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…
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
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
Equivariant preconditioners for boundary element methods
Energy Technology Data Exchange (ETDEWEB)
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.
Supervised learning method for predicting chromatin boundary associated insulator elements.
Bednarz, Paweł; Wilczyński, Bartek
2014-12-01
In eukaryotic cells, the DNA material is densely packed inside the nucleus in the form of a DNA-protein complex structure called chromatin. Since the actual conformation of the chromatin fiber defines the possible regulatory interactions between genes and their regulatory elements, it is very important to understand the mechanisms governing folding of chromatin. In this paper, we show that supervised methods for predicting chromatin boundary elements are much more effective than the currently popular unsupervised methods. Using boundary locations from published Hi-C experiments and modEncode tracks as features, we can tell the insulator elements from randomly selected background sequences with great accuracy. In addition to accurate predictions of the training boundary elements, our classifiers make new predictions. Many of them correspond to the locations of known insulator elements. The key features used for predicting boundary elements do not depend on the prediction method. Because of its miniscule size, chromatin state cannot be measured directly, we need to rely on indirect measurements, such as ChIP-Seq and fill in the gaps with computational models. Our results show that currently, at least in the model organisms, where we have many measurements including ChIP-Seq and Hi-C, we can make accurate predictions of insulator positions.
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...
Application of the boundary element method to transient heat conduction
Dargush, G. F.; Banerjee, P. K.
1991-01-01
An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.
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 ...
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Boundary element method solution for large scale cathodic protection problems
Rodopoulos, D. C.; Gortsas, T. V.; Tsinopoulos, S. V.; Polyzos, D.
2017-12-01
Cathodic protection techniques are widely used for avoiding corrosion sequences in offshore structures. The Boundary Element Method (BEM) is an ideal method for solving such problems because requires only the meshing of the boundary and not the whole domain of the electrolyte as the Finite Element Method does. This advantage becomes more pronounced in cathodic protection systems since electrochemical reactions occur mainly on the surface of the metallic structure. The present work aims to solve numerically a sacrificial cathodic protection problem for a large offshore platform. The solution of that large-scale problem is accomplished by means of “PITHIA Software” a BEM package enhanced by Hierarchical Matrices (HM) and Adaptive Cross Approximation (ACA) techniques that accelerate drastically the computations and reduce memory requirements. The nonlinear polarization curves for steel and aluminium in seawater are employed as boundary condition for the under protection metallic surfaces and aluminium anodes, respectively. The potential as well as the current density at all the surface of the platform are effectively evaluated and presented.
Boundary element method for surface nonlinear optics of nanoparticles.
Mäkitalo, Jouni; Suuriniemi, Saku; Kauranen, Martti
2011-11-07
We present the frequency-domain boundary element formulation for solving surface second-harmonic generation from nanoparticles of virtually arbitrary shape and material. We use the Rao-Wilton-Glisson basis functions and Galerkin's testing, which leads to very accurate solutions for both near and far fields. This is verified by a comparison to a solution obtained via multipole expansion for the case of a spherical particle. The frequency-domain formulation allows the use of experimentally measured linear and nonlinear material parameters or the use of parameters obtained using ab-initio principles. As an example, the method is applied to a non-centrosymmetric L-shaped gold nanoparticle to illustrate the formation of surface nonlinear polarization and the second-harmonic radiation properties of the particle. This method provides a theoretically well-founded approach for modelling nonlinear optical phenomena in nanoparticles.
A cut finite element method for the Bernoulli free boundary value problem
National Research Council Canada - National Science Library
Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G; Larsson, Karl
2017-01-01
We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion...
On modelling three-dimensional piezoelectric smart structures with boundary spectral element method
Zou, Fangxin; Aliabadi, M. H.
2017-05-01
The computational efficiency of the boundary element method in elastodynamic analysis can be significantly improved by employing high-order spectral elements for boundary discretisation. In this work, for the first time, the so-called boundary spectral element method is utilised to formulate the piezoelectric smart structures that are widely used in structural health monitoring (SHM) applications. The resultant boundary spectral element formulation has been validated by the finite element method (FEM) and physical experiments. The new formulation has demonstrated a lower demand on computational resources and a higher numerical stability than commercial FEM packages. Comparing to the conventional boundary element formulation, a significant reduction in computational expenses has been achieved. In summary, the boundary spectral element formulation presented in this paper provides a highly efficient and stable mathematical tool for the development of SHM applications.
Hong, C. P.; Umeda, T.; Kimura, Y.
1984-01-01
A new numerical model, which is based on the boundary element method, was proposed for the simulation of solidification problems, and its application was demonstrated for solidification of metals in metal and sand molds. Comparisons were made between results from this model and those from the explicit finite difference method. Temperature recovery method was successfully adopted to estimate the liberation of latent heat of freezing in the boundary element method. A coupling method was proposed for problems in which the boundary condition of the interface consisting of inhomogeneous bodies is governed by Newton’s law of cooling in the boundary element method. It was concluded that the boundary element method which has several advantages, such as the wide variety of element shapes, simplicity of data preparation, and small CPU times, will find wide application as an alternative for finite difference or finite element methods, in the fields of solidification problems, especially for complex, three-dimensional geometries.
Johnson, Anthony N; Hromadka, T V
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
Kruyt, Nicolaas P.; Cuvelier, C.; Segal, A.; van der Zanden, J.
1988-01-01
In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method.
Gravenkamp, Hauke; Prager, Jens; Saputra, Albert A; Song, Chongmin
2012-09-01
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries
Simone, A.; Duarte, C. A.; Van der Giessen, E.
2006-01-01
We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of
Korobanov, Yurii M.; Lishchuk, Ohnieslav M.; Lishchuk, Ivan M.
2014-01-01
The generalization of theoretical bases for engineering calculations of ship structures in the Ukrainian computer-aided design systems is performed. The mathematical base of the boundary elements method is set out; the boundary integral equation is presented. The method of fictitious loads is considered as the basis of ship structures calculation realization.
DEFF Research Database (Denmark)
Cutanda Henríquez, Vicente; Juhl, Peter Møller
2008-01-01
It is well known that the Boundary Element Method (BEM) in its standard version cannot readily handle situations where the calculation point is very close to a surface. These problems are found: i) when two boundary surfaces are very close together, such as in narrow gaps and thin bodies, and ii)...
Directory of Open Access Journals (Sweden)
Dina V. Lazareva
2015-06-01
Full Text Available A new mathematical model of asymmetric support structure frame type is built on the basis of numerical-analytical boundary elements method (BEM. To describe the design scheme used is the graph theory. Building the model taken into account is the effect of frame members restrained torsion, which presence is due to the fact that these elements are thin-walled. The built model represents a real object as a two-axle semi-trailer platform. To implement the BEM algorithm obtained are analytical expressions of the fundamental functions and vector load components. The effected calculations are based on the semi-trailer two different models, using finite elements and boundary elements methods. The analysis showed that the error between the results obtained on the basis of two numerical methods and experimental data is about 4%, that indicates the adequacy of the proposed mathematical model.
A Hybrid Boundary Element-Finite Volume Method for Unsteady Transonic Airfoil Flows
Hu, Hong; Kandil, Osama A.
1996-01-01
A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.
Application of a boundary element method to the study of dynamical torsion of beams
Czekajski, C.; Laroze, S.; Gay, D.
1982-01-01
During dynamic torsion of beam elements, consideration of nonuniform warping effects involves a more general technical formulation then that of Saint-Venant. Nonclassical torsion constants appear in addition to the well known torsional rigidity. The adaptation of the boundary integral element method to the calculation of these constants for general section shapes is described. The suitability of the formulation is investigated with some examples of thick as well as thin walled cross sections.
Stress Wave Propagation in Soils Modelled by the Boundary Element Method
DEFF Research Database (Denmark)
Rasmussen, K. M.
This thesis deals with different aspects of the boundary element method (BEM) applied to stress wave propagation problems in soils. Among other things BEM formulations for coupled FEM and BEM, moving loads, direct BEM and indirect BEM are presented. For all the formulations both analytical...
Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method
Directory of Open Access Journals (Sweden)
Luiz Carlos Facundo Sanches
2007-01-01
Full Text Available A direct version of the boundary element method (BEM is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs. Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane and for the out-of-plane state (bending. These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs. A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM.
An accurate boundary element method for the exterior elastic scattering problem in two dimensions
Bao, Gang; Xu, Liwei; Yin, Tao
2017-11-01
This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.
The Boundary Element Method Applied to the Two Dimensional Stefan Moving Boundary Problem
1991-03-15
ier Wirmelcitung," S.-B. \\Vein. Akad. Mat. Natur., 98: 173-484 (1889). 22.-. "flber (lie Theorie der Eisbildung insbesondere fiber die lisbildung im...and others. "Moving Boundary Problems in Phase Change Mod- els," SIGNUM Newsletter, 20: 8-12 (1985). 21. Stefan, J. "Ober einige Probleme der Theorie
Free surface simulation of a two-layer fluid by boundary element method
Directory of Open Access Journals (Sweden)
Weoncheol Koo
2010-09-01
Full Text Available A two-layer fluid with free surface is simulated in the time domain by a two-dimensional potential-based Numerical Wave Tank (NWT. The developed NWT is based on the boundary element method and a leap-frog time integration scheme. A whole domain scheme including interaction terms between two layers is applied to solve the boundary integral equation. The time histories of surface elevations on both fluid layers in the respective wave modes are verified with analytic results. The amplitude ratios of upper to lower elevation for various density ratios and water depths are also compared.
International Symposium on Boundary Element Methods : Advances in Solid and Fluid Mechanics
Tseng, Kadin
1990-01-01
The Boundary Element Method (BEM) has become established as an effective tool for the solutions of problems in engineering science. The salient features of the BEM have been well documented in the open literature and therefore will not be elaborated here. The BEM research has progressed rapidly, especially in the past decade and continues to evolve worldwide. This Symposium was organized to provide an international forum for presentation of current research in BEM for linear and nonlinear problems in solid and fluid mechanics and related areas. To this end, papers on the following topics were included: rotary wing aerodynamics, unsteady aerodynamics, design and optimization, elasticity, elasto dynamics and elastoplasticity, fracture mechanics, acoustics, diffusion and wave motion, thermal analysis, mathematical aspects and boundary/finite element coupled methods. A special session was devoted to parallel/vector supercomputing with emphasis on mas sive parallelism. This Symposium was sponsored by United ...
Implementation aspects of the Boundary Element Method including viscous and thermal losses
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2014-01-01
The implementation of viscous and thermal losses using the Boundary Element Method (BEM) is based on the Kirchhoff’s dispersion relation and has been tested in previous work using analytical test cases and comparison with measurements. Numerical methods that can simulate sound fields in fluids...... including losses are particularly interesting whenever small cavities and narrow passages are present, as is the case with many acoustic devices such as transducers and small audio appliances. The present paper describes current work aimed at improving the method by addressing some specific issues related...
Application of hybrid boundary element method: Example of semishperical ground inhomogeneity
Directory of Open Access Journals (Sweden)
Cvetković Nenad N.
2014-01-01
Full Text Available One new, so-called hybrid boundary element method (HBEM is presented in this paper. It is a recently proposed numerical method for stationary and quasi-stationary EM field analysis. The method application is illustrated on the example of solving the problem of modelling hemispherical ground inhomogeneity influence on grounding system. The applied procedure also includes using of quasi-stationary image-theory. The obtained results are compared with those ones based on using the Green’s function for the point source inside semi-spherical inhomogeneities as well as with the results obtained by applying COMSOL program package. [TR 33008
Dual reciprocity boundary element method for solving thermal wave model of bioheat transfer.
Liu, J; Lu, W
1997-12-01
The newly developed dual reciprocity boundary element method (DRBEM) was extended to solve the thermal wave model of bioheat transfer (TWMBT) and a practical algorithm was established. A preliminary simulation of the temperature evolution in a two dimensional zone under certain boundary conditions and micro wave heating was conducted as a numerical illustration for the method and some meaningful conclusions were drawn. The validity of DRBEM was testified through a comparison with finite difference method (FDM) under one-dimensional calculation. Owing to its unique advantages like not confined by the complex shape of biological bodies, no need of discretization of the inner domain, save vast CPU time and easy to deal with different bioheat models, DRBEM may become an important approach for predicting and controlling the transient temperature field of biological bodies under hyperthermia or hypothermia.
Simulation of electrochemical machining using the boundary element method with no saturation
Petrov, A. G.; Sanduleanu, S. V.
2016-10-01
The simulation of electrochemical machining (ECM) is based on determining the surface shape at each point in time. The change in the shape of the surface depends on the rate of the electrochemical dissolution of the metal (conducting material), which is assumed to be proportional to the electric field strength on the boundary of the workpiece. The potential of the electric field is a harmonic function outside the two domains—the tool electrode and the workpiece. Constant potentials are specified on the boundaries of the tool electrode and the workpiece. A scheme with no saturation in which the strength of the electric field created by the potential difference on the boundary of the workpiece is proposed. The scheme converges exponentially in the number of grid elements on the workpiece boundary. Given the rate of electrochemical dissolution, the workpiece boundary, which depends on time, is found. The numerical solutions are compared with exact solutions, examples of the ECM simulation are discussed, and the results are compared with those obtained by other numerical methods and the ones obtained using ECM machines.
A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics
Brovont, Aaron D.
The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.
Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics
Chaillat, Stéphanie; Darbas, Marion; Le Louër, Frédérique
2017-07-01
The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non-smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.
Sapountzakis, E. J.; Tsipiras, V. J.; Argyridi, A. K.
2015-10-01
In this paper a boundary element method (BEM) is developed for the torsional vibration problem of bars of arbitrary doubly symmetric constant cross section, taking into account the nonuniform warping and secondary torsional shear deformation effects (STSDE). The bar is subjected to arbitrarily distributed or concentrated dynamic torsional loading along its length, while its edges are subjected to the most general torsional and warping boundary conditions. Apart from the angle of twist, the primary angle of twist per unit length is considered as an additional 1-D degree of freedom in order to account for the STSDE in the equations of motion of the bar. The warping shear stress distribution and the pertinent secondary torsional rigidity are computed by satisfying local equilibrium considerations under dynamic conditions without adhering to assumptions of Thin Tube Theory (TTT). By employing a distributed mass model system accounting for rotatory and warping inertia, an initial boundary value and two boundary value problems with respect to the variable along the bar time-dependent 1-D kinematical components, to the primary and secondary warping functions, respectively, are formulated. The latter are solved employing a pure BE method, requiring exclusively boundary discretization of the bar's cross section. The numerical solution of the aforementioned initial boundary value problem is performed through a BE method leading to a system of differential equations with displacement only unknowns, which is solved using an efficient direct time integration technique. Additionally, for the free vibrations case, a generalized eigenvalue problem is formulated through a similar BE technique. The accuracy and reliability of the results is assessed by FEM solutions employing solid or shell modelling. Both open- and closed-shaped cross section bars are examined and the necessity to include nonuniform torsional and STSD effects in the dynamic analysis of bars is demonstrated.
A simplified two-dimensional boundary element method with arbitrary uniform mean flow
Directory of Open Access Journals (Sweden)
Bassem Barhoumi
2017-07-01
Full Text Available To reduce computational costs, an improved form of the frequency domain boundary element method (BEM is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation (BIE representation solves the two-dimensional convected Helmholtz equation (CHE and its fundamental solution, which must satisfy a new Sommerfeld radiation condition (SRC in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Greenâs kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole, dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation. Keywords: Two-dimensional convected Helmholtz equation, Two-dimensional convected Greenâs function, Two-dimensional convected boundary element method, Arbitrary uniform mean flow, Two-dimensional acoustic sources
E. Yari; H. Ghassemi
2016-01-01
The main objective of this paper is to provide an applied algorithm for analyzing propeller-shaft vibrations in marine vessels. Firstly an underwater marine vehicle has been analyzed at different speed in unsteady condition using the finite volume method. Based on the results of this analysis, flow field of marine vehicle (wake of stern) and velocity inlet to the marine propeller is extracted at different times. Propeller inlet flow field is applied in the boundary element code and usin...
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1997-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Multidirectional random wave diffraction in a real harbor by using 3-D boundary element method
Kumar, Prashant; Gulshan, Rajni
2017-10-01
The mathematical model is constructed based on 3-D Boundary Element Method (BEM) with the consideration of diffraction, reflection and refraction of multidirectional incident waves utilizing the Laplace equation in a complex geometry harbors. The geometry of the harbor is divided into bounded and open sea region. The partial reflection boundary with variable bathymetry is also considered to analyze the wave spectrum. A Mitsuyasu's wave spectrum is applied to estimate the wave spectrum with multidirectional incident waves. The current numerical approach is practically applied on realistic Pohang New Harbor (PNH), Pohang South Korea. The validation of numerical scheme is done by comparison of measurement data with simulation results at different port stations. Therefore, the current numerical approach is provide the efficient numerical tool to foster the prediction of wave-induced oscillation in a harbor with irregular geometry.
Simulations of micron-scale fracture using atomistic-based boundary element method
Wu, Xiaojie; Li, Xiantao
2017-12-01
A new formulation of a boundary element method (BEM) is proposed in this paper to simulate cracks at the micron scale. The main departure from the traditional BEMs is that the current model is derived from the underlying atomistic model, which involves the interactions of atoms at the scale of Angstroms. By using the lattice Green’s function, the new BEM formulation eliminates the excessive atomic degrees of freedom away from crack tips, and directly couples the process zones with the physical boundary conditions. We show that with such a drastic reduction, one can simulate brittle fracture process on the scale of microns, for which the entire system consists of a few billion atoms. We discuss several numerical issues to make the implementation more efficient. Examples will be presented for cracks in the bcc iron system.
