multipliers for Stokes Problem
Yaqin Jiang
2007-01-01
In this paper, we propose a mortar element method with Lagrange multiplier for incompressible Stokes problem, i.e., the matching constraints of velocity on mortar edges are expressed in terms of Lagrange multipliers. We also present P1 nonconforming element attached to the subdomains. By proving inf-sup condition, we derive optimal error estimates for velocity and pressure. Moreover, we obtain satisfactory approximation for normal derivatives of the velocity across the interfaces.
Symmetric Matrix Fields in the Finite Element Method
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Multimineral optimization processing method based on elemental capture spectroscopy logging
Feng Zhou; Li Xin-Tong; Wu Hong-Liang; Xia Shou-Ji; Liu Ying-Ming
2014-01-01
Calculating the mineral composition is a critical task in log interpretation. Elemental capture spectroscopy (ECS) log provides the weight percentages of twelve common elements, which lays the foundation for the accurate calculation of mineral compositions. Previous processing methods calculated the formation composition via the conversion relation between the formation chemistry and minerals. Thus, their applicability is limited and the method precision is relatively low. In this study, we present a multimineral optimization processing method based on the ECS log. We derived the ECS response equations for calculating the formation composition, then, determined the logging response values for the elements of common minerals using core data and theoretical calculations. Finally, a software module was developed. The results of the new method are consistent with core data and the mean absolute error is less than 10%.
INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD
郭书祥; 吕震宙
2001-01-01
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters,median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
NURBS-enhanced finite element method for Euler equations
Sevilla Cárdenas, Rubén; Fernandez Mendez, Sonia; Huerta, Antonio , coaut.
2008-01-01
This is the pre-peer reviewed version of the following article: Sevilla, R.; Fernandez, S.; Huerta, A. NURBS-enhanced finite element method for Euler equations. "International journal for numerical methods in fluids", Juliol 2008, vol. 57, núm. 9, p. 1051-1069., which has been published in final form at http://www3.interscience.wiley.com/journal/117905455/abstract In this work, the NURBS-enhanced finite element method (NEFEM) is combined with a discontinuous Galerkin (DG) formulation for t...
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Nucleon matrix elements using the variational method in lattice QCD
Dragos, Jack; Kamleh, Waseem; Leinweber, Derek B; Nakamura, Yoshifumi; Rakow, Paul E L; Schierholz, Gerrit; Young, Ross D; Zanotti, James M
2016-01-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current $g_{A}$, the scalar current $g_{S}$ and the quark momentum fraction $\\left$ of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING
党发宁; 荣廷玉; 孙训方
2001-01-01
Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors,so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some illconditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.
The Finite Element Method An Introduction with Partial Differential Equations
Davies, A J
2011-01-01
The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is alsoexplained. This book is written at an introductory level, developing all the necessary concepts where required. Co
Identification of Molecular Laser Transitions Using the Finite Element Method
1995-12-01
Vibration Levels," Physical Review, Vol. 34, 1929 12 Arfken , George Mathematical Methods for Physicists. San Diego: Academic Press, Inc. 1985 13...unsolvable. Mathematical techniques such as the classical Rayleigh-Ritz method , variational calculus, and Galerkin’s weighted residuals method , much...AFIT/GAP/ENP/95D-14 IDENTIFICATION OF MOLECULAR LASER TRANSITIONS USING THE FINITE ELEMENT METHOD THESIS Matthew C. Smitham, Captain, USAF AFIT/GAP
A new photoacoustic method based on the modulation of the light induced absorption coefficient
Engel, S.; Wenisch, C.; Müller, F. A.; Gräf, S.
2016-04-01
The present study reports on a new photoacoustic (PA) measurement method that is suitable for the investigation of light induced absorption effects including e.g. excited state absorption. Contrary to the modulation of the radiation intensity used in conventional PA-methods, the key principle of this novel setup is based on the modulation of the induced absorption coefficient by light. For this purpose, a pump-probe setup with a pulsed pump laser beam and a continuous probe laser beam is utilized. In this regime, the potential influence of heat on the PA-signal is much smaller when compared to arrangements with pulsed probe beam and continuous pump beam. Beyond that, the negative effect of thermal lenses can be neglected. Thus, the measurement technique is well-suited for materials exhibiting a strong absorption at the pump wavelength. The quantitative analysis of the induced absorption coefficient was achieved by the calibration of the additional PA-signal caused by the continuous probe laser to the PA-signal resulting from the pulsed pump laser using thallium bromoiodide (KRS-5) as sample material.
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Instrumental methods for analysis of some elements in flour
Zagrodzki, P.; Dutkiewicz, E.M.; Malec, P. [Uniwersytet Jagiellonski, Cracow (Poland); Krosniak, M. [Akademia Medyczna, Cracow (Poland); Knap, W. [Akademia Gorniczo-Hutnicza, Cracow (Poland). Inst. Wiertniczo-Naftowy; Bichonski, A. [Instytut Hodowli i Aklimatyzacji Roslin, Radzikow (Poland)
1993-10-01
For ten various brands of flour contents of chosen (heavy) elements were determined by means of ICP, GF-AAS, PIXE and ASV/CSV methods. General performance of participating laboratories as well as pros and cons of different analytical methods were compared and discussed. (author). 6 refs, 6 figs, 7 tabs.
DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS
Abdellatif Agouzal
2000-01-01
A discontinuous finite element method for convection-diffusion equations is proposed and analyzed. This scheme is designed to produce an approximate solution which is completely discontinuous. Optimal order of convergence is obtained for model problem. This is the same convergence rate known for the classical methods.
Complex variable element-free Galerkin method for viscoelasticity problems
Cheng Yu-Min; Li Rong-Xin; Peng Miao-Juan
2012-01-01
Based on the complex variable moving least-square (CVMLS) approximation,the complex variable element-free Galerkin (CVEFG) method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper.The Galerkin weak form is employed to obtain the equation system,and the penalty method is used to apply the essential boundary conditions,then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin (EFG) method,with the same node distribution,the CVEFG method has higher precision,and to obtain the similar precision,the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.
A Variable Coefficient Method for Accurate Monte Carlo Simulation of Dynamic Asset Price
Li, Yiming; Hung, Chih-Young; Yu, Shao-Ming; Chiang, Su-Yun; Chiang, Yi-Hui; Cheng, Hui-Wen
2007-07-01
In this work, we propose an adaptive Monte Carlo (MC) simulation technique to compute the sample paths for the dynamical asset price. In contrast to conventional MC simulation with constant drift and volatility (μ,σ), our MC simulation is performed with variable coefficient methods for (μ,σ) in the solution scheme, where the explored dynamic asset pricing model starts from the formulation of geometric Brownian motion. With the method of simultaneously updated (μ,σ), more than 5,000 runs of MC simulation are performed to fulfills basic accuracy of the large-scale computation and suppresses statistical variance. Daily changes of stock market index in Taiwan and Japan are investigated and analyzed.
Pravir Dutt; Satyendra Tomar
2003-11-01
In this paper we show that the ℎ- spectral element method developed in [3,8,9] applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska–Brezzi inf-sup conditions are satisfied. We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are continuous only at the vertices of the elements. We obtain a stability estimate when the spectral element functions vanish at the vertices of the elements, which is needed for parallelizing the numerical scheme. Finally, we indicate how the mesh refinement strategy and choice of polynomial degree depends on the regularity of the coefficients of the differential operator, smoothness of the sides of the polygon and the regularity of the data to obtain the maximum accuracy achievable.
Certain Discrete Element Methods in Problems of Fracture Mechanics
P. P. Procházka
2002-01-01
Full Text Available In this paper two discrete element methods (DEM are discussed. The free hexagon element method is considered a powerful discrete element method, which is broadly used in mechanics of granular media. It substitutes the methods for solving continuum problems. The great disadvantage of classical DEM, such as the particle flow code (material properties are characterized by spring stiffness, is that they have to be fed with material properties provided from laboratory tests (Young's modulus, Poisson's ratio, etc.. The problem consists in the fact that the material properties of continuum methods (FEM, BEM are not mutually consistent with DEM. This is why we utilize the principal idea of DEM, but cover the continuum by hexagonal elastic, or elastic-plastic, elements. In order to complete the study, another one DEM is discussed. The second method starts with the classical particle flow code (PFC - which uses dynamic equilibrium, but applies static equilibrium. The second method is called the static particle flow code (SPFC. The numerical experience and comparison numerical with experimental results from scaled models are discussed in forthcoming paper by both authors.
Xi F. XU
2015-01-01
The Green-function-based multiscale stochastic finite element method （MSFEM） has been formulated based on the stochastic variational principle. In this study a fast computing procedure based on the MSFEM is developed to solve random field geotechnical problems with a typical coefficient of variance less than 1. A unique fast computing advantage of the procedure enables computation performed only on those locations of interest, therefore saving a lot of computation. The numerical example on soil settlement shows that the procedure achieves significant computing efficiency compared with Monte Carlo method.
Fernández-Oliveras, Alicia; Carrasco, Irene M.; Ghinea, Razvan; Pérez, María M.; Rubiño, Manuel
2012-06-01
Understanding the behaviour of light propagation in biological materials is essential for biomedical engineering and its applications. Among the key optical properties of biological media is the angular distribution of the scattered light, characterized by the average cosine of the scattering angle, called the scattering anisotropy coefficient (g). The value of g can be determined by experimentally irradiating the material with a laser beam and making angular-scattering measurements in a goniometer. In this work, an experimental technique was used to determine g by means of goniometric measurements of the laser light scattered off two different dental-resin composites (classified as nano and hybrid). To assess the accuracy of the experimental method, a Mie theory-based computational model was used. Independent measurements were used to determine some of the required input parameters for computation of the theoretical model. The g values estimated with the computational method (nano-filled: 0.9399; hybrid: 0.8975) and the values calculated with the experimental method presented (nano-filled: 0.98297 +/- 0.00021; hybrid: 0.95429 +/- 0.00014) agreed well for both dental resins, with slightly higher experimental values. The higher experimental values may indicate that the scattering particle causes more narrow-angle scattering than does a perfect sphere of equal volume, assuming that with more spherical scattering particles the scattering anisotropy coefficient increases. Since g represents the angular distribution of the scattered light, values provided by both the experimental and the computational methods show a strongly forward-directed scattering in the dental resins studied, more pronounced in the nano-filled composite than in the hybrid composite.
Scalable fast multipole methods for vortex element methods
Hu, Qi
2012-11-01
We use a particle-based method to simulate incompressible flows, where the Fast Multipole Method (FMM) is used to accelerate the calculation of particle interactions. The most time-consuming kernelsâ\\'the Biot-Savart equation and stretching term of the vorticity equationâ\\'are mathematically reformulated so that only two Laplace scalar potentials are used instead of six, while automatically ensuring divergence-free far-field computation. Based on this formulation, and on our previous work for a scalar heterogeneous FMM algorithm, we develop a new FMM-based vortex method capable of simulating general flows including turbulence on heterogeneous architectures, which distributes the work between multi-core CPUs and GPUs to best utilize the hardware resources and achieve excellent scalability. The algorithm also uses new data structures which can dynamically manage inter-node communication and load balance efficiently but with only a small parallel construction overhead. This algorithm can scale to large-sized clusters showing both strong and weak scalability. Careful error and timing trade-off analysis are also performed for the cutoff functions induced by the vortex particle method. Our implementation can perform one time step of the velocity+stretching for one billion particles on 32 nodes in 55.9 seconds, which yields 49.12 Tflop/s. © 2012 IEEE.