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
2017-01-01
In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141-153, 2016), we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.
A simple finite element method for boundary value problems with a Riemann–Liouville derivative
Jin, Bangti
2016-02-01
© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-^{1} in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^{L2}(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.
Boundary element method applied to a gas-fired pin-fin-enhanced heat pipe
Energy Technology Data Exchange (ETDEWEB)
Andraka, C.E.; Knorovsky, G.A.; Drewien, C.A.
1998-02-01
The thermal conduction of a portion of an enhanced surface heat exchanger for a gas fired heat pipe solar receiver was modeled using the boundary element and finite element methods (BEM and FEM) to determine the effect of weld fillet size on performance of a stud welded pin fin. A process that could be utilized by others for designing the surface mesh on an object of interest, performing a conversion from the mesh into the input format utilized by the BEM code, obtaining output on the surface of the object, and displaying visual results was developed. It was determined that the weld fillet on the pin fin significantly enhanced the heat performance, improving the operating margin of the heat exchanger. The performance of the BEM program on the pin fin was measured (as computational time) and used as a performance comparison with the FEM model. Given similar surface element densities, the BEM method took longer to get a solution than the FEM method. The FEM method creates a sparse matrix that scales in storage and computation as the number of nodes (N), whereas the BEM method scales as N{sup 2} in storage and N{sup 3} in computation.
Fast Multipole Boundary Element Method for Three Dimensional Electromagnetic Scattering Problem
Wang, S B; Xiao, J J; Lin, Z F; Chan, C T
2012-01-01
We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary element method. Nystrom's quadrature rule with a triangular grid is employed to linearize the integral equations, which are then solved by using a right-preconditioned iterative method. We apply the fast multipole technique to accelerate the matrix-vector multiplications in the iterations. We demonstrate the broad applications and accuracy of this method with practical examples including dielectric, plasmonic and metallic objects. We then apply the method to investigate the plasmonic properties of a silver torus and a silver split-ring resonator under the incidence of an electromagnetic plane wave. We show the silver torus can be used as a trapping tool to bind small dielectric or metallic particles.
DEFF Research Database (Denmark)
Henriquez, Vicente Cutanda; Barrera Figueroa, Salvador; Juhl, Peter Møller
2008-01-01
The project Euromet-792 aims to investigate and improve methods for secondary free-field calibration of microphones. In this framework, the comparison method is being studied at DFM in relation to the more usual substitution method of microphone calibration. The design of the sound source...... is of particular importance to achieve a sound field that reaches both microphones with the same level and that is sufficiently uniform at the microphone positions, in order to reduce the effect of misalignment. An existing sound source has been modeled using the Boundary Element Method, and the simulations have...... been used to modify the source and make it suitable for this kind of calibration. It has been found that a central plug, already present in the device, can be re-shaped in such a way that makes the sound field on the microphone positions more uniform, even at rather high frequencies. Measurements have...
On the modeling of narrow gaps using the standard boundary element method
DEFF Research Database (Denmark)
Cutanda Henríquez, Vicente; Juhl, Peter Møller; Jacobsen, Finn
2001-01-01
Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin....... This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both...... with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers Like sound intensity probes and condenser microphones has...
Prediction of metallic nano-optical trapping forces by finite element-boundary integral method.
Pan, Xiao-Min; Xu, Kai-Jiang; Yang, Ming-Lin; Sheng, Xin-Qing
2015-03-09
The hybrid of finite element and boundary integral (FE-BI) method is employed to predict nano-optical trapping forces of arbitrarily shaped metallic nanostructures. A preconditioning strategy is proposed to improve the convergence of the iterative solution. Skeletonization is employed to speed up the design and optimization where iteration has to be repeated for each beam configuration. The radiation pressure force (RPF) is computed by vector flux of the Maxwell's stress tensor. Numerical simulations are performed to validate the developed method in analyzing the plasmonic effects as well as the optical trapping forces. It is shown that the proposed method is capable of predicting the trapping forces of complex metallic nanostructures accurately and efficiently.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Andersen, Peter Risby; Jensen, Jakob Søndergaard
2016-01-01
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses...
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Andersen, Peter Risby; Jensen, Jakob Søndergaard
2016-01-01
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses are app...
Transmission Loss Assessment for a Muffler by Boundary Element Method Approach
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Ovidiu Vasile
2010-01-01
Full Text Available This paper investigates the acoustic performance of two cases for reac-tive mufflers using Boundary Element Method (BEM analysis. Modeling procedures for accurate performance prediction had led to the devel-opment of new methods for practical muffler components in design. The transmission loss (TL is the more widely can be easily computed with a BEM analysis. The author presents an overview of the principles and theoretical formulation of BEM for predicting the transmission loss of a muffler, the pressure and velocity distribution on surfaces of muf-fler. At the end of the paper is presented a comparison of two cases of mufflers for transmission loss. The predicted results agreed in some limits with the experimental data published in literature.
Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method
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Mehdi Panji
2016-08-01
Full Text Available In this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method (BEM. The existing full-plane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.
Fu, Liwei; Frenner, Karsten; Osten, Wolfgang
2014-07-15
The scattering of electromagnetic waves from rough surfaces has been actively studied for more than a century now because of its involvement in vast application areas. In the past two decades, great advances have been made by incorporating multiple scattering effects into analytical approaches. However, no model can yet be applied to surfaces with arbitrary roughness. It is also very difficult to study the cross-polarization, shadowing, or multiple scattering effects. In order to study more fundamentally the interaction of polarized light with more general rough surfaces of general media, we have developed a rigorous numerical simulator to calculate the resulting speckle fields. The full Maxwell equations were solved using surface integral equations combined with a boundary element method. The rough surface was discretized by higher order quadrilateral edge elements. The effective tangential electric and magnetic fields in each element in terms of 10 edges were first solved. The scattered electric and magnetic fields everywhere in space were then calculated correspondingly. One of the great advantages of such a simulator is that both the near and far fields can be calculated directly. Preliminary results of different kinds of metallic structures are presented, by which the advantages of the method are demonstrated.
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Syarizal Fonna
2016-01-01
Full Text Available Many studies have suggested that the corrosion detection of reinforced concrete (RC based on electrical potential on concrete surface was an ill-posed problem, and thus it may present an inaccurate interpretation of corrosion. However, it is difficult to prove the ill-posed problem of the RC corrosion detection by experiment. One promising technique is using a numerical method. The objective of this study is to simulate the ill-posed problem of RC corrosion detection based on electrical potential on a concrete surface using the Boundary Element Method (BEM. BEM simulates electrical potential within a concrete domain. In order to simulate the electrical potential, the domain is assumed to be governed by Laplace’s equation. The boundary conditions for the corrosion area and the noncorrosion area of rebar were selected from its polarization curve. A rectangular reinforced concrete model with a single rebar was chosen to be simulated using BEM. The numerical simulation results using BEM showed that the same electrical potential distribution on the concrete surface could be generated from different combinations of parameters. Corresponding to such a phenomenon, this problem can be categorized as an ill-posed problem since it has many solutions. Therefore, BEM successfully simulates the ill-posed problem of reinforced concrete corrosion detection.
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Esteban Flores-Mendez
2012-01-01
Full Text Available This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.
Sound Radiation from a Loudspeaker Cabinet using the Boundary Element Method
DEFF Research Database (Denmark)
Fernandez Grande, Efren
Ideally, the walls of a loudspeaker cabinet are rigid. However, in reality, the cabinet is excited by the vibration of the loudspeaker units and by the acoustic pressure inside the cabinet. The radiation of sound caused by such vibration can influence the overall performance of the loudspeaker...... had been reported, based on subjective testing. This study aims to detect the reported problem. The radiation from the cabinet is calculated using the Boundary Element Method. The analysis examines both the frequency domain and the time domain characteristics (in other words, the steady state response...... and the impulse response) of the loudspeaker and the cabinet. A significant influence of the cabinet has been detected, which becomes especially apparent in the time domain, during the sound decay process....
OpenBEM - An open source Boundary Element Method software in Acoustics
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2010-01-01
OpenBEM is a collection of open source programs for solving the Helmholtz Equation using the Boundary Element Method. The collection is written in Matlab by the authors and contains codes for dealing with exterior and interior problems in two or three dimensions as well as implementation of axi......-symmetric and half-space problems. It also contains a number of improvements such a dealing with thin objects and close surfaces, meshing for 2D and axisymmetrical problems, analytical solutions for verification, and a number of additional functions. This paper gives an overview of the capabilities of the program...... with examples of its use. Previous research results where OpenBEM was employed will be mentioned....
PARALLEL ALGORITHM FOR THREE-DIMENSIONAL STOKES FLOW SIMULATION USING BOUNDARY ELEMENT METHOD
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D. G. Pribytok
2016-01-01
Full Text Available Parallel computing technique for modeling three-dimensional viscous flow (Stokes flow using direct boundary element method is presented. The problem is solved in three phases: sampling and construction of system of linear algebraic equations (SLAE, its decision and finding the velocity of liquid at predetermined points. For construction of the system and finding the velocity, the parallel algorithms using graphics CUDA cards programming technology have been developed and implemented. To solve the system of linear algebraic equations the implemented software libraries are used. A comparison of time consumption for three main algorithms on the example of calculation of viscous fluid motion in three-dimensional cavity is performed.
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Establishment. Process Technology and Safety Directorate)
1983-01-01
A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour.
Directory of Open Access Journals (Sweden)
Marco Gonzalez
Full Text Available Abstract The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs. The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.
Collins, J. D.; Volakis, John L.
1992-01-01
A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.
Computation of Aerodynamic Noise Radiated from Ducted Tail Rotor Using Boundary Element Method
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Yunpeng Ma
2017-01-01
Full Text Available A detailed aerodynamic performance of a ducted tail rotor in hover has been numerically studied using CFD technique. The general governing equations of turbulent flow around ducted tail rotor are given and directly solved by using finite volume discretization and Runge-Kutta time integration. The calculations of the lift characteristics of the ducted tail rotor can be obtained. In order to predict the aerodynamic noise, a hybrid method combining computational aeroacoustic with boundary element method (BEM has been proposed. The computational steps include the following: firstly, the unsteady flow around rotor is calculated using the CFD method to get the noise source information; secondly, the radiate sound pressure is calculated using the acoustic analogy Curle equation in the frequency domain; lastly, the scattering effect of the duct wall on the propagation of the sound wave is presented using an acoustic thin-body BEM. The aerodynamic results and the calculated sound pressure levels are compared with the known technique for validation. The sound pressure directivity and scattering effect are shown to demonstrate the validity and applicability of the method.
Multi-domain boundary element method for axi-symmetric layered linear acoustic systems
Reiter, Paul; Ziegelwanger, Harald
2017-12-01
Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.
Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction
Kontinos, Dean A.
1997-01-01
Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.
Niu, Jun; Ren, Yi; Liu, Qing Huo
2017-10-02
In this work, we propose a numerical solver combining the spectral element - boundary integral (SEBI) method with the periodic layered medium dyadic Green's function. The periodic layered medium dyadic Green's function is formulated under matrix representation. The surface integral equations (SIEs) are then implemented as the radiation boundary condition to truncate the top and bottom computation domain. After describing the interior computation domain with the vector wave equations, and treating the lateral boundaries with Bloch periodic boundary conditions, the whole computation domains are discretized with mixed-order Gauss- Lobatto-Legendre basis functions in the SEBI method. This method avoids the discretization of the top and bottom layered media, so it can be much more efficient than conventional methods. Numerical results validate the proposed solver with fast convergence throughout the whole computation domain and good performance for typical multiscale nano-optical applications.
Energy Technology Data Exchange (ETDEWEB)
Yokoi, T. [Building Research Institute, Tokyo (Japan); Sanchez-Sesma, F. [Universidad National Autonoma de Mexico, (Mexico). Institute de Ingenieria
1997-05-27
Formulation is introduced for discretizing a boundary integral equation into an indirect boundary element method for the solution of 3-dimensional topographic problems. Yokoi and Takenaka propose an analytical solution-capable reference solution (solution for the half space elastic body with flat free surface) to problems of topographic response to seismic motion in a 2-dimensional in-plane field. That is to say, they propose a boundary integral equation capable of effectively suppressing the non-physical waves that emerge in the result of computation in the wake of the truncation of the discretized ground surface making use of the wave field in a semi-infinite elastic body with flat free surface. They apply the proposed boundary integral equation discretized into the indirect boundary element method to solve some examples, and succeed in proving its validity. In this report, the equation is expanded to deal with 3-dimensional topographic problems. A problem of a P-wave vertically landing on a flat and free surface is solved by the conventional boundary integral equation and the proposed boundary integral equation, and the solutions are compared with each other. It is found that the new method, different from the conventional one, can delete non-physical waves from the analytical result. 4 figs.
Vitório, Paulo Cezar; Leonel, Edson Denner
2017-10-01
The structural design must ensure suitable working conditions by attending for safe and economic criteria. However, the optimal solution is not easily available, because these conditions depend on the bodies' dimensions, materials strength and structural system configuration. In this regard, topology optimization aims for achieving the optimal structural geometry, i.e. the shape that leads to the minimum requirement of material, respecting constraints related to the stress state at each material point. The present study applies an evolutionary approach for determining the optimal geometry of 2D structures using the coupling of the boundary element method (BEM) and the level set method (LSM). The proposed algorithm consists of mechanical modelling, topology optimization approach and structural reconstruction. The mechanical model is composed of singular and hyper-singular BEM algebraic equations. The topology optimization is performed through the LSM. Internal and external geometries are evolved by the LS function evaluated at its zero level. The reconstruction process concerns the remeshing. Because the structural boundary moves at each iteration, the body's geometry change and, consequently, a new mesh has to be defined. The proposed algorithm, which is based on the direct coupling of such approaches, introduces internal cavities automatically during the optimization process, according to the intensity of Von Mises stress. The developed optimization model was applied in two benchmarks available in the literature. Good agreement was observed among the results, which demonstrates its efficiency and accuracy.
1990-01-01
by the method of moments [1,3, 5,16,17). A plane wave is tapered to avoid edge effects from a finite surface using a Gaussian taper function which...Finite Element Methods in CAD: Electrical and Magnectic Fields, Springer-Verlag New York Inc., New York, 1987. [13] Shen, J. and A.A. Maradudin
Directory of Open Access Journals (Sweden)
Tongchun Li
2015-01-01
element is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.
Meng, Weijuan; Fu, Li-Yun
2017-08-01
The finite element method is a very important tool for modeling seismic wave propagation in complex media, but it usually consumes a large amount of memory which significantly decreases computational efficiency when solving large-scale seismic problems. Here, a modified finite element method (MFEM) is proposed to improve efficiency. Triangular elements are employed to mesh the topography and the discontinuous interface more flexibly. In the two-dimensional case, the Jacobian matrix is obtained by using three controlling points instead of all nodes in each element with MFEM, which separates the Jacobian matrix from the stiffness matrix. The kernel matrices of the stiffness matrix rather than the global matrix are stored, and memory requirements are thus reduced significantly. Meanwhile, the element-by-element scheme is adopted to spare large sparse matrices and make the program easily parallelized. A second-order perfectly matched layer (PML) is also implemented to eliminate artificial reflections. Finally, the accuracy and efficiency of our algorithm are validated by numerical tests.
Rockstuhl, Carsten; Salt, Martin Guy; Herzig, Hans-Peter
2008-01-01
The boundary-element method is applied to the interaction of light with resonant metallic nanoparticles. At a certain wavelength, excitation of a surface plasmon takes place, which leads to a resonantly enhanced near-field amplitude and a large scattering cross section. The resonance wavelength for different scatterer geometries is determined. Alteration of the scattering properties in the presence of other metallic nanoparticles is discussed. To treat this problem, a novel formulation of the...
Gravenkamp, Hauke; Birk, Carolin; Song, Chongmin
2014-07-01
This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior. Copyright © 2014 Elsevier B.V. All rights reserved.
A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions
Winter, M.; Schott, B.; Massing, A.; Wall, W. A.
2018-03-01
In this work a Nitsche-based imposition of generalized Navier conditions on cut meshes for the Oseen problem is presented. Other methods from literature dealing with the generalized Navier condition impose this condition by means of substituting the tangential Robin condition in a classical Galerkin way. These methods work fine for a large slip length coefficient but lead to conditioning and stability issues when it approaches zero. We introduce a novel method for the weak imposition of the generalized Navier condition which remains well-posed and stable for arbitrary choice of slip length, including zero. The method proposed here builds on the formulation done by [1]. They impose a Robin condition for the Poisson problem by means of Nitsche's method for an arbitrary combination of the Dirichlet and Neumann parts of the condition. The analysis conducted for the proposed method is done in a similar fashion as in [2], but is done here for a more general type of boundary condition. The analysis proves stability for all flow regimes and all choices of slip lengths. Also an L2-optimal estimate for the velocity error is shown, which was not conducted in the previously mentioned work. A numerical example is carried out for varying slip lengths to verify the robustness and stability of the method with respect to the choice of slip length. Even though proofs and formulations are presented for the more general case of an unfitted grid method, they can easily be reduced to the simpler case of a boundary-fitted grid with the removal of the ghost-penalty stabilization terms.
Maerten, F.; Maerten, L.; Pollard, D. D.
2014-11-01
Most analytical solutions to engineering or geological problems are limited to simple geometries. For example, analytical solutions have been found to solve for stresses around a circular hole in a plate. To solve more complex problems, mathematicians and engineers have developed powerful computer-aided numerical methods, which can be categorized into two main types: differential methods and integral methods. The finite element method (FEM) is a differential method that was developed in the 1950s and is one of the most commonly used numerical methods today. Since its development, other differential methods, including the boundary element method (BEM), have been developed to solve different types of problems. The purpose of this paper is to describe iBem3D, formally called Poly3D, a C++ and modular 3D boundary element computer program based on the theory of angular dislocations for modeling three-dimensional (3D) discontinuities in an elastic, heterogeneous, isotropic whole- or half-space. After 20 years and more than 150 scientific publications, we present in detail the formulation behind this method, its enhancements over the years as well as some important applications in several domains of the geosciences. The main advantage of using this formulation, for describing geological objects such as faults, resides in the possibility of modeling complex geometries without gaps and overlaps between adjacent triangular dislocation elements, which is a significant shortcoming for models using rectangular dislocation elements. Reliability, speed, simplicity, and accuracy are enhanced in the latest version of the computer code. Industrial applications include subseismic fault modeling, fractured reservoir modeling, interpretation and validation of fault connectivity and reservoir compartmentalization, depleted area and fault reactivation, and pressurized wellbore stability. Academic applications include earthquake and volcano monitoring, hazard mitigation, and slope
Yang, Jubiao; Yu, Feimi; Krane, Michael; Zhang, Lucy T
2018-01-01
In this work, a non-reflective boundary condition, the Perfectly Matched Layer (PML) technique, is adapted and implemented in a fluid-structure interaction numerical framework to demonstrate that proper boundary conditions are not only necessary to capture correct wave propagations in a flow field, but also its interacted solid behavior and responses. While most research on the topics of the non-reflective boundary conditions are focused on fluids, little effort has been done in a fluid-structure interaction setting. In this study, the effectiveness of the PML is closely examined in both pure fluid and fluid-structure interaction settings upon incorporating the PML algorithm in a fully-coupled fluid-structure interaction framework, the Immersed Finite Element Method. The performance of the PML boundary condition is evaluated and compared to reference solutions with a variety of benchmark test cases including known and expected solutions of aeroacoustic wave propagation as well as vortex shedding and advection. The application of the PML in numerical simulations of fluid-structure interaction is then investigated to demonstrate the efficacy and necessity of such boundary treatment in order to capture the correct solid deformation and flow field without the requirement of a significantly large computational domain.
Energy Technology Data Exchange (ETDEWEB)
Pereira, Luis Carlos Martins
1998-06-15
New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)
Directory of Open Access Journals (Sweden)
M. V. Ostrenko
2016-12-01
Full Text Available The purpose of the work. This paper offers the well founded mathematical model based on the applying of the finite element method, which allows more effective modeling of the eddy currents and losses in the tank of power transformers, reactors and elements of their constructions, caused by the dispersion fields. Research methods. Based on assumptions of equality to the zero of normal components of the magnetic and electric fields’ intensities in ferromagnetic half-space, this mathematical model enters the surface eddy current density in FEM equations. The obtained results. Conclusion that the offered mathematical model allows to calculate eddy currents and losses in the power transformers tank, reactors and elements of their constructions more effectively is done. Reduction in tens of times of the resulting system of equations is also arrived, that results to considerable decreasing of calculation time and computer resources without accuracy losses. Scientific novelty. The novelty of the offered mathematical model is the form that is comfortable for programmatic realization of the known surface impedance boundary condition describing the electromagnetic field distribution in a tank and construction elements and in addition these elements are represented as ferromagnetic conducting half-space. Practical importance. Examples of single-phase autotransformer 167MVA 345kV 161kV calculation in a program complex ELMAG - 3d software, created on the basis of the described method and in the program complex ANSYS software with the use of classic approach of solid modeling of transformer, demonstrate applicability and required accuracy of the described method in the context of problems of losses calculation in the tank and construction elements of power transformers.
Li, Qiang; Popov, Valentin L.
2017-08-01
Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation.
Ren, Shangjie; Dong, Feng
2016-06-28
Electrical capacitance tomography (ECT) is a non-destructive detection technique for imaging the permittivity distributions inside an observed domain from the capacitances measurements on its boundary. Owing to its advantages of non-contact, non-radiation, high speed and low cost, ECT is promising in the measurements of many industrial or biological processes. However, in the practical industrial or biological systems, a deposit is normally seen in the inner wall of its pipe or vessel. As the actual region of interest (ROI) of ECT is surrounded by the deposit layer, the capacitance measurements become weakly sensitive to the permittivity perturbation occurring at the ROI. When there is a major permittivity difference between the deposit and the ROI, this kind of shielding effect is significant, and the permittivity reconstruction becomes challenging. To deal with the issue, an interface and permittivity simultaneous reconstruction approach is proposed. Both the permittivity at the ROI and the geometry of the deposit layer are recovered using the block coordinate descent method. The boundary and finite-elements coupling method is employed to improve the computational efficiency. The performance of the proposed method is evaluated with the simulation tests. This article is part of the themed issue 'Supersensing through industrial process tomography'. © 2016 The Author(s).
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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.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Juhl, Peter Møller
2008-01-01
The project Euromet-792 aims to investigate and improve methods for secondary free-field calibration of microphones. In this framework, the comparison method is being studied at DFM in relation to the more usual substitution method of microphone calibration. The design of the sound source is of p...
Directory of Open Access Journals (Sweden)
Wan-You Li
2014-01-01
Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.
Ageev, A. I.; Golubkina, I. V.; Osiptsov, A. N.
2018-01-01
A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.
Harris, Chad T; Haw, Dustin W; Handler, William B; Chronik, Blaine A
2013-09-01
Eddy currents are generated in MR by the use of rapidly switched electromagnets, resulting in time varying and spatially varying magnetic fields that must be either minimized or corrected. This problem is further complicated when non-cylindrical insert magnets are used for specialized applications. Interruption of the coupling between an insert coil and the MR system is typically accomplished using active magnetic shielding. A new method of actively shielding insert gradient and shim coils of any surface geometry by use of the boundary element method for coil design with a minimum energy constraint is presented. This method was applied to shield x- and z-gradient coils for two separate cases: a traditional cylindrical primary gradient with cylindrical shield and, to demonstrate its versatility in surface geometry, the same cylindrical primary gradients with a rectangular box-shaped shield. For the cylindrical case this method produced shields that agreed with analytic solutions. For the second case, the rectangular box-shaped shields demonstrated very good shielding characteristics despite having a different geometry than the primary coils. Copyright © 2013 Elsevier Inc. All rights reserved.
Pettit, J R; Walker, A; Cawley, P; Lowe, M J S
2014-09-01
Commercially available Finite Element packages are being used increasingly for modelling elastic wave propagation problems. Demand for improved capability has resulted in a drive to maximise the efficiency of the solver whilst maintaining a reliable solution. Modelling waves in unbound elastic media to high levels of accuracy presents a challenge for commercial packages, requiring the removal of unwanted reflections from model boundaries. For time domain explicit solvers, Absorbing Layers by Increasing Damping (ALID) have proven successful because they offer flexible application to modellers and, unlike the Perfectly Matched Layers (PMLs) approach, they are readily implemented in most commercial Finite Element software without requiring access to the source code. However, despite good overall performance, this technique requires the spatial model to extend significantly outside the domain of interest. Here, a Stiffness Reduction Method (SRM) has been developed that operates within a significantly reduced spatial domain. The technique is applied by altering the damping and stiffness matrices of the system, inducing decay of any incident wave. Absorbing region variables are expressed as a function of known model constants, helping to apply the technique to generic elastodynamic problems. The SRM has been shown to perform significantly better than ALID, with results confirmed by both numerical and analytical means. Copyright © 2013 Elsevier B.V. All rights reserved.
Calculation of Head Related Transfer Functions of bats using the Boundary Element Method
DEFF Research Database (Denmark)
Juhl, Peter Møller; Cutanda Henriquez, Vicente; Vanderelst, Dieter
2009-01-01
Overskrift: ChiRoPing (Chiroptera, Robots, and Sonar) is an EU-funded research project aimed at understanding how bats use their echolocation perception ability and apply this knowledge to the design of new robotic senses. Four species of bats are selected for the study and models of their heads...... including minute details of ears, mouth and nose are obtained through CT scans. The project involves, among other things, the use of numerical methods on such scanned models to study the role of their features in the bat sensorial performance. As the bats operate at very high frequencies and as their ears...
A coupling procedure for modeling acoustic problems using finite elements and boundary elements
Coyette, J.; Vanderborck, G.; Steichen, W.
1994-01-01
Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where finite elements are used for a confined (bounded) fluid while boundary elements are selected for an e...
Legan, M. A.; Blinov, V. A.; Larichkin, A. Yu; Novoselov, A. N.
2017-10-01
Experimental study of hydraulic fracturing of thick-walled cylinders with a central circular hole was carried out using the machine that creates a high oil pressure. Experiments on the compression fracture of the solid cylinders by diameter and rectangular parallelepipeds perpendicular to the ends were carried out with a multipurpose test machine Zwick / Roell Z100. Samples were made of GF-177 material based on cement. Ultimate stresses in the material under study were determined for three types of stress state: under compression, with a pure shear on the surface of the hole under frecking conditions and under a compound stress state under conditions of diametral compression of a solid cylinder. The value of the critical stress intensity factor of GF-177 material was obtained. The modeling of the fracturing process taking into account the inhomogeneity of the stress state near the hole was carried out using the boundary elements method (in the variant of the fictitious load method) and the gradient fracture criterion. Calculation results of the ultimate pressure were compared with values obtained analytically on the basis of the Lame solution and with experimental data.
Energy Technology Data Exchange (ETDEWEB)
Salinas, F S; Lancaster, J L; Fox, P T [Research Imaging Center, University of Texas Health Science Center at San Antonio, San Antonio, TX 78229 (United States)
2009-06-21
Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.
Salinas, F S; Lancaster, J L; Fox, P T
2009-06-21
Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.
Directory of Open Access Journals (Sweden)
Roman Pohrt
2015-04-01
Full Text Available Using the concept of stress intensity factors, we suggest a way to include adhesion into boundary elements simulation of contacts. A local criterion concerning the maximum admissible surface stresses decides whether the adhesive bonds in particular grid points fail or not. By taking into account the grid spacing, a robust methodology is found. Validation is done using the theoretically derived cases of JKR adhesion.
Watanabe, M
2003-01-01
Elemental segregation to two types of boundaries in a low-alloy steel were studied by X-ray mapping using scanning transmission electron microscopy (STEM). To quantify the acquired X-ray maps, the zeta-factor method was applied, and then the compositional maps and the thickness map were obtained. Based on these quantified maps, further information about the analytical sensitivity of solute-element detection and the spatial resolution of segregation analysis were extracted. Furthermore, maps of the number of excess atoms on the boundary were also calculated from the compositional and thickness maps. It was concluded that Cr, Ni and Mo are co-segregated on the prior-austenite grain boundary and only Ni was segregated on the lath boundary. (orig.)
Mahya, M. J.; Sanny, T. A.
2017-04-01
Lembang and Cimandiri fault are active faults in West Java that thread people near the faults with earthquake and surface deformation risk. To determine the deformation, GPS measurements around Lembang and Cimandiri fault was conducted then the data was processed to get the horizontal velocity at each GPS stations by Graduate Research of Earthquake and Active Tectonics (GREAT) Department of Geodesy and Geomatics Engineering Study Program, ITB. The purpose of this study is to model the displacement distribution as deformation parameter in the area along Lembang and Cimandiri fault using 2-dimensional boundary element method (BEM) using the horizontal velocity that has been corrected by the effect of Sunda plate horizontal movement as the input. The assumptions that used at the modeling stage are the deformation occurs in homogeneous and isotropic medium, and the stresses that acted on faults are in elastostatic condition. The results of modeling show that Lembang fault had left-lateral slip component and divided into two segments. A lineament oriented in southwest-northeast direction is observed near Tangkuban Perahu Mountain separating the eastern and the western segments of Lembang fault. The displacement pattern of Cimandiri fault shows that Cimandiri fault is divided into the eastern segment with right-lateral slip component and the western segment with left-lateral slip component separated by a northwest-southeast oriented lineament at the western part of Gede Pangrango Mountain. The displacement value between Lembang and Cimandiri fault is nearly zero indicating that Lembang and Cimandiri fault are not connected each other and this area is relatively safe for infrastructure development.
Sirenko, Kostyantyn
2013-01-01
A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.
Ritz, Elizabeth; Mutlu, Ovunc; Pollard, David D.
2012-08-01
We present a two-dimensional displacement discontinuity method (DDM) in combination with a complementarity solver to simulate quasi-static slip on cracks as models for faults and fractures in an otherwise homogeneous, isotropic, linear elastic material. A complementarity algorithm enforces appropriate contact boundary conditions along the cracks so that variable friction and frictional strength can be included. This method accurately computes slip and opening distributions along the cracks, displacement and stress fields within the surrounding material, and stress intensity factors at the crack tips. The DDM with complementarity is a simple yet powerful tool to investigate many aspects of the mechanical behavior of faults and fractures in Earth's brittle crust. Implementation in Excel and Matlab enables easy saving, organization, and sharing.
Ren, Qinlong
2018-02-10
Efficient pumping of blood flow in a microfluidic device is essential for rapid detection of bacterial bloodstream infections (BSI) using alternating current (AC) electrokinetics. Compared with AC electroosmosis (ACEO) phenomenon, the advantage of AC electrothermal (ACET) mechanism is its capability of pumping biofluids with high electrical conductivities at a relatively high AC voltage frequency. In the current work, the microfluidic pumping of non-Newtonian blood flow using ACET forces is investigated in detail by modeling its multi-physics process with hybrid boundary element method (BEM) and immersed boundary-lattice Boltzmann method (IB-LBM). The Carreau-Yasuda model is used to simulate the realistic rheological behavior of blood flow. The ACET pumping efficiency of blood flow is studied in terms of different AC voltage magnitudes and frequencies, thermal boundary conditions of electrodes, electrode configurations, channel height, and the channel length per electrode pair. Besides, the effect of rheological behavior on the blood flow velocity is theoretically analyzed by comparing with the Newtonian fluid flow using scaling law analysis under the same physical conditions. The results indicate that the rheological behavior of blood flow and its frequency-dependent dielectric property make the pumping phenomenon of blood flow different from that of the common Newtonian aqueous solutions. It is also demonstrated that using a thermally insulated electrode could enhance the pumping efficiency dramatically. Besides, the results conclude that increasing the AC voltage magnitude is a more economical pumping approach than adding the number of electrodes with the same energy consumption when the Joule heating effect is acceptable. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.
Using reciprocity in Boundary Element Calculations
DEFF Research Database (Denmark)
Juhl, Peter Møller; Cutanda Henriquez, Vicente
2010-01-01
as the reciprocal radiation problem. The present paper concerns the situation of having a point source (which is reciprocal to a point receiver) at or near a discretized boundary element surface. The accuracy of the original and the reciprocal problem is compared in a test case for which an analytical solution......The concept of reciprocity is widely used in both theoretical and experimental work. In Boundary Element calculations reciprocity is sometimes employed in the solution of computationally expensive scattering problems, which sometimes can be more efficiently dealt with when formulated...
Directory of Open Access Journals (Sweden)
Yan-Lin Shao
2014-12-01
Full Text Available This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.
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
9th International Conference on Boundary Elements
Wendland, W; Kuhn, G
1987-01-01
This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conferen...
Inverse boundary element calculations based on structural modes
DEFF Research Database (Denmark)
Juhl, Peter Møller
2007-01-01
The inverse problem of calculating the flexural velocity of a radiating structure of a general shape from measurements in the field is often solved by combining a Boundary Element Method with the Singular Value Decomposition and a regularization technique. In their standard form these methods sol...
National Research Council Canada - National Science Library
Wan Cheng Yan Jin Mian Chen Guo-Sheng Jiang
2017-01-01
...） is demonstrated for the inhomogeneous body. Then the fictitious stress method is deployed to investigate the stresses for the multi-casing structure under non-uniform loading conditions and an irregular wellbore...
The Boundary Function Method. Fundamentals
Kot, V. A.
2017-03-01
The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.
1992-09-01
dof j. The K matrix is developed from material elastic stress -strain relations and linearized strain-displacement relations. During the collapse, the...Integral Equation Methods in Potential Theory and Elastostatics, Acedemic Press, New York (1977). 43 REFERENCES (Continued) 16. Anderson, D.C., Gaussian
Zimmerle, D.; Bernhard, R. J.
1985-01-01
An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.
Energy Technology Data Exchange (ETDEWEB)
Masuda, S.; Kasahara, Y.; Ashidate, I. [NKK Corp., Tokyo (Japan)
1996-12-31
In a high-speed boat of a type using hydrofoils, lifting force increases in proportion to square of its length, while displacement is proportional to the third power. Therefore, an idea has come up that speed of a large boat may be increased by combining the hydrofoils with a submerged body. In other words, the idea is to levitate a ship by using composite support consisting of buoyancy of the submerged body and lifting force caused by the hydrofoils. Insufficiency of the lifting force may be complemented by the buoyancy of the submerged body which increases in an equivalent rate as that in the displacement. However, combining a submerged body with hydrofoils render a problem that lifting force for hydrofoils decreases because of interactions among the submerged body, hydrofoils, and free surface. Therefore, assuming a model of a submerged body with a length of 85 m cruising at 40 kt, analysis was given on decrease in lifting force for hydrofoils due to interactions between the submerged and lifting body and free surface by using the boundary element method. As a result, it was verified that the lifting force for the hydrofoils decreases as a result of creation of a flow that decreases effective angle of attach of the hydrofoils. It was also made clear that making the submerging depth greater reduces the decrease in the lifting force. 9 refs., 14 figs., 1 tab.