Tian, Zhen; Jia, Xun; Jiang, Steve B
2013-01-01
In the treatment plan optimization for intensity modulated radiation therapy (IMRT), dose-deposition coefficient (DDC) matrix is often pre-computed to parameterize the dose contribution to each voxel in the volume of interest from each beamlet of unit intensity. However, due to the limitation of computer memory and the requirement on computational efficiency, in practice matrix elements of small values are usually truncated, which inevitably compromises the quality of the resulting plan. A fixed-point iteration scheme has been applied in IMRT optimization to solve this problem, which has been reported to be effective and efficient based on the observations of the numerical experiments. In this paper, we aim to point out the mathematics behind this scheme and to answer the following three questions: 1) whether the fixed-point iteration algorithm converges or not? 2) when it converges, whether the fixed point solution is same as the original solution obtained with the complete DDC matrix? 3) if not the same, wh...
REN Zhongqi; FEI Weiyang; Hans-Joerg Bart
2005-01-01
The Taylor dispersion method was used to measure diffusion coefficients of three-component liquid systems. An improved constrained nonlinear least-square method was used to evaluate the ternary diffusion coefficients directly by fitting the mathematical solutions of the dispersion equation to eluted solute peaks detected using a differential refractometer. Diffusion coefficients of the three-component system of acetone-benzene-CCl4, determined at 25℃, were used to test the procedure. The measured diffusion coefficients were compared with values obtained by optical interferometry and the diaphragm cell method. Ternary diffusion coefficients are also determinated for solutions of 1-hexanol-hexane-toluene and 1-propanol-water-ethylene glycol at 25℃, with an accuracy of approximately 0.05 m2·s-1.
The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method
Zhibo Yang
2014-01-01
Full Text Available A B-spline wavelet on interval (BSWI finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.
A HIGH ORDER ADAPTIVE FINITE ELEMENT METHOD FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS
Zhengfu Xu; Jinchao Xu; Chi-Wang Shu
2011-01-01
In this note,we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations,with the objective of achieving high order accuracy and mesh efficiency.We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem.The computational results verify that,by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al.,an order of N-3/2 accuracy can be obtained when continuous piecewise linear elements are used,where N is the number of elements.
Maity, Haripada; Wei, Alex; Chen, Ethan; Haidar, Jaafar N; Srivastava, Arvind; Goldstein, Joel
2015-01-01
Pace et al. (1995) [1] recommended an equation used to predict extinction coefficient of a protein. However, no antibody data was included in the development of this equation. The main objective of this study was to therefore investigate how the predicted value of the extinction coefficient is comparable to the experimentally determined extinction coefficient of antibodies measured by the Edelhoch method. We have measured the extinction coefficients (ɛ) of 13 IgG1 monoclonal antibodies (mAbs) in phosphate buffer at pH 7.2. The maximum variability in the experimentally measured extinction coefficient of a given mAb molecule was found to be about 2%. Experimentally determined extinction coefficients of all mAbs were found to be lower than the predicted value, with the maximum difference found to being 4.7%. The highest and lowest values of experimental extinction coefficient among the thirteen IgG1 monoclonal antibodies obtained were 230525.9M(-1)cm(-1) (i.e. 1.55(mg/ml)(-1)cm(-1)) and 191,411.6M(-1)cm(-1) (i.e. 1.29(mg/ml)(-1)cm(-1)). A difference of experimental and predicted values of the extinction coefficient. A comprehensive analysis and interpretation of the comparison of the predicted and experimentally determined extinction coefficient by the Edelhoch method is discussed in terms of structural characterization and accessible surface area (ASA).
Bahman Navidshad
2012-02-01
Full Text Available The applications of conventional culture-dependent assays to quantify bacteria populations are limited by their dependence on the inconsistent success of the different culture-steps involved. In addition, some bacteria can be pathogenic or a source of endotoxins and pose a health risk to the researchers. Bacterial quantification based on the real-time PCR method can overcome the above-mentioned problems. However, the quantification of bacteria using this approach is commonly expressed as absolute quantities even though the composition of samples (like those of digesta can vary widely; thus, the final results may be affected if the samples are not properly homogenized, especially when multiple samples are to be pooled together before DNA extraction. The objective of this study was to determine the correlation coefficients between four different methods of expressing the output data of real-time PCR-based bacterial quantification. The four methods were: (i the common absolute method expressed as the cell number of specific bacteria per gram of digesta; (ii the Livak and Schmittgen, ΔΔCt method; (iii the Pfaffl equation; and (iv a simple relative method based on the ratio of cell number of specific bacteria to the total bacterial cells. Because of the effect on total bacteria population in the results obtained using ΔCt-based methods (ΔΔCt and Pfaffl, these methods lack the acceptable consistency to be used as valid and reliable methods in real-time PCR-based bacterial quantification studies. On the other hand, because of the variable compositions of digesta samples, a simple ratio of cell number of specific bacteria to the corresponding total bacterial cells of the same sample can be a more accurate method to quantify the population.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
(Environmental and geophysical modeling, fracture mechanics, and boundary element methods)
Gray, L.J.
1990-11-09
Technical discussions at the various sites visited centered on application of boundary integral methods for environmental modeling, seismic analysis, and computational fracture mechanics in composite and smart'' materials. The traveler also attended the International Association for Boundary Element Methods Conference at Rome, Italy. While many aspects of boundary element theory and applications were discussed in the papers, the dominant topic was the analysis and application of hypersingular equations. This has been the focus of recent work by the author, and thus the conference was highly relevant to research at ORNL.
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
The spectral-element method, Beowulf computing, and global seismology.
Komatitsch, Dimitri; Ritsema, Jeroen; Tromp, Jeroen
2002-11-29
The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines. This combination of hardware and software enables us to simulate broadband seismograms without intrinsic restrictions on the level of heterogeneity or the frequency content.
A stochastic method for computing hadronic matrix elements
Alexandrou, Constantia [University of Cyprus, Department of Physics, P.O. Box 20537, Nicosia (Cyprus); The Cyprus Institute, Computation-based Science and Technology Research Center, Nicosia (Cyprus); Constantinou, Martha; Hadjiyiannakou, Kyriakos [University of Cyprus, Department of Physics, P.O. Box 20537, Nicosia (Cyprus); Dinter, Simon; Drach, Vincent; Jansen, Karl [NIC, DESY Zeuthen, Zeuthen (Germany); Renner, Dru B. [NIC, DESY Zeuthen, Zeuthen (Germany); Jefferson Lab., Newport News (United States); Collaboration: ETM Collaboration
2014-01-15
We present a stochastic method for the calculation of baryon three-point functions that is more versatile than the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume, and we found a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements. (orig.)
Stress and Deformation Analysis in Base Isolation Elements Using the Finite Element Method
Claudiu Iavornic
2011-01-01
Full Text Available In Modern tools as Finite Element Method can be used to study the behavior of elastomeric isolation systems. The simulation results obtained in this way provide a large series of data about the behavior of elastomeric isolation bearings under different types of loads and help in taking right decisions regarding geometrical optimizations needed for improve such kind of devices.
Gudmundsson, K.; Prosperetti, A.
2013-02-01
The PHYSALIS method was designed for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solution with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. A novel test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle.
SUI Da-shan; CUI Zhen-shan
2007-01-01
The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly.The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data.This paper presented a new inverse method according to Tikhonov regularization theory.A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations.One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime.This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the illposedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results.As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Habib Ammari; Gang Bao
2008-01-01
Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Beck, Joakim
2014-03-01
In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.
A New Method for Determination of Joint Roughness Coefficient of Rock Joints
Shigui Du
2015-01-01
Full Text Available The joint roughness coefficient (JRC of rock joints has the characteristic of scale effect. JRC measured on small-size exposed rock joints should be evaluated by JRC scale effect in order to obtain the JRC of actual-scale rock joints, since field rock joints are hardly fully exposed or well saved. Based on the validity analysis of JRC scale effect, concepts of rate of JRC scale effect and effective length of JRC scale effect were proposed. Then, a graphic method for determination of the effective length of JRC scale effect was established. Study results show that the JRC of actual-scale rock joints can be obtained through a fractal model of JRC scale effect according to the statistically measured results of the JRC of small-size partial exposed rock joints and by the selection of fractal dimension of JRC scale effect and the determination of effective length of JRC scale effect.
Xintao Xia
2013-07-01
Full Text Available This study proposed the bootstrap maximum-entropy method to evaluate the uncertainty of the starting torque of a slewing bearing. Addressing the variation coefficient of the slewing bearing starting torque under load, the probability density function, estimated true value and variation domain are obtained through experimental investigation of the slewing bearing starting torque under various loads. The probability density function is found to be characterized by variational figure, scale and location. In addition, the estimated true value and the variation domain vary from large to small along with increasing load, indicating better evolution of the stability and reliability of the starting friction torque. Finally, a sensitive spot exists where the estimated true value and the variation domain rise abnormally, showing a fluctuation in the immunity and a degenerative disorder in the stability and reliability of the starting friction torque.
Ping Zhang
2016-01-01
Full Text Available Variational multiscale element free Galerkin (VMEFG method is applied to Burgers’ equation. It can be found that, for the very small diffusivity coefficients, VMEFG method still suffers from instability in the presence of boundary or interior layers. In order to overcome this problem, the high order low-pass filter is used to smooth the solution. Three test examples with very small diffusion are presented and the solutions obtained are compared with exact solutions and some other numerical methods. The numerical results are found in which the VMEFG coupled with low-pass filter works very well for Burgers’ equation with very small diffusivity coefficients.
A Practical Method to Estimate the Aerodynamic Coefficients of a Small-Scale Paramotor
Razvan-Viorel MIHAI
2014-12-01
Full Text Available There are few aircraft other than lighter-than-air vehicles that have the payload carrying capability, short field take-off, and slow speed ranges afforded by a powered parafoil. One very interesting aspect of the powered parafoils or paramotors, is their tendency to fly at a constant airspeed whether it is climbing, descending, or flying straight-and-level. Not only are the aircraft speed stable, but they have pendulum stability as well, due to the mass of the airframe suspended significantly below the canopy. This allows the aircraft to maintain a safe roll attitude and effectively turn in a coordinated manner when the steering pedals are deflected. One of the challenges of flying these aircraft is the necessity of controlling altitude with thrust, and direction with asymmetric drag. The paper presents a practical method to estimate the aerodynamic coefficients of a small-scale paramotor in order to obtain a suitable mathematical model for the aerial vehicle. Thus, a reduced state linear model based on a simplified nonlinear six degree-of-freedom model (6 DOF is described. The autonomous control relies on the paramotor dynamics. And those equations depend on the aerodynamic coefficients. The task in this paper is to record the data of steady state flight regime, and to process it offline. Therefore, the system identification of the small-scale aerial vehicle can be done using the Two-Step Method, resulting an efficient six degree-of-freedom mini-paramotor model. The current work will permit the implementation of the control architecture in order to achieve the autonomous control of the small-scale paramotor through waypoints.