Ghadyani, Hamid R.; Srinivasan, Subhadra; Pogue, Brian W.; Paulsen, Keith D.
2010-01-01
The quantification of total hemoglobin concentration (HbT) obtained from multi-modality image-guided near infrared spectroscopy (IG-NIRS) was characterized using the boundary element method (BEM) for 3D image reconstruction. Multi-modality IG-NIRS systems use a priori information to guide the reconstruction process. While this has been shown to improve resolution, the effect on quantitative accuracy is unclear. Here, through systematic contrast-detail analysis, the fidelity of IG-NIRS in quantifying HbT was examined using 3D simulations. These simulations show that HbT could be recovered for medium sized (20mm in 100mm total diameter) spherical inclusions with an average error of 15%, for the physiologically relevant situation of 2:1 or higher contrast between background and inclusion. Using partial 3D volume meshes to reduce the ill-posed nature of the image reconstruction, inclusions as small as 14mm could be accurately quantified with less than 15% error, for contrasts of 1.5 or higher. This suggests that 3D IG-NIRS provides quantitatively accurate results for sizes seen early in treatment cycle of patients undergoing neoadjuvant chemotherapy when the tumors are larger than 30mm. PMID:20720975
Boundary element simulation of petroleum reservoirs with hydraulically fractured wells
Pecher, Radek
The boundary element method is applied to solve the linear pressure-diffusion equation of fluid-flow in porous media. The governing parabolic partial differential equation is transformed into the Laplace space to obtain the elliptic modified-Helmholtz equation including the homogeneous initial condition. The free- space Green's functions, satisfying this equation for anisotropic media in two and three dimensions, are combined with the generalized form of the Green's second identity. The resulting boundary integral equation is solved by following the collocation technique and applying the given time-dependent boundary conditions of the Dirichlet or Neumann type. The boundary integrals are approximated by the Gaussian quadrature along each element of the discretized domain boundary. Heterogeneous regions are represented by the sectionally-homogeneous zones of different rock and fluid properties. The final values of the interior pressure and velocity fields and of their time-derivatives are found by numerically inverting the solutions from the Laplace space by using the Stehfest's algorithm. The main extension of the mostly standard BEM-procedure is achieved in the modelling of the production and injection wells represented by internal sources and sinks. They are treated as part of the boundary by means of special single-node and both-sided elements, corresponding to the line and plane sources respectively. The wellbore skin and storage effects are considered for the line and cylindrical sources. Hydraulically fractured wells of infinite conductivity are handled directly according to the specified constraint type, out of the four alternatives. Fractures of finite conductivity are simulated by coupling the finite element model of their 1D-interior with the boundary element model of their 2D- exterior. Variable fracture width, fractures crossing zone boundaries, ``networking'' of fractures, fracture-tip singularity handling, or the 3D-description are additional advanced
Finite element analysis of three dimensional crack growth by the use of a boundary element sub model
DEFF Research Database (Denmark)
Lucht, Tore
2009-01-01
A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...
Sound source reconstruction using inverse boundary element calculations
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo
2001-01-01
suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularisation is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov...... regularisation and parameter-choice methods not requiring an error norm estimate for choosing the right amount of regularisation. We demonstrate that the L-curve criterion is robust with respect to the errors in real measurement situations....
Sound source reconstruction using inverse boundary element calculations
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo
2003-01-01
for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors., In the present work the emphasis is on Tikhonov regularization...... and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work...
Quantum algorithms and the finite element method
Montanaro, Ashley; Pallister, Sam
2015-01-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution t...
Boundary element analysis of sound scattered by a moving surface
Myers, M. K.; Hausmann, J. S.
1990-01-01
A solution for the acoustic field scattered from a uniformly moving rigid body in the presence of a harmonic incident source has been obtained using a boundary integral method. A derivation of the Kirchhoff formula given by Farassat and Myers (1988) for moving surfaces forms the basis for the analysis, and the development of a boundary integral method for the solution of scattering problems from moving rigid bodies is described. Finite elements are used in conjunction with the Galerkin method in order to solve the integral equation that results from the Kirchhoff formula when the observer point is placed on the moving body surface. Once appropriate surface field values are known they are inserted back into the formula in order to predict the field scattered off the body. Tests, including the so called superposition method, are carried out in order to validate the technique and to establish some confidence in its accuracy. Application of the superposition method to moving bodies is presented, and results of the two approaches are discussed. Sample calculations of scattering from a simple body are presented to illustrate the effects of variations in relevant parameters.
Finite element solution theory for three-dimensional boundary flows
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
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
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses ar...
A coupled boundary element-finite difference solution of the elliptic modified mild slope equation
DEFF Research Database (Denmark)
Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.
2011-01-01
The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...
The boundary-domain integral method for elliptic systems
Pomp, Andreas
1998-01-01
This monograph gives a description of all algorithmic steps and a mathematical foundation for a special numerical method, namely the boundary-domain integral method (BDIM). This method is a generalization of the well-known boundary element method, but it is also applicable to linear elliptic systems with variable coefficients, especially to shell equations. The text should be understandable at the beginning graduate-level. It is addressed to researchers in the fields of numerical analysis and computational mechanics, and will be of interest to everyone looking at serious alternatives to the well-established finite element methods.
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
The nonconforming virtual element method
de Dios, B. Ayuso; Lipnikov, K.; Manzini, G
2014-01-01
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
Yang, Yongqin; Chen, Shaochun
2010-03-01
A new nonconforming triangular element for the equations of planar linear elasticity with pure traction boundary conditions is considered. By virtue of construction of the element, the discrete version of Korn's second inequality is directly proved to be valid. Convergence rate of the finite element methods is uniformly optimal with respect to [lambda]. Error estimates in the energy norm and L2-norm are O(h2) and O(h3), respectively.
Green's function and boundary elements of multifield materials
Qin, Qing-Hua
2007-01-01
Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically important challenges. You will benefit from the authors' thorough coverage of general principles for each topic, followed by detailed mathematical derivation and worked examples as well as tables and figures where appropriate. In-depth explanations of the concept of Green's function Coupled thermo-magneto-electro-elastic analysis Detailed mathematical derivation for Green's functions.
Energy Technology Data Exchange (ETDEWEB)
Helldoerfer, Bastian
2009-07-01
Many technical failures are caused by cracks. As a consequence fracture mechanical assessment becomes more and more important during the design of security-relevant components. The simulation of stable crackgrowth provides an essential contribution for understanding these failures and as a consequence for preventing these. In order to benefit from the advantages of the Boundary Element Method (BEM) in the field of fracture mechanical problems as well as from the numerical advantages of the Finite Element Methode (FEM) a combined simulation technique is applied within this work. Here the domain containing the crackfront is discretized with boundary elements, the remaining structure is meshed with finite elements. The direct coupling of both techniques is achieved by applying the Symmetric Galerkin BEM (SGBEM) leading to a stiffness formulation for the boundary element domain. The nonlinearity of crackgrowth requires an incremental simulation procedure. In each increment the state of stress has to be obtained firstly, whereon the fracture mechanical assessment within the framework of linear elastic fracture mechanics is carried out based on the results of the boundary element domain only. The simulation of stable crackgrowth is implemented within a predictor/corrector scheme. For increasing the efficiency several approaches were put into practice, e.g. the parallelization of the SGBEM-code, integrated submodel computations and the adaptive enlargement of the boundary element domain. Using ABAQUS it is shown exemplarily how to combine the boundary element based crackgrowth module with commercial FE-Systems. A series of examples underline the efficiency of the presented simulation technique. (orig.)
Jia, Pin; Cheng, Linsong; Huang, Shijun; Xu, Zhongyi; Xue, Yongchao; Cao, Renyi; Ding, Guanyang
2017-08-01
This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the
Partridge, P; Boundary Elements in Fluid Dynamics
1992-01-01
This book Boundary Elements in Fluid Dynamics is the second volume of the two volume proceedings of the International Conference on Computer Modelling of Seas and Coastal Regions and Boundary Elements and Fluid Dynamics, held in Southampton, U.K., in April 1992. The Boundary Element Method (BEM) is now fully established as an ac curate and successful technique for solving engineering problems in a wide range of fields. The success of the method is due to its advantages in data reduction, as only the boundary of the region is modelled. Thus moving boundaries may be more easily handled, which is not the case if domain methods are used. In addition, the method is easily able to model regions to extending to infinity. Fluid mechanics is traditionally one of the most challenging areas of engi neering, the simulation of fluid motion, particularly in three dimensions, is always a serious test for any numerical method, and is an area in which BEM analysis may be used taking full advantage of its special character...
Modelling of fabric draping: Finite elements versus a geometrical method
Lamers, E.A.D.; Wijskamp, Sebastiaan; Akkerman, Remko
2001-01-01
Thermoplastic composite materials can be processed by Rubber Press Forming at elevated temperatures. Process specific boundary conditions are difficult to incorporate in the classical geometric drape simulation methods. Therefore, a fabric reinforced fluid model was implemented in the Finite Element
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
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.
THERM3D -- A boundary element computer program for transient heat conduction problems
Energy Technology Data Exchange (ETDEWEB)
Ingber, M.S. [New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering
1994-02-01
The computer code THERM3D implements the direct boundary element method (BEM) to solve transient heat conduction problems in arbitrary three-dimensional domains. This particular implementation of the BEM avoids performing time-consuming domain integrations by approximating a ``generalized forcing function`` in the interior of the domain with the use of radial basis functions. An approximate particular solution is then constructed, and the original problem is transformed into a sequence of Laplace problems. The code is capable of handling a large variety of boundary conditions including isothermal, specified flux, convection, radiation, and combined convection and radiation conditions. The computer code is benchmarked by comparisons with analytic and finite element results.
Stochastic finite element method with simple random elements
Starkloff, Hans-Jörg
2008-01-01
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
Experimental validation of a boundary element solver for exterior acoustic radiation problems
Visser, Rene; Nilsson, A.; Boden, H.
2003-01-01
The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for
DEFF Research Database (Denmark)
Duggen, Lars; Lopes, Natasha; Willatzen, Morten
2011-01-01
The finite-element method (FEM) is used to simulate the photoacoustic signal in a cylindrical resonant photoacoustic cell. Simulations include loss effects near the cell walls that appear in the boundary conditions for the inhomogeneous Helmholtz equation governing the acoustic pressure. Reasonab...
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 ...
Design of Meteorological Element Detection Platform for Atmospheric Boundary Layer Based on UAV
Directory of Open Access Journals (Sweden)
Yonghong Zhang
2017-01-01
Full Text Available Among current detection methods of the atmospheric boundary layer, sounding balloon has disadvantages such as low recovery and low reuse rate, anemometer tower has disadvantages such as fixed location and high cost, and remote sensing detection has disadvantages such as low data accuracy. In this paper, a meteorological element sensor was carried on a six-rotor UAV platform to achieve detection of meteorological elements of the atmospheric boundary layer, and the influence of different installation positions of the meteorological element sensor on the detection accuracy of the meteorological element sensor was analyzed through many experiments. Firstly, a six-rotor UAV platform was built through mechanical structure design and control system design. Secondly, data such as temperature, relative humidity, pressure, elevation, and latitude and longitude were collected by designing a meteorological element detection system. Thirdly, data management of the collected data was conducted, including local storage and real-time display on ground host computer. Finally, combined with the comprehensive analysis of the data of automatic weather station, the validity of the data was verified. This six-rotor UAV platform carrying a meteorological element sensor can effectively realize the direct measurement of the atmospheric boundary layer and in some cases can make up for the deficiency of sounding balloon, anemometer tower, and remote sensing detection.
Nonconforming hp spectral element methods for elliptic problems
Indian Academy of Sciences (India)
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 ...
About the Finite Element Method Applied to Thick Plates
Directory of Open Access Journals (Sweden)
Mihaela Ibănescu
2006-01-01
Full Text Available The present paper approaches of plates subjected to transverse loads, when the shear force and the actual boundary conditions are considered, by using the Finite Element Method. The isoparametric finite elements create real facilities in formulating the problems and great possibilities in creating adequate computer programs.
Boundary element analysis on vector and parallel computers
Kane, J. H.
1994-01-01
Boundary element analysis (BEA) can be characterized as a numerical technique that generally shifts the computational burden in the analysis toward numerical integration and the solution of nonsymmetric and either dense or blocked sparse systems of algebraic equations. Researchers have explored the concept that the fundamental characteristics of BEA can be exploited to generate effective implementations on vector and parallel computers. In this paper, the results of some of these investigations are discussed. The performance of overall algorithms for BEA on vector supercomputers, massively data parallel single instruction multiple data (SIMD), and relatively fine grained distributed memory multiple instruction multiple data (MIMD) computer systems is described. Some general trends and conclusions are discussed, along with indications of future developments that may prove fruitful in this regard.
Perucchio, R.; Ingraffea, A. R.
1984-01-01
The establishment of the boundary element method (BEM) as a valid tool for solving problems in structural mechanics and in other fields of applied physics is discussed. The development of an integrated interactive computer graphic system for the application of the BEM to three dimensional problems in elastostatics is described. The integration of interactive computer graphic techniques and the BEM takes place at the preprocessing and postprocessing stages of the analysis process, when, respectively, the data base is generated and the results are interpreted. The interactive computer graphic modeling techniques used for generating and discretizing the boundary surfaces of a solid domain are outlined.
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...
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
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
An Immersed Boundary Method for Rigid Bodies
Bhalla, Amneet Pal Singh; Kallemov, Bakytzhan; Donev, Aleksandar; Griffith, Boyce
2014-11-01
The traditional immersed boundary (IB) method is a very flexible method for coupling elastic structures to fluid flow. When rigid bodies are modeled using an IB approach, a penalty method is usually employed to approximately enforce the rigidity of the body; this requires small time step sizes and leads to difficult-to-control errors in the solution. We develop a method that exactly enforces a rigidity constraint by solving a linear system coupling a standard semi-implicit discretization of the fluid equations with a rigidity constraint. We develop a preconditioned iterative solver that combines an approximate multigrid solver for the fluid problem with an approximate direct solver for the Schur complement system. We demonstrate the efficiency and study the accuracy of the method on several test problems for both zero and finite Reynolds numbers.
Numerical Methods for Free Boundary Problems
1991-01-01
About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...
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.
Numerical methods for hypersonic boundary layer stability
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Auken, Esben; Han, Muran; Li, Jianhui
2017-10-01
We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.
Directory of Open Access Journals (Sweden)
Rai Nath Kabindra Rajeev
2009-01-01
Full Text Available In this paper, the solution of the one dimensional moving boundary problem with periodic boundary conditions is obtained with the help of variational iterational method. By using initial and boundary values, the explicit solutions of the equations have been derived, which accelerate the rapid convergence of the series solution. The method performs extremely well in terms of efficiency and simplicity. The temperature distribution and the position of moving boundary are evaluated and numerical results are presented graphically.
Solution of Boundary-Value Problems using Kantorovich Method
Directory of Open Access Journals (Sweden)
Gusev A.A.
2016-01-01
Full Text Available We propose a computational scheme for solving the eigenvalue problem for an elliptic differential equation in a two-dimensional domain with Dirichlet boundary conditions. The solution is sought in the form of Kantorovich expansion over the basis functions of one of the independent variables with the second variable treated as a parameter. The basis functions are calculated as solutions of the parametric eigenvalue problem for an ordinary second-order differential equation. As a result, the initial problem is reduced to a boundary-value problem for a set of self-adjoint second-order differential equations for functions of the second independent variable. The discrete formulation of the problem is implemented using the finite element method with Hermite interpolation polynomials. The effciency of the calculation scheme is shown by benchmark calculations for a square membrane with a degenerate spectrum.
hp Spectral element methods for three dimensional elliptic problems ...
Indian Academy of Sciences (India)
Abstract. This is the first of a series of papers devoted to the study of h-p spec- tral element methods for solving three dimensional elliptic boundary value problems on non-smooth domains using parallel computers. In three dimensions there are three different types of singularities namely; the vertex, the edge and the ...
Variational Problems with Moving Boundaries Using Decomposition Method
Directory of Open Access Journals (Sweden)
Reza Memarbashi
2007-10-01
Full Text Available The aim of this paper is to present a numerical method for solving variational problems with moving boundaries. We apply Adomian decomposition method on the Euler-Lagrange equation with boundary conditions that yield from transversality conditions and natural boundary conditions.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
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.
Method Suitable for Updating the Boundary Condition of Continuous Beam Bridges
Cao, JianXin; Zheng, Honglan; Liu, Yang
2017-10-01
The boundary support conditions of continuous beam bridges play the great influence on the results of the structural analysis, but it is difficult to accurately model the boundaries owing to the complexity structure of constraint conditions. To address this issue, a parameterized method is proposed to update the boundary support conditions in this study. First, the connection stiffness at boundary is considered as the optimization variable, and then the optimization problem of updating the boundary conditions are described in detail based on the theory of finite element model updating. Second, for verifying the proposed method, a loading test was conducted on an actual three-span continuous beam bridge. With the proposed method, the discrepancy between the measured modal parameters and the analytical results are greatly reduced; therefore, it is shown that the proposed method is effective for updating the boundary support conditions of actual continuous beam bridges.
Seismic wave propagation in non-homogeneous elastic media by boundary elements
Manolis, George D; Rangelov, Tsviatko V; Wuttke, Frank
2017-01-01
This book focuses on the mathematical potential and computational efficiency of the Boundary Element Method (BEM) for modeling seismic wave propagation in either continuous or discrete inhomogeneous elastic/viscoelastic, isotropic/anisotropic media containing multiple cavities, cracks, inclusions and surface topography. BEM models may take into account the entire seismic wave path from the seismic source through the geological deposits all the way up to the local site under consideration. The general presentation of the theoretical basis of elastodynamics for inhomogeneous and heterogeneous continua in the first part is followed by the analytical derivation of fundamental solutions and Green's functions for the governing field equations by the usage of Fourier and Radon transforms. The numerical implementation of the BEM is for antiplane in the second part as well as for plane strain boundary value problems in the third part. Verification studies and parametric analysis appear throughout the book, as do both ...
Tissue-fluid interface analysis using biphasic finite element method.
Unnikrishnan, G U; Unnikrishnan, V U; Reddy, J N
2009-04-01
Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.
Direct displacement-based design of special composite RC shear walls with steel boundary elements
Directory of Open Access Journals (Sweden)
H. Kazemi
2016-06-01
Full Text Available Special composite RC shear wall (CRCSW with steel boundary elements is a kind of lateral force resisting structural system which is used in earthquake-prone regions. Due to their high ductility and energy dissipation, CRCSWs have been widely used in recent years by structural engineers. However, there are few studies in the literature on the seismic design of such walls. Although there are many studies in the literature on the Direct Displacement-Based Design (DDBD of RC structures, however, no study can be found on DDBD of CRCSWs. Therefore, the aim of present study is to evaluate the ability of DDBD method for designing CRCSWs. In this study, four special composite reinforced concrete shear walls with steel boundary elements of 4, 8, 12 and 16 story numbers were designed using the DDBD method for target drift of 2%. The seismic behavior of the four CRCSWs was studied using nonlinear time-history dynamic analyses. Dynamic analyses were performed for the mentioned walls using 7 selected earthquake records. The seismic design parameters considered in this study includes: lateral displacement profile, inelastic dynamic inter-story drift demand, failure pattern and the composite RC shear walls overstrength factor. For each shear wall, the overall overstrength factor was calculated by dividing the ultimate dynamic base shear demand (Vu by the base shear demand (Vd as per the Direct Displacement Based-Design (DDBD method. The results show that the DDBD method can be used to design CRCSWs safely in seismic regions with predicted behavior.
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.
Cojocaru, E.
2009-01-01
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic triangular elements may lead to an improved accuracy. Here we present a collection of elemental matrices evaluated analytically for quadratic triangular elements. They could be useful for the finite element method in advanced electromagnetics.
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.
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
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.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
Galerkin ﬁnite element methods for wave problems ... hp-Finite element method; continuous Galerkin methods; wave solutions; Gibbs' phenomenon. ... Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208 016, India; Institute of High Performance Computing, 1, Science Park Road, Singapore ...
Nonconforming mortar element methods: Application to spectral discretizations
Maday, Yvon; Mavriplis, Cathy; Patera, Anthony
1988-01-01
Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.
Development of CAD implementing the algorithm of boundary elements’ numerical analytical method
Directory of Open Access Journals (Sweden)
Yulia V. Korniyenko
2015-03-01
Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...... developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce...
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
Automatic Recognition of Element Classes and Boundaries in the Birdsong with Variable Sequences.
Directory of Open Access Journals (Sweden)
Takuya Koumura
Full Text Available Researches on sequential vocalization often require analysis of vocalizations in long continuous sounds. In such studies as developmental ones or studies across generations in which days or months of vocalizations must be analyzed, methods for automatic recognition would be strongly desired. Although methods for automatic speech recognition for application purposes have been intensively studied, blindly applying them for biological purposes may not be an optimal solution. This is because, unlike human speech recognition, analysis of sequential vocalizations often requires accurate extraction of timing information. In the present study we propose automated systems suitable for recognizing birdsong, one of the most intensively investigated sequential vocalizations, focusing on the three properties of the birdsong. First, a song is a sequence of vocal elements, called notes, which can be grouped into categories. Second, temporal structure of birdsong is precisely controlled, meaning that temporal information is important in song analysis. Finally, notes are produced according to certain probabilistic rules, which may facilitate the accurate song recognition. We divided the procedure of song recognition into three sub-steps: local classification, boundary detection, and global sequencing, each of which corresponds to each of the three properties of birdsong. We compared the performances of several different ways to arrange these three steps. As results, we demonstrated a hybrid model of a deep convolutional neural network and a hidden Markov model was effective. We propose suitable arrangements of methods according to whether accurate boundary detection is needed. Also we designed the new measure to jointly evaluate the accuracy of note classification and boundary detection. Our methods should be applicable, with small modification and tuning, to the songs in other species that hold the three properties of the sequential vocalization.
Automatic Recognition of Element Classes and Boundaries in the Birdsong with Variable Sequences.
Koumura, Takuya; Okanoya, Kazuo
2016-01-01
Researches on sequential vocalization often require analysis of vocalizations in long continuous sounds. In such studies as developmental ones or studies across generations in which days or months of vocalizations must be analyzed, methods for automatic recognition would be strongly desired. Although methods for automatic speech recognition for application purposes have been intensively studied, blindly applying them for biological purposes may not be an optimal solution. This is because, unlike human speech recognition, analysis of sequential vocalizations often requires accurate extraction of timing information. In the present study we propose automated systems suitable for recognizing birdsong, one of the most intensively investigated sequential vocalizations, focusing on the three properties of the birdsong. First, a song is a sequence of vocal elements, called notes, which can be grouped into categories. Second, temporal structure of birdsong is precisely controlled, meaning that temporal information is important in song analysis. Finally, notes are produced according to certain probabilistic rules, which may facilitate the accurate song recognition. We divided the procedure of song recognition into three sub-steps: local classification, boundary detection, and global sequencing, each of which corresponds to each of the three properties of birdsong. We compared the performances of several different ways to arrange these three steps. As results, we demonstrated a hybrid model of a deep convolutional neural network and a hidden Markov model was effective. We propose suitable arrangements of methods according to whether accurate boundary detection is needed. Also we designed the new measure to jointly evaluate the accuracy of note classification and boundary detection. Our methods should be applicable, with small modification and tuning, to the songs in other species that hold the three properties of the sequential vocalization.
A system boundary identification method for life cycle assessment
DEFF Research Database (Denmark)
Li, Tao; Zhang, Hongchao; Liu, Zhichao
2014-01-01
Life cycle assessment (LCA) is a useful tool for quantifying the overall environmental impacts of a product, process, or service. The scientific scope and boundary definition are important to ensure the accuracy of LCA results. Defining the boundary in LCA is difficult and there are no commonly...... of processes considered, and the gradient of the fitting curve trends to zero gradually. According to the threshold rules, a relatively accurate system boundary could be obtained.It is found from this research that the system boundary curve describes the growth of life cycle impact assessment (LCIA) results...... accepted scientific methods yet. The objective of this research is to present a comprehensive discussion of system boundaries in LCA and to develop an appropriate boundary delimitation method.A product system is partitioned into the primary system and interrelated subsystems. The hierarchical relationship...
A boundary element model for diffraction of water waves on varying water depth
Energy Technology Data Exchange (ETDEWEB)
Poulin, Sanne
1997-12-31
In this thesis a boundary element model for calculating diffraction of water waves on varying water depth is presented. The varying water depth is approximated with a perturbed constant depth in the mild-slope wave equation. By doing this, the domain integral which is a result of the varying depth is no longer a function of the unknown wave potential but only a function of position and the constant depth wave potential. The number of unknowns is the resulting system of equations is thus reduced significantly. The integration procedures in the model are tested very thoroughly and it is found that a combination of analytical integration in the singular region and standard numerical integration outside works very well. The gradient of the wave potential is evaluated successfully using a hypersingular integral equation. Deviations from the analytical solution are only found on the boundary or very close to, but these deviations have no significant influence on the accuracy of the solution. The domain integral is evaluated using the dual reciprocity method. The results are compared with a direct integration of the integral, and the accuracy is quite satisfactory. The problem with irregular frequencies is taken care of by the CBIEM (or CHIEF-method) together with a singular value decomposition technique. This method is simple to implement and works very well. The model is verified using Homma`s island as a test case. The test cases are limited to shallow water since the analytical solution is only valid in this region. Several depth ratios are examined, and it is found that the accuracy of the model increases with increasing wave period and decreasing depth ratio. Short waves, e.g. wind generated waves, can allow depth variations up to approximately 2 before the error exceeds 10%, while long waves can allow larger depth ratios. It is concluded that the perturbation idea is highly usable. A study of (partially) absorbing boundary conditions is also conducted. (EG)
Solution of potential flow past an elastic body using the boundary element technique
Taylor, Norma F.
1988-12-01
This thesis describes the development of a Fortran computer code which models the interaction between an incompressible, potential flow and a homogeneous, elastic structure. The boundary element technique was chosen because of its ability to numerically approximate both the fluid and structural behavior with a common definition of the fluid/structure boundary. The ability to accurately model solid and fluid boundaries can be quite important in the fields of aeroelasticity and structural analysis. The nature of these boundaries is what determines the final solution to a problem of fluid flow past an elastic body. Often the complexity of defining and tracking the boundary and its associated boundary conditions has led the user to assumptions of rigid bodies, and therefore rigid boundaries. Certainly the tasks of defining the domain grids for finite difference and finite element techniques have not simplified this process. In the computer code developed for this thesis the fluid and structural governing equations are simultaneously solved to determine the pressure about the structure and the corresponding elastic deformations. The deformations are applied to the original boundary, resulting in a new geometry. This new geometry is used to recalculate the pressure field about the structure, and the process is iterated until a final steady-state solution is obtained.
Unconstrained paving and plastering method for generating finite element meshes
Staten, Matthew L.; Owen, Steven J.; Blacker, Teddy D.; Kerr, Robert
2010-03-02
Computer software for and a method of generating a conformal all quadrilateral or hexahedral mesh comprising selecting an object with unmeshed boundaries and performing the following while unmeshed voids are larger than twice a desired element size and unrecognizable as either a midpoint subdividable or pave-and-sweepable polyhedra: selecting a front to advance; based on sizes of fronts and angles with adjacent fronts, determining which adjacent fronts should be advanced with the selected front; advancing the fronts; detecting proximities with other nearby fronts; resolving any found proximities; forming quadrilaterals or unconstrained columns of hexahedra where two layers cross; and establishing hexahedral elements where three layers cross.
Finite element method for eigenvalue problems in electromagnetics
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
Stability estimates for h-p spectral element methods for general ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
be noted that the method is assymptotically faster then the h-p finite element method. For problems with mixed boundary conditions we cannot use this stability theorem to parallelize our method since the factor in the stability estimate can grow as M4. To get around this problem we make the spectral element functions ...
A corrected solid boundary treatment method for Smoothed Particle Hydrodynamics
Chen, Yun-sai; Zheng, Xing; Jin, Shan-qin; Duan, Wen-yang
2017-04-01
Smoothed Particle Hydrodynamics method (SPH) has a good adaptability for simulating of free surface flow problems. However, there are some shortcomings of SPH which are still in open discussion. This paper presents a corrected solid boundary handling method for weakly compressible SPH. This improved method is very helpful for numerical stability and pressure distribution. Compared with other solid boundary handling methods, this corrected method is simpler for virtual ghost particle interpolation and the ghost particle evaluation relationship is clearer. Several numerical tests are given, like dam breaking, solitary wave impact and sloshing tank waves. The results show that the corrected solid boundary processing method can recover the spurious oscillations of pressure distribution when simulating the problems with complex geometry boundary.
DIFFERENT ELEMENT METHODS IN ENGINEERING PRACTICE
African Journals Online (AJOL)
2012-11-03
Nov 3, 2012 ... (or system) in the sense that the behavior at discrete number of ... squares method can be used in deriving the element equation. Whichever formulation approach is used, the result- ing element equation are solved using appropriate ma- trix solvers .... symmetric stiffness matrix, but also the non-essential.
Energy Technology Data Exchange (ETDEWEB)
Corcelli, S.A.; Kress, J.D.; Pratt, L.R.
1995-08-07
This paper develops and characterizes mixed direct-iterative methods for boundary integral formulations of continuum dielectric solvation models. We give an example, the Ca{sup ++}{hor_ellipsis}Cl{sup {minus}} pair potential of mean force in aqueous solution, for which a direct solution at thermal accuracy is difficult and, thus for which mixed direct-iterative methods seem necessary to obtain the required high resolution. For the simplest such formulations, Gauss-Seidel iteration diverges in rare cases. This difficulty is analyzed by obtaining the eigenvalues and the spectral radius of the non-symmetric iteration matrix. This establishes that those divergences are due to inaccuracies of the asymptotic approximations used in evaluation of the matrix elements corresponding to accidental close encounters of boundary elements on different atomic spheres. The spectral radii are then greater than one for those diverging cases. This problem is cured by checking for boundary element pairs closer than the typical spatial extent of the boundary elements and for those cases performing an ``in-line`` Monte Carlo integration to evaluate the required matrix elements. These difficulties are not expected and have not been observed for the thoroughly coarsened equations obtained when only a direct solution is sought. Finally, we give an example application of hybrid quantum-classical methods to deprotonation of orthosilicic acid in water.
Spectral analysis method for detecting an element
Blackwood, Larry G [Idaho Falls, ID; Edwards, Andrew J [Idaho Falls, ID; Jewell, James K [Idaho Falls, ID; Reber, Edward L [Idaho Falls, ID; Seabury, Edward H [Idaho Falls, ID
2008-02-12
A method for detecting an element is described and which includes the steps of providing a gamma-ray spectrum which has a region of interest which corresponds with a small amount of an element to be detected; providing nonparametric assumptions about a shape of the gamma-ray spectrum in the region of interest, and which would indicate the presence of the element to be detected; and applying a statistical test to the shape of the gamma-ray spectrum based upon the nonparametric assumptions to detect the small amount of the element to be detected.
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.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
Vorona Yu.V.
2015-12-01
Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
A Finite Element Removal Method for 3D Topology Optimization
Directory of Open Access Journals (Sweden)
M. Akif Kütük
2013-01-01
Full Text Available Topology optimization provides great convenience to designers during the designing stage in many industrial applications. With this method, designers can obtain a rough model of any part at the beginning of a designing stage by defining loading and boundary conditions. At the same time the optimization can be used for the modification of a product which is being used. Lengthy solution time is a disadvantage of this method. Therefore, the method cannot be widespread. In order to eliminate this disadvantage, an element removal algorithm has been developed for topology optimization. In this study, the element removal algorithm is applied on 3-dimensional parts, and the results are compared with the ones available in the related literature. In addition, the effects of the method on solution times are investigated.
System and method for free-boundary surface extraction
Algarni, Marei
2017-10-26
A method of extracting surfaces in three-dimensional data includes receiving as inputs three-dimensional data and a seed point p located on a surface to be extracted. The method further includes propagating a front outwardly from the seed point p and extracting a plurality of ridge curves based on the propagated front. A surface boundary is detected based on a comparison of distances between adjacent ridge curves and the desired surface is extracted based on the detected surface boundary.
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.
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.
A Review of Methods for Moving Boundary Problems
2009-07-01
numerical methods that can be used to approximate multiphase flow models (e.g. the Lattice - Boltzmann method (Frisch et al., 1986) and the particle finite...exist. Furthermore, direct evaluation of the surface force term is also feasi- ble as are related immersed boundary methods described in (Li and Ito...C oa st al an d H yd ra ul ic s La bo ra to ry ER D C /C H L TR -0 9- 10 Navigation Systems Research Program A Review of Methods for Moving Boundary
Li, Ping
2014-07-01
This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens\\' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing the total mesh elements. Furthermore, low frequency waves can be efficiently absorbed, and the field outside the truncation domain can be conveniently calculated using the same BI formulation. Numerical examples are benchmarked to demonstrate the accuracy and versatility of the proposed method.
Consolidating boundary methods for finding the eigenstates of billiards
Cohen, Doron; Lepore, Natasha; Heller, Eric J.
2001-01-01
The plane-wave decomposition method (PWDM), a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the Gauge Freedom Method (GFM) is derived from the BIM equations. This opens the way to further improvements in eigenstate search techn...
Consolidating boundary methods for finding the eigenstates of billiards
Energy Technology Data Exchange (ETDEWEB)
Cohen, Doron [Department of Physics, Ben-Gurion University, Beer-Sheva (Israel); Lepore, Natasha [Department of Physics, Harvard University, Cambridge, MA (United States); Heller, Eric J [Department of Physics, Harvard University, Cambridge, MA (United States)
2004-02-13
The plane-wave decomposition method, a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the gauge freedom method is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.
Efficient ghost cell reconstruction for embedded boundary methods
Rapaka, Narsimha; Al-Marouf, Mohamad; Samtaney, Ravi
2016-11-01
A non-iterative linear reconstruction procedure for Cartesian grid embedded boundary methods is introduced. The method exploits the inherent geometrical advantage of the Cartesian grid and employs batch sorting of the ghost cells to eliminate the need for an iterative solution procedure. This reduces the computational cost of the reconstruction procedure significantly, especially for large scale problems in a parallel environment that have significant communication overhead, e.g., patch based adaptive mesh refinement (AMR) methods. In this approach, prior computation and storage of the weightage coefficients for the neighbour cells is not required which is particularly attractive for moving boundary problems and memory intensive stationary boundary problems. The method utilizes a compact and unique interpolation stencil but also provides second order spatial accuracy. It provides a single step/direct reconstruction for the ghost cells that enforces the boundary conditions on the embedded boundary. The method is extendable to higher order interpolations as well. Examples that demonstrate the advantages of the present approach are presented. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1394-01.