Impact of post-processing methods on apparent diffusion coefficient values
Zeilinger, Martin Georg; Lell, Michael; Uder, Michael [University of Erlangen-Nuremberg, Institute of Diagnostic Radiology, Erlangen (Germany); Baltzer, Pascal Andreas Thomas [Medical University Vienna, Department of Radiology and Nuclear Medicine, Vienna (Austria); Doerfler, Arnd; Dietzel, Matthias [University of Erlangen-Nuremberg, Department of Neuroradiology, Erlangen (Germany)
2017-03-15
The apparent diffusion coefficient (ADC) is increasingly used as a quantitative biomarker in oncological imaging. ADC calculation is based on raw diffusion-weighted imaging (DWI) data, and multiple post-processing methods (PPMs) have been proposed for this purpose. We investigated whether PPM has an impact on final ADC values. Sixty-five lesions scanned with a standardized whole-body DWI-protocol at 3 T served as input data (EPI-DWI, b-values: 50, 400 and 800 s/mm{sup 2}). Using exactly the same ROI coordinates, four different PPM (ADC{sub 1}-ADC{sub 4}) were executed to calculate corresponding ADC values, given as [10{sup -3} mm{sup 2}/s] of each lesion. Statistical analysis was performed to intra-individually compare ADC values stratified by PPM (Wilcoxon signed-rank tests: α = 1 %; descriptive statistics; relative difference/∇; coefficient of variation/CV). Stratified by PPM, mean ADCs ranged from 1.136-1.206 *10{sup -3} mm{sup 2}/s (∇ = 7.0 %). Variances between PPM were pronounced in the upper range of ADC values (maximum: 2.540-2.763 10{sup -3} mm{sup 2}/s, ∇ = 8 %). Pairwise comparisons identified significant differences between all PPM (P ≤ 0.003; mean CV = 7.2 %) and reached 0.137 *10{sup -3} mm{sup 2}/s within the 25th-75th percentile. Altering the PPM had a significant impact on the ADC value. This should be considered if ADC values from different post-processing methods are compared in patient studies. (orig.)
Hoche, S; Hussein, M A; Becker, T
2015-03-01
The accuracy of density, reflection coefficient, and acoustic impedance determination via multiple reflection method was validated experimentally. The ternary system water-maltose-ethanol was used to execute a systematic, temperature dependent study over a wide range of densities and viscosities aiming an application as inline sensor in beverage industries. The validation results of the presented method and setup show root mean square errors of: 1.201E-3 g cm(-3) (±0.12%) density, 0.515E-3 (0.15%) reflection coefficient and 1.851E+3 kg s(-1) m(-2) (0.12%) specific acoustic impedance. The results of the diffraction corrected absorption showed an average standard deviation of only 0.12%. It was found that the absorption change shows a good correlation to concentration variations and may be useful for laboratory analysis of sufficiently pure liquids. The main part of the observed errors can be explained by the observed noise, temperature variation and the low signal resolution of 50 MHz. In particular, the poor signal-to-noise ratio of the second reflector echo was found to be a main accuracy limitation. Concerning the investigation of liquids the unstable properties of the reference material PMMA, due to hygroscopicity, were identified to be an additional, unpredictable source of uncertainty. While dimensional changes can be considered by adequate methodology, the impact of the time and temperature dependent water absorption on relevant reference properties like the buffer's sound velocity and density could not be considered and may explain part of the observed deviations.
Gudmundsson, Kristjan
2011-01-01
The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solutions with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significan...
Band structure of one-dimensional plasma photonic crystals using the Fresnel coefficients method
Jafari, A.; Rahmat, A.
2016-11-01
The current study has examined the band structures of two types of photonic crystals (PCs). The first is a one-dimensional metamaterial photonic crystal (1DMMPC) composed of double-layered units for which both layers of each unit are dielectric. The second type is a very similar one-dimensional plasma photonic crystal (1DPPC) also composed of double-layered units in which the first layer is a dielectric material but the second is a plasma layer. This study compares the band structures of the 1DMMPC with specific optical characteristics of the 1DPPC using the Fresnel coefficients method and also compares the results of this method with the results of the transfer matrix method. It is concluded that the dependency of the electric permittivity of the plasma layer on the incident field frequency causes differences in the band structures in 1DMMPC and 1DPPC for both TE and TM polarizations and their gaps reside in different frequencies. The band structures of the 1DMMPC and 1DPPC are confirmed by the results of the transfer matrix method.
Yamaikina, Irene V.; Furmanchuk, Dmitryi A.
1998-06-01
Method of erythrocyte sedimentation rate (ESR) measurement is non-specific one. The ESR are tightly correlated to increase or decrease of aggregation coefficient (N). The variations of N could happen due to two main reasons: either changes in concentration of plasma proteins (first of all of fibrinogen) or changes of erythrocyte membrane characteristics (surface charge, transmembrane potential). The cross-method of ESR analysis has been proposed, using blood samples from patient and healthy donor of the same ABO blood groups and Rh-factors. The hematocrit (Ho)-ESR dependencies were measured in four variants: (1) patient's erythrocytes in patient's plasma; (2) patient's erythrocytes in donor's plasma; (3) donor's erythrocytes in donor's plasma; (4) donor's erythrocytes in patient's plasma. On presenting the ESR data for more than 100 patients with different bone marrow disorders after chemotherapy in the coordinates Ho-ESR three conventional zones could be marked out: high-ESR zone, medium zone and zone of low level of Ho. Proposed cross-method allows to estimate which of the two aforementioned reasons results in ESR variation. Some patients revealed not only changed fibrinogen level but additional changes in membrane affinity to fibrinogen. The modificated ESR cross-method opens us some new capacities in medical diagnostics.
Application of least-squares spectral element solver methods to incompressible flow problems
Proot, M.M.J.; Gerritsma, M.I.; Nool, M.
2003-01-01
Least-squares spectral element methods are based on two important and successful numerical methods: spectral /hp element methods and least-squares finite element methods. In this respect, least-squares spectral element methods are very powerfull since they combine the generality of finite element me
An Adaptive WENO Collocation Method for Differential Equations with Random Coefficients
Wei Guo
2016-05-01
Full Text Available The stochastic collocation method for solving differential equations with random inputs has gained lots of popularity in many applications, since such a scheme exhibits exponential convergence with smooth solutions in the random space. However, in some circumstance the solutions do not fulfill the smoothness requirement; thus a direct application of the method will cause poor performance and slow convergence rate due to the well known Gibbs phenomenon. To address the issue, we propose an adaptive high-order multi-element stochastic collocation scheme by incorporating a WENO (Weighted Essentially non-oscillatory interpolation procedure and an adaptive mesh refinement (AMR strategy. The proposed multi-element stochastic collocation scheme requires only repetitive runs of an existing deterministic solver at each interpolation point, similar to the Monte Carlo method. Furthermore, the scheme takes advantage of robustness and the high-order nature of the WENO interpolation procedure, and efficacy and efficiency of the AMR strategy. When the proposed scheme is applied to stochastic problems with non-smooth solutions, the Gibbs phenomenon is mitigated by the WENO methodology in the random space, and the errors around discontinuities in the stochastic space are significantly reduced by the AMR strategy. The numerical experiments for some benchmark stochastic problems, such as the Kraichnan-Orszag problem and Burgers’ equation with random initial conditions, demonstrate the reliability, efficiency and efficacy of the proposed scheme.
ON FINITE ELEMENT METHODS FOR INHOMOGENEOUS DIELECTRIC WAVEGUIDES
Zhiming Chen; Jian-hua Yuan
2004-01-01
We investigate the problem of computing electromagnetic guided waves in a closed,inhomogeneous, pillared three-dimensional waveguide at a given frequency. The problem is formulated as a generalized eigenvalue problem. By modifying the sesquilinear form associated with the eigenvalue problem, we provide a new convergence analysis for the finite element approximations. Numerical results are reported to illustrate the performance of the method.
Surface processing methods for point sets using finite elements
Clarenz, Ulrich; Rumpf, Martin; Telea, Alexandru
2004-01-01
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs
Piezoelectric Accelerometers Modification Based on the Finite Element Method
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
A FINITE VOLUME ELEMENT METHOD FOR THERMAL CONVECTION PROBLEMS
芮洪兴
2004-01-01
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.
On the Approaching Domain Obtained by Finite Element Method
邹青松; 李永海
2002-01-01
The use of finite element method leads to replacing the initial domain by an approaching domain,Under some appropriate assumptions,we prove that there exists a W1,+∞-diffeomorphism from the original domain to the approaching domain.
A Geometrical Approach to the Boundary Element Method
Auchmann, B; Rjasanow, S
2008-01-01
We introduce a geometric formulation of the boundary element method (BEM), using concepts of the discrete electromagnetic theory. Geometric BEM is closely related to Galerkin-BEM and to the generalized collocation scheme. It is easy to implement, accurate, and computationally efficient. We validate our approach with 2-D examples and give an outlook to 3-D results.
Nonconforming ℎ- Spectral Element Methods for Elliptic Problems
P K Dutt; N Kishore Kumar; C S Upadhyay
2007-02-01
In this paper we show that we can use a modified version of the ℎ- spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. In the neighbourhood of the corners, modified polar coordinates are used and a global coordinate system elsewhere. A stability estimate is derived for the functional which is minimized based on the regularity estimate in [2]. We examine how to parallelize the method and show that the set of common boundary values consists of the values of the function at the corners of the polygonal domain. The method is faster than that proposed in [6,7,14] and the ℎ- finite element method and stronger error estimates are obtained.
Space-time discontinuous Galerkin finite element methods
Vegt, van der J.J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilizati
The use of discrete orthogonal projections in boundary element methods
Brandts, J.
2001-01-01
In recent papers by Sloan and Wendland Grigorie and Sloan and Grigorie Sloan and Brandts a formalismwas developed that serves many important and interesting applications in boundary element methods the commutator property for splines Based on superapproximation results this property is for exam
Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.
2017-02-01
A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.
Scaldaferri, M M; Freitas, J S; Vieira, J G P; Gonçalves, Z S; Souza, A M; Cerqueira-Silva, C B M
2014-07-25
We investigated 10 similarity (and disimilarity) coefficients in a set of 40 wild genotypes of Croton linearifolius subjected to analyses using hierarchical grouping methods, grouping methods by optimization and data projection in two-dimensional space. Genotypes were characterized by analyzing DNA polymorphism with the use of 15 ISSR and 12 RAPD markers. The distance measurements were compared by the Spearman correlation test, projection in two-dimensional space and grouping efficiency evaluation. The Spearman correlation coefficients between the 10 coefficients evaluated were significant (P Croton.
A new method for constructing analytic elements for groundwater flow.
Strack, O. D.
2007-12-01
The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.
Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method
赵明; 滕斌
2004-01-01
The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional NavierStokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from 100 to 1000. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.
Leser, William P.; Yuan, Fuh-Gwo; Leser, William P.
2013-01-01
A method of numerically estimating dynamic Green's functions using the finite element method is proposed. These Green's functions are accurate in a limited frequency range dependent on the mesh size used to generate them. This range can often match or exceed the frequency sensitivity of the traditional acoustic emission sensors. An algorithm is also developed to characterize an acoustic emission source by obtaining information about its strength and temporal dependence. This information can then be used to reproduce the source in a finite element model for further analysis. Numerical examples are presented that demonstrate the ability of the band-limited Green's functions approach to determine the moment tensor coefficients of several reference signals to within seven percent, as well as accurately reproduce the source-time function.
A new weak Galerkin finite element method for elliptic interface problems
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan
2016-11-01
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. Extensive numerical experiments have been conducted to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.
Convergence of a residual based artificial viscosity finite element method
Nazarov, Murtazo
2013-02-01
We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.
PROGRAM-PATTERN MULTIPOLE BOUNDARY ELEMENT METHOD FOR FRICTIONAL CONTACT
Yu Chunxiao; Shen Guangxian; Liu Deyi
2005-01-01
A mathematical program is proposed for the highly nonlinear problem involving frictional contact. A program-pattern using the fast multipole boundary element method (FMBEM) is given for 3-D elastic contact with friction to replace the Monte Carlo method. A new optimized generalized minimal residual (GMRES) algorithm is presented. Numerical examples demonstrate the validity of the program-pattern optimization model for node-to-surface contact with friction. The GMRES algorithm greatly improves the computational efficiency.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Changyong Cao; Qing-Hua Qin
2015-01-01
An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed. The formulations for...