Analysis of the role of diffraction in topographic site effects using boundary element techniques
Gomez, Juan; Restrepo, Doriam; Jaramillo, Juan; Valencia, Camilo
2013-10-01
The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.
Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow
Soliman, M. O.; Baker, A. J.
1981-08-01
The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.
Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry
DEFF Research Database (Denmark)
Volakis, John L.; Sertel, Kubilay; Jørgensen, Erik
2004-01-01
n this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons of volume integral equation formulations with the finite element-boundary integral method are given in terms...... of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications....
General method of boundary correction in kernel regression estimation
African Journals Online (AJOL)
Kernel estimators of both density and regression functions are not consistent near the nite end points of their supports. In other words, boundary eects seriously aect the performance of these estimators. In this paper, we combine the transformation and the reflection methods in order to introduce a new general method of ...
Analysis and Modeling of Boundary Layer Separation Method (BLSM).
Pethő, Dóra; Horváth, Géza; Liszi, János; Tóth, Imre; Paor, Dávid
2010-09-01
Nowadays rules of environmental protection strictly regulate pollution material emission into environment. To keep the environmental protection laws recycling is one of the useful methods of waste material treatment. We have developed a new method for the treatment of industrial waste water and named it boundary layer separation method (BLSM). We apply the phenomena that ions can be enriched in the boundary layer of the electrically charged electrode surface compared to the bulk liquid phase. The main point of the method is that the boundary layer at correctly chosen movement velocity can be taken out of the waste water without being damaged, and the ion-enriched boundary layer can be recycled. Electrosorption is a surface phenomenon. It can be used with high efficiency in case of large electrochemically active surface of electrodes. During our research work two high surface area nickel electrodes have been prepared. The value of electrochemically active surface area of electrodes has been estimated. The existence of diffusion part of the double layer has been experimentally approved. The electrical double layer capacity has been determined. Ion transport by boundary layer separation has been introduced. Finally we have tried to estimate the relative significance of physical adsorption and electrosorption.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
One-dimensional wave equation. First, we briefly discuss the Galerkin method that employs piecewise quadratic polynomials for the basis or interpolating functions. We will call this as G2FEM for ease of reference. Here, one would have three quadratic functions for each element (see Reddy 2001, for details). In figure 1, we ...
Image segmentation with a finite element method
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Steam generator tube rupture simulation using extended finite element method
Energy Technology Data Exchange (ETDEWEB)
Mohanty, Subhasish, E-mail: smohanty@anl.gov; Majumdar, Saurin; Natesan, Ken
2016-08-15
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
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.
Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times
Directory of Open Access Journals (Sweden)
Kosuke Hayashi
2012-06-01
Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
Mixed Finite Element Method for Melt Migration
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Energy Technology Data Exchange (ETDEWEB)
Feng, Xiaobing [Univ. of Tennessee, Knoxville, TN (United States)
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
DEFF Research Database (Denmark)
Andersen, Lars; Nielsen, Søren R. K.
2003-01-01
The paper deals with the boundary element method formulation of the steady-state wave propagation through elastic media due to a source moving with constant velocity. The Greens' function for the three-dimensional full-space is formulated in a local frame of reference following the source...... is approximated, but the error which is introduced in this way is insignificant. Numerical examples are given for a moving rectangular load on an elastic half-space. The result from a boundary element code based on the derived Green's function are compared with a semi-analytic solution....
Study on boundary search method for DFM mesh generation
Directory of Open Access Journals (Sweden)
Li Ri
2012-08-01
Full Text Available The boundary mesh of the casting model was determined by direct calculation on the triangular facets extracted from the STL file of the 3D model. Then the inner and outer grids of the model were identified by the algorithm in which we named Inner Seed Grid Method. Finally, a program to automatically generate a 3D FDM mesh was compiled. In the paper, a method named Triangle Contraction Search Method (TCSM was put forward to ensure not losing the boundary grids; while an algorithm to search inner seed grids to identify inner/outer grids of the casting model was also brought forward. Our algorithm was simple, clear and easy to construct program. Three examples for the casting mesh generation testified the validity of the program.
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
A multilevel correction adaptive finite element method for Kohn-Sham equation
Hu, Guanghui; Xie, Hehu; Xu, Fei
2018-02-01
In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.
A new boundary correction method for lung parenchyma
Liang, Junfang; Jiang, Huiqin; Ma, Ling; Liu, Yumin; Toshiya, Nakaguchi
2017-02-01
In order to repair the boundary depressions caused by juxtapleural nodules and improve the lung segmentation accuracy, we propose a new boundary correction method for lung parenchyma. Firstly, the top-hat filter is used to enhance the image contrast; Secondly, we employ the Ostu algorithm for image binarization; Thirdly, the connected component labeling algorithm is utilized to remove the main trachea; Fourthly, the initial mask image is obtained by morphological region filling algorithm; Fifthly, the boundary tracing algorithm is applied to extract the initial lung contour; Afterwards, we design a sudden change degree algorithm to modify the initial lung contour; Finally, the complete lung parenchyma image is obtained. The novelty is that sudden change degree algorithm can detect the inflection points more accurately than other methods, which contributes to repairing lung contour efficiently. The experimental results show that the proposed method can incorporate the juxtapleural nodules into the lung parenchyma effectively, and the precision is increased by 6.46% and 2.72% respectively compared with the other two methods, providing favorable conditions for the accurate detection of pulmonary nodules and having important clinical value.
Directory of Open Access Journals (Sweden)
Paul Eloe
2002-01-01
Full Text Available The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic.
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 ...
Mixed Finite Element Methods for Melt Migration
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
A goal-oriented adaptive finite element method with convergence rates
Mommer, M.S.; Stevenson, R.
2009-01-01
An adaptive finite element method is analyzed for approximating functionals of the solution of symmetric elliptic second order boundary value problems. We show that the method converges and derive a favorable upper bound for its convergence rate and computational complexity. We illustrate our
Space-time discontinuous Galerkin finite element method for inviscid gas dynamics
van der Ven, H.; van der Vegt, Jacobus J.W.; Bouwman, E.G.; Bathe, K.J.
2003-01-01
In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated
Variational finite element method to study the absorption rate of drug ...
African Journals Online (AJOL)
Methods: The finite element method has been used to obtain the solution of the mass diffusion equation with appropriate boundary conditions. The tissue absorption rate of drug has been taken as the decreasing function of drug concentration from the skin surface towards the target site. The concentration at nodal points ...
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
Modeling of Airfoil Trailing Edge Flap with Immersed Boundary Method
DEFF Research Database (Denmark)
Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær
2011-01-01
The present work considers incompressible flow over a 2D airfoil with a deformable trailing edge. The aerodynamic characteristics of an airfoil with a trailing edge flap is numerically investigated using computational fluid dynamics. A novel hybrid immersed boundary (IB) technique is applied...... to simulate the moving part of the trailing edge. Over the main fixed part of the airfoil the Navier-Stokes (NS) equations are solved using a standard body-fitted finite volume technique whereas the moving trailing edge flap is simulated with the immersed boundary method on a curvilinear mesh. The obtained...... results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing edge flap and flow control using trailing edge flap is an efficient way to regulate the aerodynamic loading on airfoils....
Mathematical theory of finite and boundary element methods
National Research Council Canada - National Science Library
Schatz, Alfred H; Thomée, Vidar; Wendland, W. L
1990-01-01
... ; V. Thomee ; W. L. Wendland. - Basel ; Boston Berlin : Birkhiiuser, 1990 (DMV-Seminar ; Bd. 15) ISBN 978-3-7643-2211-3 ISBN 978-3-0348-7630-8 (eBook) DOI 10.1007/978-3-0348-7630-8 NE: Schatz, A...
Energy Technology Data Exchange (ETDEWEB)
Yokoi, T. [Akita University, Akita (Japan). Mining College
1996-05-01
As a method of computation of wave fields in irregularly stratified media by use of the indirect boundary element method, an induction formula was proposed in a previous report, utilizing the reference solution representing the wave field in corresponding horizontally stratified media. This algorithm applies to other types of vibration source. In computation of a wave field with the focus in presence on the ground or in the ground, the algorithm is incorporated into the computation as a vector including the reference solution as a variable. There exists no need to modify the algorithm. Once the reference solution is obtained, the wave field in the irregularly stratified media is automatically constructed by the proposed algorithm. The wave field to be the reference solution to a point source in the horizontally stratified media, is determined when the solution is obtained of the frequency/wavenumber domain by use of the reflection/transmission matrix of Kennet (1983) and converted into the solution of the spatial domain by use of the discrete wavenumber representation of Bouchon and Aki (1977). 8 refs., 2 figs.
Final Report of the Project "From the finite element method to the virtual element method"
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.
The absorbing boundary method. III. Tunneling decay and scattering resonances
Bacskay, George; Nordholm, Sture
1980-02-01
The recently developed absorbing boundary method (ABM) is applied to the calculation of tunneling decay rates and corresponding shape resonances in the scattering cross section. The analysis is carried out in terms of the contribution to the density of states from the resonant region of the spatial domain. One-dimensional test calculations have been carried out using the ABM and several related continuum state methods. While the ABM produces practically useful predictions for the location and shape of the resonance lines, it cannot in its present forms match the accuracy of the best continuum state methods. We have compared results obtained by the ABM (SMA and ISMA), the R-matrix method, the recently developed CGFEM and Bloch corrected R-matrix method, the stabilization method of Hazi and Taylor, and a simple pseudo bound state method.
Energy Technology Data Exchange (ETDEWEB)
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.
Immersed molecular electrokinetic finite element method
Kopacz, Adrian M.; Liu, Wing K.
2013-07-01
A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier-Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid-structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
Well test imaging - a new method for determination of boundaries from well test data
Energy Technology Data Exchange (ETDEWEB)
Slevinsky, B.A.
1997-08-01
A new method has been developed for analysis of well test data, which allows the direct calculation of the location of arbitrary reservoir boundaries which are detected during a well test. The method is based on elements of ray tracing and information theory, and is centered on the calculation of an instantaneous {open_quote}angle of view{close_quote} of the reservoir boundaries. In the absence of other information, the relative reservoir shape and boundary distances are retrievable in the form of a Diagnostic Image. If other reservoir information, such as 3-D seismic, is available; the full shape and orientation of arbitrary (non-straight line or circular arc) boundaries can be determined in the form of a Reservoir Image. The well test imaging method can be used to greatly enhance the information available from well tests and other geological data, and provides a method to integrate data from multiple disciplines to improve reservoir characterization. This paper covers the derivation of the analytical technique of well test imaging and shows examples of application of the technique to a number of reservoirs.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Directory of Open Access Journals (Sweden)
T. Islam
2012-01-01
Full Text Available This paper presents an efficient model for estimation of soil electric resistivity with depth and layer thickness in a multilayer earth structure. This model is the improvement of conventional two-layer earth model including Wenner resistivity formulations with boundary conditions. Two-layer soil model shows the limitations in specific soil characterizations of different layers with the interrelationships between soil apparent electrical resistivity (ρ and several soil physical or chemical properties. In the multilayer soil model, the soil resistivity and electric potential at any points in multilayer anisotropic soil medium are expressed according to the variation of electric field intensity for geotechnical investigations. For most soils with varying layers, multilayer soil resistivity profile is therefore more suitable to get soil type, bulk density of compacted soil and to detect anomalous materials in soil. A boundary element formulation is implemented to show the multilayer soil model with boundary conditions in soil resistivity estimations. Numerical results of soil resistivity ratio and potential differences for different layers are presented to illustrate the application, accuracy, and efficiency of the proposed model. The nobility of the research is obtaining multilayer soil characterizations through soil electric properties in near surface soil profile.
Energy Technology Data Exchange (ETDEWEB)
Carpenter, D.C.
1998-01-01
This bibliography provides a list of references on finite element and related methods analysis in reactor physics computations. These references have been published in scientific journals, conference proceedings, technical reports, thesis/dissertations and as chapters in reference books from 1971 to the present. Both English and non-English references are included. All references contained in the bibliography are sorted alphabetically by the first author`s name and a subsort by date of publication. The majority of the references relate to reactor physics analysis using the finite element method. Related topics include the boundary element method, the boundary integral method, and the global element method. All aspects of reactor physics computations relating to these methods are included: diffusion theory, deterministic radiation and neutron transport theory, kinetics, fusion research, particle tracking in finite element grids, and applications. For user convenience, many of the listed references have been categorized. The list of references is not all inclusive. In general, nodal methods were purposely excluded, although a few references do demonstrate characteristics of finite element methodology using nodal methods (usually as a non-conforming element basis). This area could be expanded. The author is aware of several other references (conferences, thesis/dissertations, etc.) that were not able to be independently tracked using available resources and thus were not included in this listing.
New formulation of the discrete element method
Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon
2018-01-01
A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.
A Meshless Solution Method for Unsteady Flow with Moving Boundary
Directory of Open Access Journals (Sweden)
Jun Zhang
2014-02-01
Full Text Available Using the concept of overlapping mesh method for reference, a new method called as Overlapping Clouds of Points Method (OCPM is firstly proposed to simulate unsteady flow with moving boundary problems based on meshless method. Firstly, a set of static background discrete points is generated in the whole calculation zone. Secondly, moving discrete points are created around moving body. According to the initial position of moving object in the flow field, the two sets of discrete points can be overlapped. With the motion of moving objects in the calculation field, moving discrete points around the moving body will inherently move. The exchange of flow field information between static points and moving points is realized by the solution of the clouds of points made up of static and moving discrete points using weighted meshless method nearby overlapping boundary. Four cases including piston problem, NACA0012 airfoil vibration flow around a moving sphere in supersonic and multibody separation are given to verify accuracy and practicability of OCPM. The numerical results agree well with exact solution and experimental results, which shows that the proposed OCPM can be applied to the simulation of unsteady flow problem.
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
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.
Energy Technology Data Exchange (ETDEWEB)
Neki, I.; Tada, T. [Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo (Japan)
1996-12-31
This paper reports a method to develop a new finite element by source (FES) for a two-dimensional plane problem and a three-dimensional solid problem as a method to analyze ship body structures. The paper describes development of a plate bending element by using a similar method, and the fundamental principle thereof. The present method can prepare a finite element of an arbitrary shape by simply providing a contact point only on a boundary. It can also derive good calculation accuracy with less number of contact points and elements. These facts are shown by examples of analyses on a square plate, a triangle plate and a semi-circular plate. Particularly, since a plate bending problem has a large order of differential calculus in a governing equation, this method being a semi-analytical method derives a result with very good accuracy even with less number of contact points. A hypothetical boundary method or a hypothetical electric charge method presents not a very high accuracy even if a large number of contact points are provided. This is because the method hypothesizes only a bending moment vertical to the boundary, but does not consider a source of the moment relative to the boundary. In contrast, the present method hypothesizes both of bending and twisting as the sources, hence its accuracy is better than with the above two methods. 5 refs., 11 figs., 7 tabs.
An overview of integration methods for hypersingular boundary integrals
Energy Technology Data Exchange (ETDEWEB)
Lutz, E.; Ingraffea, A.R. (Cornell Univ., Ithaca, NY (United States)); Gray, L.J. (Oak Ridge National Lab., TN (United States))
1991-01-01
Several methods of analyzing the hypersignular gradient BIE have been developed recently. This paper is a review highlighting the numerous common aspects and several differences among the methods. Significant common aspects include (a) a regularization of constant and linear terms, (b) analysis of integration points near rather than on the surface, and (c) analysis of the neighborhood of the singular point rather than of individual elements. 26 refs.
Method for Achieving Irregular Boundary Area for Complete Fluidic Sprinkler
Liu, Junping; Yuan, Shouqi; Li, Hong; Zhu, Xingye
For resolving the problem of sprinkle repeated, overtaken and went beyond in irrigation, it is important to research the approach of irregular boundary area. The equation of range and flow for achieving the square and triangle spray were deduced. Pressure is proportional to range. Specific method of changing the sectional area was put forward for achieving square and triangle spray. Adopted MATLAB language editor to analyzing the theoretical relation and emulate for achieving square and triangle spray. The experiments of theory pressure were carried out. The results showed that the experimental value were consistent with the theoretical value.
Solution of higher order boundary value problems by spline methods
Chaurasia, Anju; Srivastava, P. C.; Gupta, Yogesh
2017-10-01
Spline solution of Boundary Value Problems has received much attention in recent years. It has proven to be a powerful tool due to the ease of use and quality of results. This paper concerns with the survey of methods that try to approximate the solution of higher order BVPs using various spline functions. The purpose of this article is to thrash out the problems as well as conclusions, reached by the numerous authors in the related field. We critically assess many important relevant papers, published in reputed journals during last six years.
Topological Design for Acoustic-Structure Interaction Problems with a Mixed Finite Element Method
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz...... acoustic-structure interaction problems are optimized to show the validity of the proposed method....
Singularity Preserving Numerical Methods for Boundary Integral Equations
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Application of finite-element-methods in food processing
DEFF Research Database (Denmark)
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....