Numerical Simulation of Friction Stir Welding by Natural Element Methods
Alfaro, I.; Fratini, L.; CUETO, Elias; Chinesta, Francisco
2009-01-01
International audience; In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatm...
Holzheid, A.; Borisov, A.; Palme, H.
1993-01-01
New, precise data on the solubilities of Ni, Co, and Mo in silicate melts at 1400 C and fO2 from IW to IW-2 are presented. The results suggest NiO, CoO as stable species in the melt. No evidence for metallic Ni or Co was found. Equilibrium was ensured by reversals with initially high Ni and Co in the glass. Mo appears to change oxidation state at IW-1, from MoO3 to MoO2. Metal-silicate partition coefficients calculated from these data and recent data on Pd indicate similar partition coefficients for Pd and Mo at the conditions of core formation. This unexpected result constrains models of core formation in the Earth.
2009-08-01
10 4.1 Plane Poiseuille and Couette Flow ... Couette Flow First we consider steady-state flow between two parallel plates of infinite extent, where the flow is driven by the movement of the top...al., 2006). The flow domain is again Ω = [0,1] × [0,1]. The analytical ERDC/CHL TR-09-12 12 Table 2. Grid refinement study for 3D Poiseuille problem. h
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna. (University of Michigan, Ann Arbor, MI); Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Extended Finite Element Method for Fracture Analysis of Structures
Mohammadi, Soheil
2008-01-01
This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications.One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been
CASCADIC MULTIGRID METHODS FOR MORTAR WILSON FINITE ELEMENT METHODS ON PLANAR LINEAR ELASTICITY
陈文斌; 汪艳秋
2003-01-01
Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented.
High-order finite element methods for cardiac monodomain simulations
Kevin P Vincent
2015-08-01
Full Text Available Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.
Chang-Jun Zheng; Hai-Bo Chen; Lei-Lei Chen
2013-01-01
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Liu, Meilin
2012-08-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE CE m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE CE) m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required. © 1963-2012 IEEE.
Effects of Linear Induction Motor Parameters in Its Optimum Design Based on Finite Element Method
Mehrdad JafarBoland
2009-03-01
Full Text Available Effective parameters in performance of linear induction motors such as air gap, number of poles and the thickness of secondary must be selected and optimized to increase power coefficients and motor performance significantly. In this paper a double sided linear induction motor in different conditions is designed and next by finite element method analyzed. Then for comparing analytical model and numerical model a linear motor using Matlab software is simulated in different condition. It is clear from the results that with optimal value of effective parameters, power losses decreased the performance of motor is improved and efficiency of linear motor is increased.
A Finite Element Method for Cracked Components of Structures
刘立名; 段梦兰; 秦太验; 刘玉标; 柳春图; 余建星
2003-01-01
In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.
Toward Distinct Element Method Simulations of Carbon Nanotube Systems
Akatyeva, Evgeniya; Anderson, Tyler; Nikiforov, Ilia; Potyondy, David; Ballarini, Roberto; Dumitrica, Traian
2011-03-01
We propose distinct element method modeling of carbon nanotube systems. The atomic-level description of an individual nanotube is coarse-grained into a chain of spherical elements that interact by parallel bonds located at their contacts. The spherical elements can lump multiple translational unit cells of the carbon nanotube and have both translational and rotational degrees of freedom. The discrete long ranged interaction between nanotubes is included in a van der Waals contact of nonmechanical nature that acts simultaneously with the parallel bonds. The created mesoscopic model is put into service by simulating a realistic carbon nanotube ring. The ring morphology arises from the energy balance stored in both parallel and van der Waals bonds. We thank NSF CAREER under Grant No. CMMI-0747684, NSF under Grant No. CMMI 0800896.
An implicit finite element method for discrete dynamic fracture
Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Bodor, Sándor; Zook, Justin M; Lindner, Erno; Tóth, Klára; Gyurcsányi, Róbert E
2008-05-01
The diffusion coefficients of active components in ion-selective membranes have a decisive influence on the life-time and detection limit of the respective ion-selective electrodes, as well as influencing the rate of polarization and relaxation processes of electrically perturbed ion sensors. Therefore, the rational design of mass transport controlled ion-selective electrodes with sub-nanomolar detection limits requires reliable data on the diffusion coefficients. We have implemented electrochemical methods for the quantitative assessment of both the diffusion coefficients of free ionophores and ion-ionophore complexes. The diffusion coefficients of the pH-sensitive chromoionophore ETH 5294 and the calcium-selective ionophore ETH 5234 were determined in plasticized PVC membranes with different PVC to plasticizer ratios. The diffusion coefficient of the free chromoionophore determined by a chronoamperometric method was validated with optical methods for a variety of membrane compositions. The calcium-selective ionophore ETH 5234 was used as a model compound to assess the diffusion coefficient of the ion-ionophore complex calculated from the time required for the complexes to cross a freshly prepared membrane during potentiometric ion-breakthrough experiments. The difference between the diffusion coefficients of the free ionophore ETH 5234 and the ion-ionophore complex was found to be significant and correlated well with the geometry of the respective species.
Gliding Box method applied to trace element distribution of a geochemical data set
Paz González, Antonio; Vidal Vázquez, Eva; Rosario García Moreno, M.; Paz Ferreiro, Jorge; Saa Requejo, Antonio; María Tarquis, Ana
2010-05-01
The application of fractal theory to process geochemical prospecting data can provide useful information for evaluating mineralization potential. A geochemical survey was carried out in the west area of Coruña province (NW Spain). Major elements and trace elements were determined by standard analytical techniques. It is well known that there are specific elements or arrays of elements, which are associated with specific types of mineralization. Arsenic has been used to evaluate the metallogenetic importance of the studied zone. Moreover, as can be considered as a pathfinder of Au, as these two elements are genetically associated. The main objective of this study was to use multifractal analysis to characterize the distribution of three trace elements, namely Au, As, and Sb. Concerning the local geology, the study area comprises predominantly acid rocks, mainly alkaline and calcalkaline granites, gneiss and migmatites. The most significant structural feature of this zone is the presence of a mylonitic band, with an approximate NE-SW orientation. The data set used in this study comprises 323 samples collected, with standard geochemical criteria, preferentially in the B horizon of the soil. Occasionally where this horizon was not present, samples were collected from the C horizon. Samples were taken in a rectilinear grid. The sampling lines were perpendicular to the NE-SW tectonic structures. Frequency distributions of the studied elements departed from normal. Coefficients of variation ranked as follows: Sb coefficients between Au, Sb, and As were found, even if these were low. The so-called ‘gliding box' algorithm (GB) proposed originally for lacunarity analysis has been extended to multifractal modelling and provides an alternative to the ‘box-counting' method for implementing multifractal analysis. The partitioning method applied in GB algorithm constructs samples by gliding a box of certain size (a) over the grid map in all possible directions. An "up
Kuehner, S. M.; Laughlin, J. R.; Grossman, L.; Johnson, M. L.; Burnett, D. S.
1989-01-01
The applicability of ion microprobe (IMP) for quantitative analysis of minor elements (Sr, Y, Zr, La, Sm, and Yb) in the major phases present in natural Ca-, Al-rich inclusions (CAIs) was investigated by comparing IMP results with those of an electron microprobe (EMP). Results on three trace-element-doped glasses indicated that it is not possible to obtain precise quantitative analysis by using IMP if there are large differences in SiO2 content between the standards used to derive the ion yields and the unknowns.
Foundations of the complex variable boundary element method
Hromadka, Theodore
2014-01-01
This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending and using the CVBEM in various applications. Relevant mathematics and principles are assembled and the reader is guided through the key topics necessary for an understanding of the development of the CVBEM in both the usual two- as well as three- or higher dimensions. In addition to this, problems are provided that build upon the material presented. The Complex Variable Boundary Element Method (CVBEM) is an approximation method useful for solving problems involving the Laplace equation in two dimensions. It has been shown to be a useful modelling technique for solving two-dimensional problems involving the Laplace or Poisson equations on arbitrary domains. The CVBEM has recently been extended to 3 or higher spatial dimensions, which enables the precision of the CVBEM in solving the Laplace equation to be now ava...
Nucleon matrix elements using the variational method in lattice QCD
Dragos, J.; Horsley, R.; Kamleh, W.; Leinweber, D. B.; Nakamura, Y.; Rakow, P. E. L.; Schierholz, G.; Young, R. D.; Zanotti, J. M.
2016-10-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current gA, the scalar current gS, the scalar current gT and the quark momentum fraction ⟨x ⟩ of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
Continuum damage growth analysis using element free Galerkin method
C O Arun; B N Rao; S M Srinivasan
2010-06-01
This paper presents an elasto-plastic element free Galerkin formulation based on Newton–Raphson algorithm for damage growth analysis. Isotropic ductile damage evolution law is used. A study has been carried out in this paper using the proposed element free Galerkin method to understand the effect of initial damage and its growth on structural response of single and bi-material problems. A simple method is adopted for enforcing EBCs by scaling the function approximation using a scaling matrix, when non-singular weight functions are used over the entire domain of the problem deﬁnition. Numerical examples comprising of one-and two-dimensional problems are presented to illustrate the effectiveness of the proposed method in analysis of uniform and non-uniform damage evolution problems. Effect of material discontinuity on damage growth analysis is also presented.
A Method of Assembling Wall or Floor Elements
2002-01-01
The invention relates to a method of constructing, at the site of use, a building wall (1) or a building floor (1) using a plurality of prefabricated concrete or lightweight concrete plate-shaped wall of floor elements (10), in particular cast elements, which have a front side and a rear side...... as well as longitudinal side edges faces (12), wherein the elements (10), in a first step, are arranged at the site of use in mutual extension and then, in a second step, are connected with each other by means of at least one force-transferring device to form a tight connection. The invention...... is characterized in that a circular ring-shaped depression (20) is provided on the front side and/or the rear side of two adjoining elements (10) after the first step, said circular ring-shaped depression extending in the one as well as the other element (10), that the force-transferring device is a pipe (25...
Han, Xu; Suo, Shiteng; Sun, Yawen; Zu, Jinyan; Qu, Jianxun; Zhou, Yan; Chen, Zengai; Xu, Jianrong
2017-03-01
To compare four methods of region-of-interest (ROI) placement for apparent diffusion coefficient (ADC) measurements in distinguishing low-grade gliomas (LGGs) from high-grade gliomas (HGGs). Two independent readers measured ADC parameters using four ROI methods (single-slice [single-round, five-round and freehand] and whole-volume) on 43 patients (20 LGGs, 23 HGGs) who had undergone 3.0 Tesla diffusion-weighted imaging and time required for each method of ADC measurements was recorded. Intraclass correlation coefficients (ICCs) were used to assess interobserver variability of ADC measurements. Mean and minimum ADC values and time required were compared using paired Student's t-tests. All ADC parameters (mean/minimum ADC values of three single-slice methods, mean/minimum/standard deviation/skewness/kurtosis/the10(th) and 25(th) percentiles/median/maximum of whole-volume method) were correlated with tumor grade (low versus high) by unpaired Student's t-tests. Discriminative ability was determined by receiver operating characteristic curves. All ADC measurements except minimum, skewness, and kurtosis of whole-volume ROI differed significantly between LGGs and HGGs (all P value of single-round ROI had the highest effect size (0.72) and the greatest areas under the curve (0.872). Three single-slice methods had good to excellent ICCs (0.67-0.89) and the whole-volume method fair to excellent ICCs (0.32-0.96). Minimum ADC values differed significantly between whole-volume and single-round ROI (P = 0.003) and, between whole-volume and five-round ROI (P = 0.001). The whole-volume method took significantly longer than all single-slice methods (all P measurements are influenced by ROI determination methods. Whole-volume histogram analysis did not yield better results than single-slice methods and took longer. Mean ADC value derived from single-round ROI is the most optimal parameter for differentiating LGGs from HGGs. 3 J. Magn. Reson. Imaging 2017;45:722-730.
Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung
1996-01-01
The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.
Jiang, Ruifen; Lin, Wei; Wen, Sijia; Zhu, Fang; Luan, Tiangang; Ouyang, Gangfeng
2015-08-07
A fully automated solid phase microextraction (SPME) depletion method was developed to study the partition coefficient of organic compound between complex matrix and water sample. The SPME depletion process was conducted by pre-loading the fiber with a specific amount of organic compounds from a proposed standard gas generation vial, and then desorbing the fiber into the targeted samples. Based on the proposed method, the partition coefficients (Kmatrix) of 4 polyaromatic hydrocarbons (PAHs) between humic acid (HA)/hydroxypropyl-β-cyclodextrin (β-HPCD) and aqueous sample were determined. The results showed that the logKmatrix of 4 PAHs with HA and β-HPCD ranged from 3.19 to 4.08, and 2.45 to 3.15, respectively. In addition, the logKmatrix values decreased about 0.12-0.27 log units for different PAHs for every 10°C increase in temperature. The effect of temperature on the partition coefficient followed van't Hoff plot, and the partition coefficient at any temperature can be predicted based on the plot. Furthermore, the proposed method was applied for the real biological fluid analysis. The partition coefficients of 6 PAHs between the complex matrices in the fetal bovine serum and water were determined, and compared to ones obtained from SPME extraction method. The result demonstrated that the proposed method can be applied to determine the sorption coefficients of hydrophobic compounds between complex matrix and water in a variety of samples.
Information Hiding Method Using Best DCT and Wavelet Coefficients and ItsWatermark Competition
Hyunho Kang
2015-03-01
Full Text Available In recent years, information hiding and its evaluation criteria have been developed by the IHC (Information Hiding and its Criteria Committee of Japan. This committee was established in 2011 with the aim of establishing standard evaluation criteria for robust watermarks. In this study, we developed an information hiding method that satisfies the IHC evaluation criteria. The proposed method uses the difference of the frequency coefficients derived from a discrete cosine transform or a discrete wavelet transform. The algorithm employs a statistical analysis to find the best positions in the frequency domains for watermark insertion. In particular, we use the BCH (Bose-Chaudhuri-Hocquenghem (511,31,109 code to error correct the watermark bits and the BCH (63,16,11 code as the sync signal to withstand JPEG (Joint Photographic Experts Group compression and cropping attacks. Our experimental results showed that there were no errors in 10 HDTV-size areas after the second decompression. It should be noted that after the second compression, the file size should be less than 1 25 of the original size to satisfy the IHC evaluation criteria.
Singan, Vasanth R
2012-06-08
AbstractBackgroundThe localization of proteins to specific subcellular structures in eukaryotic cells provides important information with respect to their function. Fluorescence microscopy approaches to determine localization distribution have proved to be an essential tool in the characterization of unknown proteins, and are now particularly pertinent as a result of the wide availability of fluorescently-tagged constructs and antibodies. However, there are currently very few image analysis options able to effectively discriminate proteins with apparently similar distributions in cells, despite this information being important for protein characterization.FindingsWe have developed a novel method for combining two existing image analysis approaches, which results in highly efficient and accurate discrimination of proteins with seemingly similar distributions. We have combined image texture-based analysis with quantitative co-localization coefficients, a method that has traditionally only been used to study the spatial overlap between two populations of molecules. Here we describe and present a novel application for quantitative co-localization, as applied to the study of Rab family small GTP binding proteins localizing to the endomembrane system of cultured cells.ConclusionsWe show how quantitative co-localization can be used alongside texture feature analysis, resulting in improved clustering of microscopy images. The use of co-localization as an additional clustering parameter is non-biased and highly applicable to high-throughput image data sets.
张时锋; 李自良
2011-01-01
Heat transfer coefficient is the main parameters of assessing the cooling capacity of quenching cooling medium, and it also is the key parameters of establishing the thermal boundary conditions. Using the inverse method for heat transfer coefficient, the heat transfer coefficient is taken as the unknown variables to solve the problem, which is classified as inverse heat conduction problems. Such problems have the extremely vital significance in practical engineering application research. This article presented a program of the inverse method for heat transfer coefficient using MATLAB software. The program based on the finite element method verified by Ansys software simulations and experiments. The results show that the method described in this article is a kind of effective method of calculating heat transfer coefficient.%换热系数是评定淬火介质冷却能力的主要参数,也是建立热边界条件的关键参数.换热系数反求法就是把换热系数作为未知量来求解,属于反向热传导问题,这类问题的研究在实际工程应用中具有十分重要的意义.本文用Matlab编写了基于有限元的换热系数反求法程序,用Ansys软件模拟和试验相结合的方法,进行了相应的验证,结果表明,本文所述的方法是一种有效的计算换热系数的方法.
MULTIGRID FOR THE MORTAR ELEMENT METHOD WITH LOCALLY P1 NONCONFORMING ELEMENTS
毕春加; 李立康
2003-01-01
In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform.We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps.The variable V-cycle multigrid preconditioner are also available.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U. [Technische Universitaet Chemnitz-Zwickau (Germany)
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
He-Ling Wang
2013-01-01
Full Text Available Magnetoelectric composite material is effective in transferring magnetic field into electric signal. In this paper, a nonlinear finite element method is present to model the magnetoelectric composite of ferroelectric and magnetostrictive material. In the method, the nonlinear and coupling behavior of magnetostrictive material such as Terfenol-D is considered. The nonuniform magnetic, electric, and mechanical field distributions are present. An interfacial transferring coefficient is defined to investigate the performance of interfacial mechanical coupling quantitatively, and the influence of the properties of interfacial bonding material and interfacial cracks on magnetoelectric coefficient is discussed. A new laminate ME composite of curved interface is proposed to overcome weak interfacial bonding.
Generalization of mixed multiscale finite element methods with applications
Lee, C S [Texas A & M Univ., College Station, TX (United States)
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
Improved fixed point iterative method for blade element momentum computations
Sun, Zhenye; Shen, Wen Zhong; Chen, Jin
2017-01-01
to the physical solution, especially for the locations near the blade tip and root where the failure rate of the iterative method is high. The stability and accuracy of aerodynamic calculations and optimizations are greatly reduced due to this problem. The intrinsic mechanisms leading to convergence problems......The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge...
The Iris biometric feature segmentation using finite element method
David Ibitayo LANLEGE
2015-05-01
Full Text Available This manuscript presents a method for segmentation of iris images based on a deformable contour (active contour paradigm. The deformable contour is a novel approach in image segmentation. A type of active contour is the Snake. Snake is a parametric curve defined within the domain of the image. Snake properties are specified through a function called energy functional. This means they consist of packets of energy which expressed as partial Differential Equations. The partial Differential Equation is the controlling engine of the active contour since this project, the Finite Element Method (Standard Galerkin Method implementation for deformable model is presented.
The Matrix Element Method in the LHC era
Wertz, Sébastien
2017-03-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. The method is reviewed in depth, and several recent applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of Standard Model observables in Higgs and Top physics. Finally, a new implementation of the MEM is presented. This project builds on established phase-space parametrisations known to greatly improve the speed of the calculations, and aims at a much improved modularity and maintainability compared to previous software, easing the use of the MEM for high-statistics data analyses.
Dual Formulations of Mixed Finite Element Methods with Applications.
Gillette, Andrew; Bajaj, Chandrajit
2011-10-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.
A multi-mesh finite element method for Lagrange elements of arbitrary degree
Witkowski, Thomas
2010-01-01
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational runtime can be more than halved in such cases. Our multi-mesh method works for Lagrange finite elements of arbitrary degree and is independent of the spatial dimension. The approach is well defined, and can be implemented in existing adaptive finite element codes with minimal effort. We show computational examples in 2D and 3D ranging from dendritic growth to solid-solid phase-transitions. A further application comes from fluid dynamics where we demonstrate the applicability of the approach for solving the incompressible Navier-Stokes equations with Lagrange finite elements of the same order for velocity and pressure. The...
无
2005-01-01
A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interestfor (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
Method for measuring recovery of catalytic elements from fuel cells
Shore, Lawrence [Edison, NJ; Matlin, Ramail [Berkeley, NJ
2011-03-08
A method is provided for measuring the concentration of a catalytic clement in a fuel cell powder. The method includes depositing on a porous substrate at least one layer of a powder mixture comprising the fuel cell powder and an internal standard material, ablating a sample of the powder mixture using a laser, and vaporizing the sample using an inductively coupled plasma. A normalized concentration of catalytic element in the sample is determined by quantifying the intensity of a first signal correlated to the amount of catalytic element in the sample, quantifying the intensity of a second signal correlated to the amount of internal standard material in the sample, and using a ratio of the first signal intensity to the second signal intensity to cancel out the effects of sample size.
Multiscale finite-element method for linear elastic geomechanics
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Changyong Cao
2015-01-01
Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
Development of methods to evaluate uranium distribution coefficients in unsaturated media
Sautman, M.T.; Simonson, S.A. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Dept. of Nuclear Engineering
1993-12-31
To date, batch sorption and dynamic column experiments have been performed for many elements as part of site characterization programs. These experiments were often conducted with samples having relatively high liquid/solid ratios (in some cases the solid volume was much smaller than the solution volume). The development of methods for measuring sorption parameters at low liquid/solid ratios was undertaken to attempt to judge whether or not results of saturated experiments are valid for use in performance assessments of sites located in unsaturated rocks. The amount of hydrologic saturation can affect the ionic strength, pH, and redox potential which can in turn affect sorption. In addition, the presence of the gas phase may affect the amount of wetting occurring on the solid`s surface. This paper describes experimental procedures which were developed to evaluate the sorption of uranium by silica sand at predetermined levels of unsaturation.
Kim, Jin Sub; An, Seok Chan; Ko, Tae Kuk [Yonsei University, Seoul (Korea, Republic of); Chu, Yong [National Fusion Research Institute(NFRI), Daejeon (Korea, Republic of)
2016-09-15
A quench detection system of KSTAR Poloidal Field (PF) coils is inevitable for stable operation because normal zone generates overheating during quench occurrence. Recently, new voltage quench detection method, combination of Central Difference Averaging (CDA) and Mutual Inductance Compensation (MIK) for compensating mutual inductive voltage more effectively than conventional voltage detection method, has been suggested and studied. For better performance of mutual induction cancellation by adjacent coils of CDA+MIK method for KSTAR coil system, balance coefficients of CDA must be estimated and adjusted preferentially. In this paper, the balance coefficients of CDA for KSTAR PF coils were numerically estimated. The estimated result was adopted and tested by using simulation. The CDA method adopting balance coefficients effectively eliminated mutual inductive voltage, and also it is expected to improve performance of CDA+MIK method for quench detection of KSTAR PF coils.
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
Vladimír KUTIŠ; Gabriel GÁLIK; Ivan RÝGER; Murín, Justín; Juraj HRABOVSKÝ; Juraj PAULECH; Tibor LALINSKÝ
2013-01-01
In this contribution modeling and simulation of surface acoustic waves (SAW) sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses ...
Model refinements of transformers via a subproblem finite element method
Dular, Patrick; Kuo-Peng, Patrick; Ferreira Da Luz, Mauricio,; Krähenbühl, Laurent
2015-01-01
International audience; A progressive modeling of transformers is performed via a subproblem finite element method. A complete problem is split into subproblems with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, 1-D to 2-D to 3-D models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings, and homogenized to fine models of cores and coils, with any coupling of these changes. The proposed unif...