Hybrid immersed interface-immersed boundary methods for AC dielectrophoresis
Energy Technology Data Exchange (ETDEWEB)
Hossan, Mohammad Robiul [School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920 (United States); Department of Engineering and Physics, University of Central Oklahoma, Edmond, OK 73034-5209 (United States); Dillon, Robert [Department of Mathematics, Washington State University, Pullman, WA 99164-3113 (United States); Dutta, Prashanta, E-mail: dutta@mail.wsu.edu [School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920 (United States)
2014-08-01
Dielectrophoresis, a nonlinear electrokinetic transport mechanism, has become popular in many engineering applications including manipulation, characterization and actuation of biomaterials, particles and biological cells. In this paper, we present a hybrid immersed interface–immersed boundary method to study AC dielectrophoresis where an algorithm is developed to solve the complex Poisson equation using a real variable formulation. An immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles and an immersed boundary method is used for the fluid equations and particle transport. The convergence of the proposed algorithm as well as validation of the hybrid scheme with experimental results is presented. In this paper, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, this study eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. A comparative study between Maxwell stress tensor and point dipole methods for computing dielectrophoretic forces are presented. The hybrid method is used to investigate the physics of dielectrophoresis in microfluidic devices using an AC electric field. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis. Our numerical results also show that electrically neutral particles form a chain parallel to the applied electric field irrespective of their initial orientation when an AC electric field is applied. This proposed hybrid numerical scheme will help to better understand dielectrophoresis and to design and optimize microfluidic devices.
Nonconforming finite element methods on quadrilateral meshes
Hu, Jun; Zhang, ShangYou
2013-12-01
It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated to these Gauss-Legendre points are not all linearly independent for usual expected polynomial spaces, which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature. The present paper proposes two families of nonconforming finite elements of any odd order and one family of nonconforming finite elements of any even order on quadrilateral meshes. Degrees of freedom are given for these elements, which are proved to be well-defined for their corresponding shape function spaces in a unifying way. These elements generalize three lower order nonconforming finite elements on quadrilaterals to any order. In addition, these nonconforming finite element spaces are shown to be full spaces which is somehow not discussed for nonconforming finite elements in literature before.
DEFF Research Database (Denmark)
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin
2017-01-01
We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler...... method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping...
Directory of Open Access Journals (Sweden)
Ping Zhang
2014-01-01
Full Text Available The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.
Superconvergence for tetrahedral quadratic finite element methods for elliptic equations
Brandts, J.H.; Krizek, M.
2005-01-01
For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of the domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This
A cartesian grid embedded boundary method for hyperbolic conservation laws
Energy Technology Data Exchange (ETDEWEB)
Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J.; Modiano, David
2004-10-03
We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L{sup 1} for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Energy Technology Data Exchange (ETDEWEB)
De Corato, M., E-mail: marco.decorato@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Slot, J.J.M., E-mail: j.j.m.slot@tue.nl [Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); Hütter, M., E-mail: m.huetter@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); D' Avino, G., E-mail: gadavino@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Maffettone, P.L., E-mail: pierluca.maffettone@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Hulsen, M.A., E-mail: m.a.hulsen@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands)
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
An embedded boundary method for viscous, conducting compressibleflow
Energy Technology Data Exchange (ETDEWEB)
Dragojlovic, Zoran; Najmabadi, Farrokh; Day, Marcus
2004-10-20
The evolution of an Inertial Fusion Energy (IFE) chamberinvolves a repetition of short, intense depositions of energy (fromtarget ignition) into a reaction chamber, followed by the turbulentrelaxation of that energy through shock waves and thermal conduction tothe vessel walls. We present an algorithm for 2D simulations of the fluidinside an IFE chamber between fueling repetitions. Our finite-volumediscretization for the Navier-Stokes equations incorporates a Cartesiangrid treatment for irregularly-shaped domain boundaries. The discreteconservative update is based on a time-explicit Godunov method foradvection, and a two-stage Runge-Kutta update for diffusion accommodatingstate-dependent transport properties. Conservation is enforced on cutcells along the embedded boundary interface using a local redistributionscheme so that the explicit time step for the combined approach isgoverned by the mesh spacing in the uniform grid. The test problemsdemonstrate second-order convergence of the algorithm on smooth solutionprofiles, and the robust treatment of discontinuous initial data in anIFE-relevant vessel geometry.
Functional Element Test Tool and Method
2001-07-03
functional element 6 involved in the run test case step 8 6 of a test. SAFE test tool 7 10 preferably operates in several selectable modes of...options 9 (e.g., data initiation buttons) are displayed as dictated by 10 each test case. The run test case step 86 is then performed 11 under...19 object functional element being tested during run test case step 20 8 6 would be maintained via SAFE test tool 10 for later 21 comparison or
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.
2013-10-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
A stabilised nonconforming finite element method for steady incompressible flows
Huang, Pengzhan; Feng, Xinlong; Liu, Demin
2012-02-01
A stabilised nonconforming finite element method for the steady incompressible flow problem with damping based on local Gauss integration is considered in this article. The method combines the nonconforming finite element method with the stabilised strategy. Moreover, the stability and error estimates are analysed. Finally, numerical results are shown to support the developed theory analysis. Compared with some classical, closely related mixed finite element methods, the results of the present method show its better performance than others.
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.
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
Stynes, Martin; Zhang, Zhimin
2017-01-01
This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed diffe...
Li, Huiping; He, Lianfang; Zhang, Chunzhi; Cui, Hongzhi
2016-04-01
The thermal physical parameters have significant effects on the calculation accuracy of physical fields, and the boundary heat transfer coefficient between the die and water is one of the most important thermal physical parameters in the hot stamping. In order to attain the boundary heat transfer coefficient, the testing devices and test procedures are designed according to the characteristic of heat transfer in the hot stamping die. A method of estimating the temperature-dependent boundary heat transfer coefficient is presented, and an inverse heat conduction software is developed based on finite element method, advance-retreat method and golden section method. The software is used to calculate the boundary heat transfer coefficient according to the temperatures measured by NiCr-NiSi thermocouples in the experiment. The research results show that, the convergence of the method given in the paper is well, the surface temperature of sample has a significant effect on the boundary heat transfer coefficient between the die and water. The boundary heat transfer coefficient increases as the surface temperature of sample reduces, and the variation is nonlinear.
Hu, Pan; Wu, Tao; Wang, Hui-Zhi; Qi, Xin-Zheng; Yao, Jie; Cheng, Xiao-Dong; Chen, Wei; Zhang, Ying-Ze
2017-02-01
To observe the effects of boundary conditions and connect conditions on biomechanics predictions in finite element (FE) pelvic models. Three FE pelvic models were constructed to analyze the effect of boundary conditions and connect conditions in the hip joint: an intact pelvic model assumed contact of the hip joint on both sides (Model I); and a pelvic model assumed the hip joint connecting surfaces fused together with (Model II) or without proximal femurs (Model III). The model was validated by bone surface strains obtained from strain gauges in an in vitro pelvic experiment. Vertical load was applied to the pelvic specimen, and the same load was simulated in the FE model. There was a strong correlation between the FE analysis results of Model I and the experimental results (R 2 = 0.979); meanwhile, the correlation coefficient and the linear regression function increased slightly with increasing load force. Comparing the three models, the stress values in the point near the pubic symphysis in Model III were 48.52 and 39.1% lower, respectively, in comparison with Models I and II. Furthermore, the stress values on the dome region of the acetabulum in Models II and III were 103.61 and 390.53% less than those of Model I. Besides, the posterior acetabular wall stress values of Model II were 197.15 and 305.17% higher than those of Models I and III, respectively. These findings suggest that the effect of the connect condition in the hip joint should not be neglected, especially in studies related to clinical applications. © 2017 Chinese Orthopaedic Association and John Wiley & Sons Australia, Ltd.
Solving the ECG forward problem by means of a meshless finite element method
Energy Technology Data Exchange (ETDEWEB)
Li, Z S [College of Electrical Engineering, Zhejiang University, Hangzhou (China); Zhu, S A [College of Electrical Engineering, Zhejiang University, Hangzhou (China); He Bin [Department of Biomedical Engineering, University of Minnesota, 7-105 NHH, Church Street, SE, Minneapolis, MN 55455 (United States)
2007-07-07
The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions. (note)
Abedi, Reza; Mudaliar, Saba
2017-12-01
We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous Galerkin discretization for arbitrary domains in spacetime. The elements are discretized with electric and magnetic basis functions that are discontinuous across all inter-element boundaries and can have arbitrary high and per element spacetime orders. When restricted to unstructured grids that satisfy a specific causality constraint, the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements. We numerically investigate the convergence properties of the method for 1D to 3D uniform grids for energy dissipation, an error relative to the exact solution, and von Neumann dissipation and dispersion errors. Two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Methods and results of boundary layer measurements on a glider
Nes, W. V.
1978-01-01
Boundary layer measurements were carried out on a glider under natural conditions. Two effects are investigated: the effect of inconstancy of the development of static pressure within the boundary layer and the effect of the negative pressure difference in a sublaminar boundary layer. The results obtained by means of an ion probe in parallel connection confirm those results obtained by means of a pressure probe. Additional effects which have occurred during these measurements are briefly dealt with.
Immersed boundary methods for particles in viscoelastic drilling muds
Krishnan, Sreenath; Shaqfeh, Eric; Iaccarino, Gianluca
2014-11-01
In fracture stimulation of oil and gas wells, polymeric solution with suspended solids (proppants) are pumped to prop open the fracture. The primary aim of our work is to understand the dynamics of such proppants under various flow conditions through numerical computations. The study is concerned with fully resolved simulations, wherein all scales associated with the particle motion and the flow are resolved. The present effort is based on the algorithm proposed by Patankar (CTR Annual Research Briefs 2001:185), i.e. the Immersed Boundary (IB) methods, in which the domain grids do not conform to particle geometry and for simplicity are chosen to be Cartesian. Since Cartesian grids cannot efficiently represent a fracture geometry, our focus is on the development of an IB method for viscoelastic flows in unstructured domain grids. This method is implemented in a massively parallel, unstructured finite-volume-based fluid solver developed at Stanford University. The main theme of the presentation will be the description of the algorithm, measures taken to enable efficient parallelization and transfer of information between the underlying fluid grid and the particle mesh. A number of flow simulations will be presented, which validates the accuracy and correctness of the algorithm.
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
Directory of Open Access Journals (Sweden)
Mohammad Maleki
2012-01-01
Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.
Matched Interface and Boundary Method for Elasticity Interface Problems
Wang, Bao; Xia, Kelin; Wei, Guo-Wei
2015-01-01
Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms. PMID:25914439
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
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.
2003-01-01
A Galerkin finite element scheme furnished with 1st-order Bayliss-Gunzberger-Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic material with diagonal permitivity tensor. The scheme is formulated using
An immersed-boundary method for conjugate heat transfer analysis
Energy Technology Data Exchange (ETDEWEB)
Song, Jeong Chul; Lee, Joon Sik [Seoul National University, Seoul (Korea, Republic of); Ahn, Joon [Kookmin University, Seoul (Korea, Republic of)
2017-05-15
An immersed-boundary method is proposed for the analysis of conjugate problems of convective heat transfer in conducting solids. In- side the solid body, momentum forcing is applied to set the velocity to zero. A thermal conductivity ratio and a heat capacity ratio, between the solid body and the fluid, are introduced so that the energy equation is reduced to the heat diffusion equation. At the solid fluid interface, an effective conductivity is introduced to satisfy the heat flux continuity. The effective thermal conductivity is obtained by considering the heat balance at the interface or by using a harmonic mean formulation. The method is first validated against the analytic solution to the heat transfer problem in a fully developed laminar channel flow with conducting solid walls. Then it is applied to a laminar channel flow with a heated, block-shaped obstacle to show its validity for geometry with sharp edges. Finally the validation for a curvilinear solid body is accomplished with a laminar flow through arrayed cylinders.
Simulating biofilm deformation and detachment with the immersed boundary method
Sudarsan, Rangarajan; Stockie, John M; Eberl, Hermann J
2015-01-01
We apply the immersed boundary (or IB) method to simulate deformation and detachment of a periodic array of wall-bounded biofilm colonies in response to a linear shear flow. The biofilm material is represented as a network of Hookean springs that are placed along the edges of a triangulation of the biofilm region. The interfacial shear stress, lift and drag forces acting on the biofilm colony are computed by using fluid stress jump method developed by Williams, Fauci and Gaver [Disc. Contin. Dyn. Sys. B 11(2):519-540, 2009], with a modified version of their exclusion filter. Our detachment criterion is based on the novel concept of an averaged equivalent continuum stress tensor defined at each IB point in the biofilm which is then used to determine a corresponding von Mises yield stress; wherever this yield stress exceeds a given critical threshold the connections to that node are severed, thereby signalling the onset of a detachment event. In order to capture the deformation and detachment behaviour of a bio...
Wave breaking over sloping beaches using a coupled boundary integral-level set method
Energy Technology Data Exchange (ETDEWEB)
Garzon, M.; Adalsteinsson, D.; Gray, L.; Sethian, J.A.
2003-12-08
We present a numerical method for tracking breaking waves over sloping beaches. We use a fully non-linear potential model for in-compressible, irrotational and inviscid flow, and consider the effects of beach topography on breaking waves. The algorithm uses a Boundary Element Method (BEM) to compute the velocity at the interface, coupled to a Narrow Band Level Set Method to track the evolving air/water interface, and an associated extension equation to update the velocity potential both on and off the interface. The formulation of the algorithm is applicable to two and three dimensional breaking waves; in this paper, we concentrate on two-dimensional results showing wave breaking and rollup, and perform numerical convergence studies and comparison with previous techniques.
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
An optimal adaptive finite element method for the Stokes problem
Kondratyuk, Y.; Stevenson, R.
2008-01-01
A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur
Survey of the status of finite element methods for partial differential equations
Temam, Roger
1986-01-01
The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.
Discrete element analysis methods of generic differential quadratures
Chen, Chang-New
2008-01-01
Presents generic differential quadrature, the extended differential quadrature and the related discrete element analysis methods. This book demonstrated their ability for solving generic scientific and engineering problems.
h-p Spectral element methods for three dimensional elliptic ...
Indian Academy of Sciences (India)
Keywords. Spectral element method; non-smooth domains; geometric mesh; vertex singularity; edge singularity; vertex-edge singularity; differentiability estimates; stability estimates; exponential accuracy.
Spectral/hp element methods: Recent developments, applications, and perspectives
DEFF Research Database (Denmark)
Xu, Hui; Cantwell, Chris; Monteserin, Carlos
2018-01-01
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation...... regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp...... element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element...
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
1991-01-01
The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.
Energy Technology Data Exchange (ETDEWEB)
Lundquist, K A [Univ. of California, Berkeley, CA (United States)
2010-05-12
Mesoscale models, such as the Weather Research and Forecasting (WRF) model, are increasingly used for high resolution simulations, particularly in complex terrain, but errors associated with terrain-following coordinates degrade the accuracy of the solution. Use of an alternative Cartesian gridding technique, known as an immersed boundary method (IBM), alleviates coordinate transformation errors and eliminates restrictions on terrain slope which currently limit mesoscale models to slowly varying terrain. In this dissertation, an immersed boundary method is developed for use in numerical weather prediction. Use of the method facilitates explicit resolution of complex terrain, even urban terrain, in the WRF mesoscale model. First, the errors that arise in the WRF model when complex terrain is present are presented. This is accomplished using a scalar advection test case, and comparing the numerical solution to the analytical solution. Results are presented for different orders of advection schemes, grid resolutions and aspect ratios, as well as various degrees of terrain slope. For comparison, results from the same simulation are presented using the IBM. Both two-dimensional and three-dimensional immersed boundary methods are then described, along with details that are specific to the implementation of IBM in the WRF code. Our IBM is capable of imposing both Dirichlet and Neumann boundary conditions. Additionally, a method for coupling atmospheric physics parameterizations at the immersed boundary is presented, making IB methods much more functional in the context of numerical weather prediction models. The two-dimensional IB method is verified through comparisons of solutions for gentle terrain slopes when using IBM and terrain-following grids. The canonical case of flow over a Witch of Agnesi hill provides validation of the basic no-slip and zero gradient boundary conditions. Specified diurnal heating in a valley, producing anabatic winds, is used to validate the
Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.
2018-01-01
We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.
Stein, David B.; Guy, Robert D; Thomases, Becca
2015-01-01
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given sm...
Wave Scattering in Heterogeneous Media using the Finite Element Method
2016-10-21
AFRL-AFOSR-JP-TR-2016-0086 Wave Scattering in Heterogeneous Media using the Finite Element Method Chiruvai Vendhan INDIAN INSTITUTE OF TECHNOLOGY...Scattering in Heterogeneous Media using the Finite Element Method 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-12-1-4026 5c. PROGRAM ELEMENT NUMBER 61102F 6...heterogeneous ocean acoustic waveguide. 15. SUBJECT TERMS Acoustics, Finite Element Methods , Wave propagation 16. SECURITY CLASSIFICATION OF: 17
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.
Modified Immersed Finite Element Method For Fully-Coupled Fluid-Structure Interations
Wang, Xingshi; Zhang, Lucy T.
2013-01-01
In this paper, we develop a “modified” immersed finite element method (mIFEM), a non-boundary-fitted numerical technique, to study fluid-structure interactions. Using this method, we can more precisely capture the solid dynamics by solving the solid governing equation instead of imposing it based on the fluid velocity field as in the original immersed finite element (IFEM). Using the IFEM may lead to severe solid mesh distortion because the solid deformation is been over-estimated, especially for high Reynolds number flows. In the mIFEM, the solid dynamics is solved using appropriate boundary conditions generated from the surrounding fluid, therefore produces more accurate and realistic coupled solutions. We show several 2-D and 3-D testing cases where the mIFEM has a noticeable advantage in handling complicated fluid-structure interactions when the solid behavior dominates the fluid flow. PMID:24223445
A finite difference method for free boundary problems
Fornberg, Bengt
2010-04-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.