Material nonlinear analysis via mixed-iterative finite element method
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Finite Element Method for Stochastic Extended KdV Equations
Karczewska, Anna; Rozmej, Piotr; Boguniewicz, Bartosz
2016-01-01
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves under stochastic forces are presented. Though small effects originating from second order dynamics may be obscured by stochastic forces, the main waves, both cnoidal and solitary ones, remain very robust against any distortions.
Assessment of the Sustainable Development Capacity with the Entropy Weight Coefficient Method
Qingsong Wang
2015-10-01
Full Text Available Sustainable development is widely accepted in the world. How to reflect the sustainable development capacity of a region is an important issue for enacting policies and plans. An index system for capacity assessment is established by employing the Entropy Weight Coefficient method. The results indicate that the sustainable development capacity of Shandong Province is improving in terms of its economy subsystem, resource subsystem, and society subsystem whilst degrading in its environment subsystem. Shandong Province has shown the general trend towards sustainable development. However, the sustainable development capacity can be constrained by the resources such as energy, land, water, as well as environmental protection. These issues are induced by the economy development model, the security of energy supply, the level of new energy development, the end-of-pipe control of pollution, and the level of science and technology commercialization. Efforts are required to accelerate the development of the tertiary industry, the commercialization of high technology, the development of new energy and renewable energy, and the structure optimization of energy mix. Long-term measures need to be established for the ecosystem and environment protection.
[Influence of human activities on groundwater environment based on coefficient variation method].
Zhao, Wei; Lin, Jian; Wang, Shu-Fang; Liu, Ji-Lai; Chen, Zhong-Rong; Kou, Wen-Jie
2013-04-01
Groundwater system in the plain area of Beijing can be divided into six subsystems. Due to the different hydrogeological conditions of the subsystems, the degrees to which human activities affect the subsystems are also diverse. In order to evaluate the influence of human activities on each subsystem, the first and second aquifer with relatively poor water quality were chosen to be the evaluating positions, based on the data of groundwater sampled in September, 2011. With respect to human activities affect index such as total hardness, TDS, sulfate and ammonium, variation coefficient methods were used to calculate the weight of each index. Then scores were obtained for each index with national standard as reference, and superposition calculations were used to gain comprehensive scores, finally the groundwater quality conditions were evaluated. Contrast analyses were used to evaluate the incidence of human activities with groundwater subsystems as evaluation unit and water quality partitions as evaluation factors. The results indicate that the influence of human activities on the first aquifer is greater than that of the second aquifer, the Yongding river groundwater subsystems and the Chaobai river groundwater subsystems are affected more than other groundwater subsystems.
Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty
Lai, Chen-Yao G.
1996-01-01
The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.
Ficheux, A; Gayrard, N; Duranton, F; Guzman, C; Szwarc, I; Vetromile, F; Brunet, P; Servel, M F; Argilés, A
2017-02-01
Recent randomized controlled trials suggest that sufficiently high convection post-dilutional haemodiafiltration (HC-HDF) improves survival in dialysis patients, consequently this technique is increasingly being adopted. However, when performing HC-HDF, rigorous control systems of the ultrafiltration setting are required. Assessing the global ultrafiltration coefficient of the dialysis system [GKD-UF; defined as ultrafiltration rate (QUF)/transmembrane pressure] or water permeability may be adapted to the present dialysis settings and be of value in clinics. GKD-UF was determined and its reproducibility, variability and influencing factors were specifically assessed in 15 stable patients routinely treated by high-flux haemodialysis or HC-HDF in a single unit. GKD-UF invariably followed a parabolic function with increasing QUF in dialysis and both pre- and post-dilution HC-HDF (R2 constantly >0.96). The vertex of the parabola, GKD-UF-max and related QUF were very reproducible per patient (coefficient of variation 3.9 ± 0.6 and 3.3 ± 0.3%, respectively) and they greatly varied across patients (31–42 mL/h−1/mmHg and 82–100 mL/min, respectively). GKD-UF-max and its associated QUF decreased during dialysis treatment (P < 0.01). The GKD-UF-max decrease was related to weight loss (R2 = 0.66; P = 0.0015). GKD-UF is a reliable and accurate method to assess the water permeability of a system in vivo. It varies according to dialysis setting and patient-related factors. It is an objective parameter evaluating the forces driving convection and identifies any diversion of the system during the treatment procedure. It is applicable to low- or high-flux dialysis as well as pre- or post-dilution HDF. Thus, it may be used to describe the characteristics of a dialysis system, is suitable for clinical use and may be of help for personalized prescription.
Discontinuous finite element method for vector radiative transfer
Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping
2017-03-01
The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.
Nagasawa, H.; Schreiber, H. D.; Morris, R. V.
1980-01-01
Experimental determinations of the mineral/liquid partition coefficients of REE (La, Sm, Eu, Gd, Tb, Yb and Lu), Sc and Sr are reported for the minerals perovskite, spinel and melilite in synthetic systems. Perovskite concentrates light REE with respect to the residual liquid but shows no preference for heavy REE. Spinel greatly discriminates against the incorporation of REE, especially light REE, into its crystal structure. The partition of REE into melilite from a silicate liquid is quite dependent upon both the bulk melt and melilite solid-solution (gehlenite and akermanite components) compositions. As such, melilite can be enriched in REE or will reject REE with corresponding strong negative or strong positive Eu anomalies, respectively.
Differential quadrature time element method for structural dynamics
Yu-Feng Xing; Jing Guo
2012-01-01
An accurate and efficient differential quadrature time element method (DQTEM) is proposed for solving ordinary differential equations (ODEs),the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps.Two methods of imposing initial conditions are given,which avoids the tediousness when derivative initial conditions are imposed,and the numerical comparisons indicate that the first method,in which the analog equations of initial displacements and velocities are used to directly replace the differential quadrature (DQ) analog equations of ODEs at the first and the last sampling points,respectively,is much more accurate than the second method,in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points.On the contrary to the conventional step-by-step direct integration schemes,the solutions at all sampling points can be obtained simultaneously by DQTEM,and generally,one differential quadrature time element may be enough for the whole time domain.Extensive numerical comparisons validate the efficiency and accuracy of the proposed method.
Space-Time Conservation Element and Solution Element Method Being Developed
Chang, Sin-Chung; Himansu, Ananda; Jorgenson, Philip C. E.; Loh, Ching-Yuen; Wang, Xiao-Yen; Yu, Sheng-Tao
1999-01-01
The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically
Gjorgieva, Slavica; Barandovski, Lambe
2016-03-01
The mass attenuation coefficients (μ/ρ) for 3 high purity elemental materials Al, Cu and Pb were measured in the γ-ray energy range from 81 keV up to 1333 keV using 22Na, 60Co 133Ba and 133Cs as sources of gamma radiation. Well shielded detector (NaI (Tl) semiconductor detector) was used to measure the intensity of the transmitted beam. The measurements were made under condition of good geometry, assuring that any photon absorbed or deflected appreciably does not reach the detector. The measured values are compared with the theoretical ones obtained by Seltzer (1993).
Method of Minimax Optimization in the Coefficient Inverse Heat-Conduction Problem
Diligenskaya, A. N.; Rapoport, É. Ya.
2016-07-01
Consideration has been given to the inverse problem on identification of a temperature-dependent thermal-conductivity coefficient. The problem was formulated in an extremum statement as a problem of search for a quantity considered as the optimum control of an object with distributed parameters, which is described by a nonlinear homogeneous spatially one-dimensional Fourier partial equation with boundary conditions of the second kind. As the optimality criterion, the authors used the error (minimized on the time interval of observation) of uniform approximation of the temperature computed on the object's model at an assigned point of the segment of variation in the spatial variable to its directly measured value. Pre-parametrization of the sought control action, which a priori records its description accurate to assigning parameters of representation in the class of polynomial temperature functions, ensured the reduction of the problem under study to a problem of parametric optimization. To solve the formulated problem, the authors used an analytical minimax-optimization method taking account of the alternance properties of the sought optimum solutions based on which the algorithm of computation of the optimum values of the sought parameters is reduced to a system (closed for these unknowns) of equations fixing minimax deviations of the calculated values of temperature from those observed on the time interval of identification. The obtained results confirm the efficiency of the proposed method for solution of a certain range of applied problems. The authors have studied the influence of the coordinate of a point of temperature measurement on the exactness of solution of the inverse problem.
Varkey, G.; Suresh, T.; Matondkar, S.G.P.; Desa, E.; Kamath, S.S.
total suspended matter values from water samples obtained at discrete depths at the same location. An artificial neural network (ANN) model has been used to derive suspended matter from the spectral values of beam attenuation coefficients measured using...
Seybert, A. F.; Wu, T. W.; Wu, X. F.
1994-01-01
This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
Hybrid finite-element/boundary-element method to calculate Oersted fields
Hertel, Riccardo, E-mail: hertel@ipcms.unistra.fr [Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, Strasbourg (France); Kákay, Attila [Peter Grünberg Institut (PGI-6), Forschungszentrum Jülich GmbH, D-52428 Jülich (Germany)
2014-11-15
The article presents a general-purpose hybrid finite-element/boundary-element method (FEM/BEM) to calculate magnetostatic fields generated by stationary electric currents. The efficiency of this code lies in its ability to simulate Oersted fields in complex geometries with non-uniform current density distributions. As a precursor to the calculation of the Oersted field, an FEM algorithm is employed to calculate the electric current density distribution. The accuracy of the code is confirmed by comparison with analytic results. Two examples show how this method provides important numerical data that can be directly plugged into micromagnetic simulations: The current density distribution in a thin magnetic strip with a notch, and the Oersted field in a three-dimensional contact geometry; similar to the type commonly used in spin-torque driven nano-oscillators. It is argued that a precise calculation of both, the Oersted field and the current density distribution, is essential for a reliable simulation of current-driven micromagnetic processes. - Highlights: • We present a numerical method to calculate Oersted fields for arbitrary geometries. • Description of a FEM algorithm to calculate current density distributions. • It is argued that these methods are valuable for micromagnetic STT-simulations. • Several examples are shown, highlighting the methods’ importance and accuracy.
Displacement fields denoising and strains extraction by finite element method
无
2011-01-01
Optical full-field measurement methods are now widely applied in various domains. In general,the displacement fields can be directly obtained from the measurement,however in mechanical analysis strain fields are preferred.To extract strain fields from noisy displacement fields is always a challenging topic.In this study,a finite element method for smoothing displacement fields and calculating strain fields is proposed.An experimental test case on a holed aluminum specimen under tension is applied to vali...
Finite element method for extended KdV equations
Karczewska, Anna; Szczeciński, Maciej; Boguniewicz, Bartosz
2016-01-01
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
Laser flash method for measurement of liquid metals heat transfer coefficients
Stankus, S. V.; Savchenko, I. V.
2009-12-01
New laser flash technique for the measurement of heat transfer coefficients of liquid metals is presented. The thermal diffusivity of the liquid mercury has been studied experimentally over the room temperature range. The thermal conductivity coefficient has been calculated with the use of the reference data on density and heat capacity. Analysis of systematic errors of the measurements has shown that the data error is about 3%. Comparison of the obtained results with data available in publications has proved their reliability.
Edmund Chadwick; Ali Hatam; Saeed Kazem
2016-02-01
A new approach, named the exponential function method (EFM) is used to obtain solutions to nonlinear ordinary differential equations with constant coefficients in a semi-infinite domain. The form of the solutions of these problems is considered to be an expansion of exponential functions with unknown coefficients. The derivative and product operational matrices arising from substituting in the proposed functions convert the solutions of these problems into an iterative method for finding the unknown coefficients. The method is applied to two problems: viscous flow due to a stretching sheet with surface slip and suction; and mageto hydrodynamic (MHD) flow of an incompressible viscous fluid over a stretching sheet. The two resulting solutions are compared against some standard methods which demonstrates the validity and applicability of the new approach.
Babuska, Ivo
2010-01-01
The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with values in $L^\\infty(\\Omega)$. This class of coefficients includes as examples media with micro-structure as well as media with multiple non-separated length scales. The approach taken here is based on the the generalized finite element method (GFEM) introduced in \\cite{107}, and elaborated in \\cite{102}, \\cite{103} and \\cite{104}. The GFEM is constructed by partitioning the computational domain $\\Omega$ into to a collection of preselected subsets $\\omega_{i},i=1,2,..m$ and constructing finite dimensional approximation spaces $\\Psi_{i}$ over each subset using local information. The notion of the Kolmogorov $n$-width is used to identify the optimal local approximation spaces. These spaces deliver local approximations with errors that decay almost exponentially with the degree...
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
YUAN Si; HE Xue-feng
2006-01-01
Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM),the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient.This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea,implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
8th International Conference on Boundary Element Methods
Brebbia, C
1986-01-01
The International Conference on Boundary Element Methods in Engineering was started in 1978 with the following objectives: i) To act as a focus for BE research at a time when the technique wasjust emerging as a powerful tool for engineering analysis. ii) To attract new as weIl as established researchers on Boundary Elements, in order to maintain its vitality and originality. iii) To try to relate the Boundary Element Method to other engineering techniques in an effort to help unify the field of engineering analysis, rather than to contribute to its fragmentation. These objectives were achieved during the last 7 conferences and this meeting - the eighth - has continued to be as innovative and dynamic as any ofthe previous conferences. Another important aim ofthe conference is to encourage the participation of researchers from as many different countries as possible and in this regard it is a policy of the organizers to hold the conference in different locations. It is easy to forget when working on scientific ...
The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random Field Coefficients
Michal Beres
2017-01-01
Full Text Available This article presents a study of the Stochastic Galerkin Method (SGM applied to the Darcy flow problem with a log-normally distributed random material field given by a mean value and an autocovariance function. We divide the solution of the problem into two parts. The first one is the decomposition of a random field into a sum of products of a random vector and a function of spatial coordinates; this can be achieved using the Karhunen-Loeve expansion. The second part is the solution of the problem using SGM. SGM is a simple extension of the Galerkin method in which the random variables represent additional problem dimensions. For the discretization of the problem, we use a finite element basis for spatial variables and a polynomial chaos discretization for random variables. The results of SGM can be utilised for the analysis of the problem, such as the examination of the average flow, or as a tool for the Bayesian approach to inverse problems.
Zeng, X.; Scovazzi, G.
2016-06-01
We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce. In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework. The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.
Ji-ming Yang; Yanping Chen
2011-01-01
A combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem which includes molecular diffusion and dispersion in porous media is investigated. That is to say, the mixed finite element method with Raviart-Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin (SIPG) approximation. Based on projection interpolations and induction hypotheses, a superconvergence estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration.
Steibler, P.
2000-07-01
The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet
3D mode discrete element method with the elastoplastic model
2012-01-01
The three-dimensional mode-deformable discrete element method (3MDEM) is an extended distinct element approach under the assumptions of small strain,finite displacement,and finite rotation of blocks.The deformation of blocks is expressed by the combination of the deformation modes in 3MDEM.In this paper,the elastoplastic constitutive relationship of blocks is implemented on the 3MDEM platform to simulate the integrated process from elasticity to plasticity and finally to fracture.To overcome the shortcomings of the conventional criterion for contact fracturing,a new criterion based on plastic strain is introduced.This approach is verified by two numerical examples.Finally,a cantilever beam is simulated as a comprehensive case study,which went through elastic,elastoplastic,and discontinuous fracture stages.
A weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Novel boundary element method for resolving plate bending problems
陈颂英; 王乐勤; 焦磊
2003-01-01
This paper discusses the application of the boundary contour method for resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirchhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points, even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corner point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.
无
2001-01-01
The adsorption and desorption coefficients of atrazine, methiocarb and simazine on a sandy loam soil were measured in this study with soil column liquid chromatographic (SCLC) technique. The adsorption and desorption data of all the three pesticides followed Freundlich isotherms revealing the existence of hysteresis. In comparing with other methods, SCLC method showed some characteristics such as rapidity, online and accuracy.
In Silico Methods to Identify Exapted Transposable Element Families.
Ramsay, LeeAnn; Bourque, Guillaume
2016-01-01
Transposable elements (TEs) have recently been shown to have many regulatory roles within the genome. In this chapter, we will examine two in silico methods for analyzing TEs and identifying families that may have acquired such functions. The first method will look at how the overrepresentation of a repeat family in a set of genomic features can be discovered. The example situation of OCT4 binding sites originating from LTR7 TE sequences will be used to show how this method could be applied. The second method will describe how to determine if a TE family exhibits a cell type-specific expression pattern. As an example, we will look at the expression of HERV-H, an endogenous retrovirus known to act as an lncRNA in embryonic stem cells. We will use this example to demonstrate how RNA-seq data can be used to compare cell type expression of repeats.
A robust shell element in meshfree SPH method
Fu-Ren Ming; A-Man Zhang; Xue-Yan Cao
2013-01-01
With the incorporation of total Lagrangian smoothed particle hydrodynamics (SPH) method equation and moving least square (MLS) function,the traditional SPH method is improved regarding the stability and consistency.Based on Mindlin-Ressiner plate theory,the SPH method simulating dynamic behavior via one layer of particles is applied to plate's mid-plane,i.e.,a SPH shell model is constructed.Finally,through comparative analyses on the dynamic response of square,stiffened shells and cylindrical shells under various strong impact loads with common finite element software,the feasibility,validity and numerical accuracy of the SPH shell method are verified.Consequently,further researches on SPH shell may well pave the way towards solving problems involving dynamic plastic damage,tearing or even crushing.
Feasibility study of a novel method for real-time aerodynamic coefficient estimation
Gurbacki, Phillip M.
In this work, a feasibility study of a novel technique for the real-time identification of uncertain nonlinear aircraft aerodynamic coefficients has been conducted. The major objective of this paper is to investigate the feasibility of a system for parameter identification in a real-time flight environment. This system should be able to calculate aerodynamic coefficients and derivative information using typical pilot inputs while ensuring robust, stable, and rapid convergence. The parameter estimator investigated is based upon the nonlinear sliding mode control schema; one of the main advantages of the sliding mode estimator is the ability to guarantee a stable and robust convergence. Stable convergence is ensured by choosing a sliding surface and function that satisfies the Lyapunov stability criteria. After a proper sliding surface has been chosen, the nonlinear equations of motion for an F-16 aircraft are substituted into the sliding surface yielding an estimator capable of identifying a single aircraft parameter. Multiple sliding surfaces are then developed for each of the different flight parameters that will be identified. Sliding surfaces and parameter estimators have been developed and simulated for the pitching moment, lift force, and drag force coefficients of the F-16 aircraft. Comparing the estimated coefficients with the reference coefficients shows rapid and stable convergence for a variety of pilot inputs. Starting with simple doublet and sin wave commands, and followed by more complicated continuous pilot inputs, estimated aerodynamic coefficients have been shown to match the actual coefficients with a high degree of accuracy. This estimator is also shown to be superior to model reference or adaptive estimators, it is able to handle positive and negative estimated parameters and control inputs along with guaranteeing Lyapunov stability during convergence. Accurately estimating these aerodynamic parameters in real-time during a flight is essential
Sabatier, Romuald; Fossati, Caroline; Bourennane, Salah; Di Giacomo, Antonio
2008-10-01
Model Based Optical Proximity Correction (MBOPC) is since a decade a widely used technique that permits to achieve resolutions on silicon layout smaller than the wave-length which is used in commercially-available photolithography tools. This is an important point, because masks dimensions are continuously shrinking. As for the current masks, several billions of segments have to be moved, and also, several iterations are needed to reach convergence. Therefore, fast and accurate algorithms are mandatory to perform OPC on a mask in a reasonably short time for industrial purposes. As imaging with an optical lithography system is similar to microscopy, the theory used in MBOPC is drawn from the works originally conducted for the theory of microscopy. Fourier Optics was first developed by Abbe to describe the image formed by a microscope and is often referred to as Abbe formulation. This is one of the best methods for optimizing illumination and is used in most of the commercially available lithography simulation packages. Hopkins method, developed later in 1951, is the best method for mask optimization. Consequently, Hopkins formulation, widely used for partially coherent illumination, and thus for lithography, is present in most of the commercially available OPC tools. This formulation has the advantage of a four-way transmission function independent of the mask layout. The values of this function, called Transfer Cross Coefficients (TCC), describe the illumination and projection pupils. Commonly-used algorithms, involving TCC of Hopkins formulation to compute aerial images during MBOPC treatment, are based on TCC decomposition into its eigenvectors using matricization and the well-known Singular Value Decomposition (SVD) tool. These techniques that use numerical approximation and empirical determination of the number of eigenvectors taken into account, could not match reality and lead to an information loss. They also remain highly runtime consuming. We propose an
Finite element method for solving geodetic boundary value problems
Fašková, Zuzana; Čunderlík, Róbert; Mikula, Karol
2010-02-01
The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions.
Architecting the Finite Element Method Pipeline for the GPU.
Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T
2014-02-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS
Qing-ping Deng; Xiao-ping Feng
2002-01-01
Multigrid methods are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion. It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion.To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are constructed explicitly. For nonconforming elements, it is shown that the usual local averaging technique for constructing prolongation operators can be replaced by a computationally cheaper alternative, random choice technique. Moreover, since the algorithm and analysis allows using of nonnested meshes, the abstract result also applies to low order mixed finite elements, which are usually stable only for some special mesh structures.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC)
2014-02-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a{sup N}, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Sensitivity analysis based preform die shape design using the finite element method
Zhao, G. Q.; Hufi, R.; Hutter, A.; Grandhi, R. V.
1997-06-01
This paper uses a finite element-based sensitivity analysis method to design the preform die shape for metal forming processes. The sensitivity analysis was developed using the rigid visco-plastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of the B-spline are used as the design variables. The optimization problem is to minimize the difference between the realized and the desired final forging shapes. The sensitivity analysis includes the sensitivities of the objective function, nodal coordinates, and nodal velocities with respect to the design variables. The remeshing procedure and the interpolation/transfer of the history/dependent parameters are considered. An adjustment of the volume loss resulting from the finite element analysis is used to make the workpiece volume consistent in each optimization iteration and improve the optimization convergence. In addition, a technique for dealing with fold-over defects during the forming simulation is employed in order to continue the optimization procedures of the preform die shape design. The method developed in this paper is used to design the preform die shape for both plane strain and axisymmetric deformations with shaped cavities. The analysis shows that satisfactory final forging shapes are obtained using the optimized preform die shapes.
He, Xinguang; Ren, Li
2009-07-01
SummaryIn this paper we present an adaptive multiscale finite element method for solving the unsaturated water flow problems in heterogeneous porous media spanning over many scales. The main purpose is to design a numerical method which is capable of adaptively capturing the large-scale behavior of the solution on a coarse-scale mesh without resolving all the small-scale details at each time step. This is accomplished by constructing the multiscale base functions that are adapted to the time change of the unsaturated hydraulic conductivity field. The key idea of our method is to use a criterion based on the temporal variation of the hydraulic conductivity field to determine when and where to update our multiscale base functions. As a consequence, these base functions are able to dynamically account for the spatio-temporal variability in the equation coefficients. We described the principle for constructing such a method in detail and gave an algorithm for implementing it. Numerical experiments were carried out for the unsaturated water flow equation with randomly generated lognormal hydraulic parameters to demonstrate the efficiency and accuracy of the proposed method. The results show that throughout the adaptive simulation, only a very small fraction of the multiscale base functions needs to be recomputed, and the level of accuracy of the adaptive method is higher than that of the multiscale finite element technique in which the base functions are not updated with the time change of the hydraulic conductivity.
Applications of the discrete element method in mechanical engineering
Fleissner, Florian, E-mail: fleissner@itm.uni-stuttgart.de; Gaugele, Timo, E-mail: gaugele@itm.uni-stuttgart.de; Eberhard, Peter [University of Stuttgart, Institute of Engineering and Computational Mechanics (Germany)], E-mail: eberhard@itm.uni-stuttgart.de
2007-08-15
Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples.
A method for measuring the phase of the reflection coefficient in the visible range of the spectrum
Shvets, V. A.
2017-08-01
A method for measuring the phase of the reflection coefficient in the optical wavelength range is proposed. The method is simple in experimental implementation and is based on measuring the energyreflection coefficients of a sample in two media with different refractive indices. Analytical and numerical estimates show that the measurement accuracy of the phase is on the order of 1°. The possibilities of using the results of the phase measurement in practice for a more complete characterization of materials and structures under investigation are considered.
7th International Conference on Discrete Element Methods
Feng, Yuntian; Mustoe, Graham
2017-01-01
This book presents the latest advances in Discrete Element Methods (DEM) and technology. It is the proceeding of 7th International Conference on DEM which was held at Dalian University of Technology on August 1 - 4, 2016. The subject of this book are the DEM and related computational techniques such as DDA, FEM/DEM, molecular dynamics, SPH, Meshless methods, etc., which are the main computational methods for modeling discontinua. In comparison to continua which have been already studied for a long time, the research of discontinua is relatively new, but increases dramatically in recent years and has already become an important field. This book will benefit researchers and scientists from the academic fields of physics, engineering and applied mathematics, as well as from industry and national laboratories who are interested in the DEM. .
Tangential stress analysis of myocardial wall by finite element method
Guan Qiu; Jiang Cao; Wang Xiaoyan; Chen Shengyong; Guan Fang
2011-01-01
A novel method is presented to build the triangular surface model and calculate the tangential stress and strain of myocardial wall ,which can be further used to reflect the left ventricle twisting-a sensitive index to assess the systolic and diastolic function of heart. Firstly, a point distribution model is used to obtain the feature points of the ventricular surface in medical images. Secondly, the surface model is constructed by triangular mesh, and then the subdivision strategy is introduced to refine the model. Thirdly, plane projection and finite element method ( FEM ) are applied to calculate the tangential stress and strain. Finally, the distribution of tangential modulus of elasticity is discussed. The stimulation results show that the proposed method can be used to compute the tangential stress and strain of myocardial wall effectively and the computing result is consistent with the results mentioned in the literatures.
A multilevel finite element method for Fredholm integral eigenvalue problems
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
Mey, Paula; Varges, Priscilla R.; Mendes, Paulo R. de Souza [Dept. of Mechanical Engineering. Pontificia Universidade Catolica do RJ (PUC-Rio), RJ (Brazil)], e-mails: prvarges@puc-rio.br, pmendes@puc-rio.br
2010-07-01
This research looked for a method to determine the binary diffusion coefficient D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water.D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water. (author)
Method of automatic tuning pf preset coefficient of electron gain of photoelectron multiplier
Smirnov, O Yu
2002-01-01
Paper describes technique to time the preset coefficient of electron gain of photoelectron multiplier (PEM) ensuring high accuracy at minimal involvement of an operator. Subsequent to rough setting of voltage in PEM the automatic system tunes high voltage so that coefficient of electron gain of PEM corresponds to the preset one within the limits of the required accuracy (up to 2%). The technique was efficiently used to tune two thousands of PEMs for the Borexino solar neutrino detector in the Gran Sasso National Laboratory, Italy
Practical methods to define scattering coefficients in a room acoustics computer model
Zeng, Xiangyang; Christensen, Claus Lynge; Rindel, Jens Holger
2006-01-01
To predict acoustics of rooms using computer programs based on geometrical assumptions, it is important that scattering is included in the calculations. Therefore scattering is usually included in terms of scattering coefficients which are assigned to each surface telling the software the ratio...... between the part of the reflected energy which is not being reflected specularily and the total reflected energy. However the effective scattering coefficient of a surface depends not only on the roughness of the surface material indeed diffraction caused by limited dimensions of the surface as well...
Zhan, Liwei; Li, Chengwei
2017-02-01
A hybrid PSO-SVM-based model is proposed to predict the friction coefficient between aircraft tire and coating. The presented hybrid model combines a support vector machine (SVM) with particle swarm optimization (PSO) technique. SVM has been adopted to solve regression problems successfully. Its regression accuracy is greatly related to optimizing parameters such as the regularization constant C , the parameter gamma γ corresponding to RBF kernel and the epsilon parameter \\varepsilon in the SVM training procedure. However, the friction coefficient which is predicted based on SVM has yet to be explored between aircraft tire and coating. The experiment reveals that drop height and tire rotational speed are the factors affecting friction coefficient. Bearing in mind, the friction coefficient can been predicted using the hybrid PSO-SVM-based model by the measured friction coefficient between aircraft tire and coating. To compare regression accuracy, a grid search (GS) method and a genetic algorithm (GA) are used to optimize the relevant parameters (C , γ and \\varepsilon ), respectively. The regression accuracy could be reflected by the coefficient of determination ({{R}2} ). The result shows that the hybrid PSO-RBF-SVM-based model has better accuracy compared with the GS-RBF-SVM- and GA-RBF-SVM-based models. The agreement of this model (PSO-RBF-SVM) with experiment data confirms its good performance.
2008-01-01
We give an interface between two same media whose orientation of optical axis, however, is rotated, and describe a method in detail to show how to calculate reflectance coefficient in this interface. We also give the theoretical simulation of the reflectance coefficient and discuss the effect of the rotation angle and the direction of electron vector on the reflectance coefficient. For the un-polarized lights the theoretical calculated results show that the reflectance coefficients (rx1 and ry1) are very small when the rotated angle is small, and they arrive at the maximum value as the rotation angle is equal to a decided value. For the polarized light, when the rotation angle is small, the reflectance coefficients (rx1 and ry1) are also small. Only when the rotation angle increases to a certain extent, they can reach the maximum values and be strongly affected by the direction of electronic vector. However, this effect on the reflectance coefficient in the direction of the maximum refraction is different from that in the direction of minimum refraction.
FENG ShiMeng; GHEN Ting; XIE JiaNing
2008-01-01
We give an interface between two same media whose orientation of optical axis,however, is rotated, and describe a method in detail to show how to calculate reflectance coefficient in this interface. We also give the theoretical simulation of the reflectance coefficient and discuss the effect of the rotation angle and the direction of electron vector on the reflectance coefficient. For the un-polarized lights the theoretical calculated results show that the reflectance coefficients (rx1 and ry1) are very small when the rotated angle is small, and they arrive at the maximum value as the rotation angle is equal to a decided value. For the polarized light, when the rotation angle is small, the reflectance coefficients (rx1 and ry1) are also small. Only when the rotation angle increases to a certain extent, they can reach the maximum values and be strongly affected by the direction of electronic vector. However, this effect on the reflectance coefficient in the direction of the maximum refraction is different from that in the direction of minimum refraction.
A Finite Element Method for Simulation of Compressible Cavitating Flows
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
Fuzzy and interval finite element method for heat conduction problem
Majumdar, Sarangam; Chakraverty, S
2012-01-01
Traditional finite element method is a well-established method to solve various problems of science and engineering. Different authors have used various methods to solve governing differential equation of heat conduction problem. In this study, heat conduction in a circular rod has been considered which is made up of two different materials viz. aluminum and copper. In earlier studies parameters in the differential equation have been taken as fixed (crisp) numbers which actually may not. Those parameters are found in general by some measurements or experiments. So the material properties are actually uncertain and may be considered to vary in an interval or as fuzzy and in that case complex interval arithmetic or fuzzy arithmetic has to be considered in the analysis. As such the problem is discretized into finite number of elements which depend on interval/fuzzy parameters. Representation of interval/fuzzy numbers may give the clear picture of uncertainty. Hence interval/fuzzy arithmetic is applied in the fin...
A Review of Discrete Element Method Research on Particulate Systems
Mahmood, A. A.; Elektorowicz, M.
2016-07-01
This paper summarizes research done using the Discrete Element Method (DEM) and explores new trends in its use on Particulate systems. The rationale for using DEM versus the traditional continuum-based approach is explained first. Then, DEM application is explored in terms of geotechnical engineering and mining engineering materials, since particulate media are mostly associated with these two disciplines. It is concluded that no research to date had addressed the issue of using the DEM to model the strength and weathering characteristics of peaty soil-slag-Portland cement-fly ash combinations.
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
Vladimír KUTIŠ
2013-06-01
Full Text Available In this contribution modeling and simulation of surface acoustic waves (SAW sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.
The Research of Welding Residual Stress Based Finite Element Method
Qinghua Bai
2013-06-01
Full Text Available Welding residual stress was caused by local heating during the welding process, tensile residual stress reduce fatigue strength and corrosion resistance, Compressive residual stress decreases stability limit. So it will produce brittle fracture, reduce working life and strength of workpiece; Based on the simulation of welding process with finite element method, calculate the welding temperature field and residual stress, and then measure residual stress in experiments, So as to get the best welding technology and welding parameters, to reduce welding residual stress effective, it has very important significance.
The Distinct Element Method - Application to Structures in Jointed Rock
Morris, J.P.; Glen, L.; Blair, S.; Heuze, F.
2001-11-30
The Distinct Element Method (DEM) is a meshfree method with applications to rock mechanics, mining sciences, simulations of nuclear repositories, and the stability of underground structures. Continuum mesh-based methods have been applied successfully to many problems in geophysics. Even if the geology includes fractures and faults, when sufficiently large length scales are considered a continuum approximation may be sufficient. However, a large class of problems exist where individual rock joints must be taken into account. This includes problems where the structures of interest have sizes comparable with the block size. In addition, it is possible that while the structure may experience loads which do no measurable damage to individual blocks, some joints may fail. This may launch smaller blocks as dangerous projectiles or even cause total failure of a tunnel. Traditional grid-based continuum approaches are wholly unsuited to this class of problem. It is possible to introduce discontinuities or slide lines into existing grid-based methods, however, such limited approaches can break down when new contacts form between blocks. The distinct element method (DEM) is an alternative, meshfree approach. The DEM can directly approximate the block structure of the jointed rock using arbitrary polyhedra. Using this approach, preexisting joints are readily incorporated into the DEM model. In addition, the method detects all new contacts between blocks resulting from relative block motion. We will describe the background of the DEM and review previous application of the DEM to geophysical problems. Finally we present preliminary results from a investigation into the stability of underground structures subjected to dynamic loading.
Standard and Economical Cascadic Multigrid Methods for the Mortar Finite Element Methods
Xuejun Xu; Wenbin Chen
2009-01-01
In this paper, standard and economical cascadic multigrid methods are con-sidered for solving the algebraic systems resulting from the mortar finite element meth-ods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to support our theory.
Simple Method to Determine the Partition Coefficient of Naphthenic Acid in Oil/Water
Bitsch-Larsen, Anders; Andersen, Simon Ivar
2008-01-01
The partition coefficient for technical grade naphthenic acid in water/n-decane at 295 K has been determined (K-wo = 2.1 center dot 10(-4)) using a simple experimental technique with large extraction volumes (0.09 m(3) of water). Furthermore, nonequilibrium values at different pH values are prese...