Vessel Segmentation and Blood Flow Simulation Using Level-Sets and Embedded Boundary Methods
Energy Technology Data Exchange (ETDEWEB)
Deschamps, T; Schwartz, P; Trebotich, D; Colella, P; Saloner, D; Malladi, R
2004-12-09
In this article we address the problem of blood flow simulation in realistic vascular objects. The anatomical surfaces are extracted by means of Level-Sets methods that accurately model the complex and varying surfaces of pathological objects such as aneurysms and stenoses. The surfaces obtained are defined at the sub-pixel level where they intersect the Cartesian grid of the image domain. It is therefore straightforward to construct embedded boundary representations of these objects on the same grid, for which recent work has enabled discretization of the Navier-Stokes equations for incompressible fluids. While most classical techniques require construction of a structured mesh that approximates the surface in order to extrapolate a 3D finite-element gridding of the whole volume, our method directly simulates the blood-flow inside the extracted surface without losing any complicated details and without building additional grids.
Local deformation method for measuring element tension in space deployable structures
Directory of Open Access Journals (Sweden)
Belov Sergey
2017-01-01
Full Text Available The article describes the local deformation method to determine the tension of cord and thin membrane elements in space deployable structure as antenna reflector. Possible measuring instrument model, analytical and numerical solutions and experimental results are presented. The boundary effects on measurement results of metallic mesh reflector surface tension are estimated. The study case depicting non-uniform reflector surface tension is considered.
Vibration and Buckling Analysis of Moderately Thick Plates using Natural Element Method
Mohammad Etemadi; Fakhri Etemadi; Tayeb Pourreza
2015-01-01
Using natural element method (NEM), the buckling and the free vibration behaviors of moderate thick plates is studied here. The basis of NEM is natural neighbors and Voronoi cells concepts. The shape functions of nodes located in the domain is equal to the proportion of common natural neighbors area divided by area that related by each Voronoi cells. First step in analyzing the moderate thick plates is identification boundaries. This is done by nodes scattering on problem do...
Energy Technology Data Exchange (ETDEWEB)
Carrington, David Bradley [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Monayem, A. K. M. [Univ. of New Mexico, Albuquerque, NM (United States); Mazumder, H. [Univ. of New Mexico, Albuquerque, NM (United States); Heinrich, Juan C. [Univ. of New Mexico, Albuquerque, NM (United States)
2015-03-05
A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is a fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.
Immersed boundary peridynamics (IB/PD) method to simulate aortic dissection
Bhalla, Amneet Pal Singh; Griffith, Boyce
2016-11-01
Aortic dissection occurs when an intimal tear in the aortic wall propagates into the media to form a false lumen within the vessel wall. Rupture of the false lumen and collapse of the true lumen both carry a high risk of morbidity and mortality. Surgical treatment consists of either replacement of a portion of the aorta, or stent implantation to cover the affected segment. Both approaches carry significant risks: open surgical intervention is highly invasive, whereas stents can be challenging to implant and offer unclear long-term patient outcomes. It is also difficult to time optimally the intervention to ensure that the benefits of treatment outweigh its risks. In this work we develop innovative fluid-structure interaction (FSI) model combining elements from immersed boundary (IB) and peridynamics (PD) methods to simulate tears in membranes. The new approach is termed as IB/PD method. We use non-ordinary state based PD to represent material hyperelasticity. Several test problems are taken to validate peridynamics approach to model structural dynamics, with and without accounting for failure in the structures. FSI simulations using IB/PD method are compared with immersed finite element method (IB/FE) to validate the new hybrid approach. NIH Award R01HL117163 NSF Award ACI 1450327.
A Nash-Hörmander iteration and boundary elements for the Molodensky problem
DEFF Research Database (Denmark)
Costea, Adrian; Gimperlein, Heiko; Stephan, Ernst P.
2014-01-01
We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash–Hörmander iteration, solves a sequence of exterior oblique Robin problems...... and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate...... evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral.Aboundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem....
Leapfrog/finite element method for fractional diffusion equation.
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L (2)-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.
Review on Finite Element Method * ERHUNMWUN, ID ...
African Journals Online (AJOL)
ADOWIE PERE
Again, 3D printing is a complex process that involves phase changes, thermal interactions etc. It's again a coupled problem. There have been many alternative methods proposed in the recent decades. But their commercial applicability is yet to be proved. A recent trend has also been application of cloud-computing for FEM.
Shooting method for solution of boundary-layer flows with massive blowing
Liu, T.-M.; Nachtsheim, P. R.
1973-01-01
A modified, bidirectional shooting method is presented for solving boundary-layer equations under conditions of massive blowing. Unlike the conventional shooting method, which is unstable when the blowing rate increases, the proposed method avoids the unstable direction and is capable of solving complex boundary-layer problems involving mass and energy balance on the surface.
Fractal Two-Level Finite Element Method For Free Vibration of Cracked Beams
Directory of Open Access Journals (Sweden)
A.Y.T. Leung
1998-01-01
Full Text Available The fractal two-level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial program.
Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method
Directory of Open Access Journals (Sweden)
Mustafa Inc
2014-01-01
Full Text Available We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions. These results have been compared with the results that are obtained by variational iteration method (VIM, homotopy perturbation method (HPM, Adomian decomposition method (ADM, variation of parameters method (VPM, and homotopy analysis method (HAM. Obtained results show that our method is very effective.
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),
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
An immersed boundary method for fluid-structure interaction with compressible multiphase flows
Wang, Li; Currao, Gaetano M. D.; Han, Feng; Neely, Andrew J.; Young, John; Tian, Fang-Bao
2017-10-01
This paper presents a two-dimensional immersed boundary method for fluid-structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid-structure interaction coupling. In the flow solver, the compressible multiphase Navier-Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge-Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.
The Interpolating Element-Free Galerkin Method for 2D Transient Heat Conduction Problems
Directory of Open Access Journals (Sweden)
Na Zhao
2014-01-01
Full Text Available An interpolating element-free Galerkin (IEFG method is presented for transient heat conduction problems. The shape function in the moving least-squares (MLS approximation does not satisfy the property of Kronecker delta function, so an interpolating moving least-squares (IMLS method is discussed; then combining the shape function constructed by the IMLS method and Galerkin weak form of the 2D transient heat conduction problems, the interpolating element-free Galerkin (IEFG method for transient heat conduction problems is presented, and the corresponding formulae are obtained. The main advantage of this approach over the conventional meshless method is that essential boundary conditions can be applied directly. Numerical results show that the IEFG method has high computational accuracy.
Gabdullin, N.; Khan, S. H.
2017-10-01
Magnetic shape memory effect exhibited by certain alloys at room temperature is known for almost 20 years. The most studied MSM alloys are Ni-Mn-Ga alloys which exhibit up to 12% magnetic field-induced strain (change in shape) depending on microstructure. A multibillion cycle operation without malfunction along with their “smart” properties make them very promising for application in electromagnetic (EM) actuators and sensors. However, considerable twinning stress of MSM crystals resulting in magneto-mechanical hysteresis decreases the efficiency and output force of MSM actuators. Whereas twinning stress of conventional MSM crystals has been significantly decreased over the years, novel crystals with Type II twin boundaries (TBs) possess even lower twinning stress. Unfortunately, the microstructure of MSM crystals with very low twinning stress tends to be unstable leading to their rapid crack growth. Whilst this phenomenon has been studied experimentally, the magnetic field distribution in anisotropic single twin-boundary MSM elements has not been considered yet. This paper analyses the magnetic field distribution in two-variant single twin-boundary MSM elements and discusses its effects on magnetic field-induced stress acting on the twin boundary.
Chung, T. J. (Editor); Karr, Gerald R. (Editor)
1989-01-01
Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.
Parametric Instability of Static Shafts-Disk System Using Finite Element Method
Wahab, A. M.; Rasid, Z. A.; Abu, A.
2017-10-01
Parametric instability condition is an important consideration in design process as it can cause failure in machine elements. In this study, parametric instability behaviour was studied for a simple shaft and disk system that was subjected to axial load under pinned-pinned boundary condition. The shaft was modelled based on the Nelson’s beam model, which considered translational and rotary inertias, transverse shear deformation and torsional effect. The Floquet’s method was used to estimate the solution for Mathieu equation. Finite element codes were developed using MATLAB to establish the instability chart. The effect of additional disk mass on the stability chart was investigated for pinned-pinned boundary conditions. Numerical results and illustrative examples are given. It is found that the additional disk mass decreases the instability region during static condition. The location of the disk as well has significant effect on the instability region of the shaft.
The collocation method for first-kind boundary integral equations on polygonal regions
Yan, Yi
1990-01-01
In this paper the collocation method for first-kind boundary integral equations, by using piecewise constant trial functions with uniform mesh, is shown to be equivalent to a projection method for second-kind Fredholm equations. In a certain sense this projection is an interpolation projection. By introducing this technique of analysis, we particularly consider the case of polygonal boundaries. We give asymptotic error estimates in {L_2} norm on the boundaries, and some superconvergence results for the single layer potential.
A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods
Saether, E.; Yamakov, V.; Glaessgen, E.
2007-01-01
Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.
Element Free Lattice Boltzmann Method for Fluid-Flow Problems
Energy Technology Data Exchange (ETDEWEB)
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.
Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems
Directory of Open Access Journals (Sweden)
Muhammad Aslam Noor
2006-12-01
Full Text Available We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.
DEFF Research Database (Denmark)
Jung, Jaesoon; Kook, Junghwan; Goo, Seongyeol
2017-01-01
In this paper, an accurate and efficient numerical method for sound transmission analysis is presented. As an alternative to conventional numerical methods, such as the Finite Element Method (FEM), Boundary Element Method (BEM) and Statistical Energy Analysis (SEA), the FE-ERA method, which...... and efficiency of the FE-ERA method, a novel criterion for the optimal number of elementary radiators is proposed. The criterion is based on the radiator error index that is derived to estimate the accuracy of the computation with used number of radiators. Using the proposed criterion a radiator selection method...
Farhat, Charbel; Lakshminarayan, Vinod K.
2014-04-01
Embedded Boundary Methods (EBMs) for Computational Fluid Dynamics (CFD) are usually constructed in the Eulerian setting. They are particularly attractive for complex Fluid-Structure Interaction (FSI) problems characterized by large structural motions and deformations. They are also critical for flow problems with topological changes and FSI problems with cracking. For all of these problems, the alternative Arbitrary Lagrangian-Eulerian (ALE) methods are often unfeasible because of the issue of mesh crossovers. However for viscous flows, Eulerian EBMs for CFD do not track the boundary layers around dynamic rigid or flexible bodies. Consequently, the application of these methods to viscous FSI problems requires either a high mesh resolution in a large part of the computational fluid domain, or adaptive mesh refinement. Unfortunately, the first option is computationally inefficient, and the second one is labor intensive. For these reasons, an alternative approach is proposed in this paper for maintaining all moving boundary layers resolved during the simulation of a turbulent FSI problem using an EBM for CFD. In this approach, which is simple and computationally reasonable, the underlying non-body-fitted mesh is rigidly translated and/or rotated in order to track the rigid component of the motion of the dynamic obstacle. Then, the flow computations away from the embedded surface are performed using the ALE framework, and the wall boundary conditions are treated by the chosen Eulerian EBM for CFD. Hence, the solution of the boundary layer tracking problem proposed in this paper can be described as an ALE implementation of a given EBM for CFD. Its basic features are illustrated with the Large Eddy Simulation using a non-body-fitted mesh of a turbulent flow past an airfoil in heaving motion. Its strong potential for the solution of challenging FSI problems at reasonable computational costs is also demonstrated with the simulation of turbulent flows past a family of
Method of interior boundaries in a mixed problem of acoustic scattering
Directory of Open Access Journals (Sweden)
P. A. Krutitskii
1999-01-01
Full Text Available The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.
A Method of Assembling Wall or Floor Elements
DEFF Research Database (Denmark)
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...
Stability estimates for hp spectral element methods for general ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 113; Issue 4. Stability Estimates for ℎ- Spectral ... 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 ...
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
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.
Methods to prevent turbogenerators design elements defects
Directory of Open Access Journals (Sweden)
Валентина Володимирівна Шевченко
2016-11-01
Full Text Available The paper shows that the determination of a failure probability due to the design, technological and operational drawbacks, as well as due to the turbogenerators working time exceeding from statistics data is inaccurate. Machine park of turbogenerators being rather limited in number, the classification and the distribution of generators into groups is random. It can not be used in practice to identify the pre-emergency state of turbogenerators and their timely stop. Analysis and classification of most frequent defects of turbogenerators has been performed. Methods for assessing such defects and reduction of their development have been offered. The article notes that expenses should be taken into account when setting up a monitoring system to assess the state and to identify defects. Reduction of expenditures on both operating and new turbogenerators must be justified. Rapid return of investments must be ensured. The list of additional tests has been proposed: measurement of infrared radiation outside the body of the turbogenerator for the estimation of the thermal field distribution and the defects of gas coolers identification; vibroacoustic inspection of the stator core and casing to find out the defects in the suspension of the core in the stator casing; analysis of the impurities in the cooling gas and in the dry remains of the drainage products to detect the products of the steel core and the winding insulation wear; value measurement and establishment of the partial discharges formation position; research of vibrations to reveal the cracks in the shaft, circuiting in the rotor windings and defects in the bearings. The paper notes that at upgrading as power grows overall and mounting dimensions must be preserved so that the existing foundation could be used as well as the existing security systems. Therefore, when designing or upgrading turbogenerators with an increase in power it is necessary to introduce new design decisions
A general mixed boundary model reduction method for component mode synthesis
Voormeeren, S.N.; Van der Valk, P.L.C.; Rixen, D.J.
2010-01-01
A classic issue in component mode synthesis (CMS) methods is the choice for fixed or free boundary conditions at the interface degrees of freedom (DoF) and the associated vibration modes in the components reduction base. In this paper, a novel mixed boundary CMS method called the “Mixed
Finite-element method for above-core structures. [LMFBR
Energy Technology Data Exchange (ETDEWEB)
Kennedy, J.M.; Belytschko, T.B.
1979-12-01
Three-dimensional finite-element models for the treatment of the nonlinear, transient response of a fast breeder reactor's above-core structures are described. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and the deformable elements are treated by a corotational formulation in which the coordinate system is embedded in the elements. Deformable elements may be connected either to nodes directly or through rigid bodies. The time integration is carried out by the Newmark ..beta.. method. These features have been incorporated to form the finite-element program SAFE/RAS (Safety Analysis by Finite Elements/Reactor Analysis and Safety Division). Computations are presented for semianalytical comparisons, simple scoping studies, and Stanford Research Institute (SRI) test comparisons.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
Fai, Thomas; Kusters, Remy; Rycroft, Chris
2015-11-01
Our understanding of how neuronal connections in the brain are maintained and reorganized is being revolutionized by new experimental and computational techniques. Existing high-resolution 3D images show that neuronal axons often terminate onto micron-sized structures known as dendritic spines, which are characterized by their thin necks and bulbous heads. Vesicles containing membrane receptors must deform significantly to squeeze into the bulbous heads of the spines, but more quantitative estimates of the force and energy required are still lacking. We have used three-dimensional immersed boundary method simulations to capture the fluid dynamics of vesicle transport into spines. We vary the applied force and neck geometry to identify the region in phase space in which the vesicle can squeeze into the spine. These results are compared to pass-stuck diagrams computed previously in the case of vesicles squeezing through open channels with rigid walls. The resulting force estimates are found to be consistent with the physiological density of motor proteins. Resolving the thin lubricating layers between the vesicles and spine poses significant numerical challenges, and we have used elements from lubrication theory to help resolve these boundary layers.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
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.
Tsang, L.; Lou, S. H.; Chan, C. H.
1991-01-01
The extended boundary condition method is applied to Monte Carlo simulations of two-dimensional random rough surface scattering. The numerical results are compared with one-dimensional random rough surfaces obtained from the finite-element method. It is found that the mean scattered intensity from two-dimensional rough surfaces differs from that of one dimension for rough surfaces with large slopes.
van der Stelt, A.A.; Bor, Teunis Cornelis; Geijselaers, Hubertus J.M.; Quak, W.; Akkerman, Remko; Huetink, Han; Menary, G
2011-01-01
In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of the disc is clamped. Two numerical methods are used to
Methods and devices for fabricating and assembling printable semiconductor elements
Energy Technology Data Exchange (ETDEWEB)
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.
Analysis of Finite Element Methods for Vector Laplacians on Surfaces
Hansbo, Peter; Larson, Mats G.; Larsson, Karl
2016-01-01
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as elastic membranes and shells. The method is based on standard continuous parametric Lagrange elements with one order higher polynomial degree for the mapping. The tangent condition is weakly enforced using a penalization term. We derive error estimates that take...
Methods and devices for fabricating and assembling printable semiconductor elements
Energy Technology Data Exchange (ETDEWEB)
Nuzzo, Ralph G.; Rogers, John A.; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2017-09-12
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.
Integral method for the calculation of three-dimensional, laminar and turbulent boundary layers
Stock, H. W.
1978-01-01
The method for turbulent flows is a further development of an existing method; profile families with two parameters and a lag entrainment method replace the simple entrainment method and power profiles with one parameter. The method for laminar flows is a new development. Moment of momentum equations were used for the solution of the problem, the profile families were derived from similar solutions of boundary layer equations. Laminar and turbulent flows at the wings were calculated. The influence of wing tapering on the boundary layer development was shown. The turbulent boundary layer for a revolution ellipsoid is calculated for 0 deg and 10 deg incidence angles.
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Energy Technology Data Exchange (ETDEWEB)
McCorquodale, Peter; Colella, Phillip; Johansen, Hans
2001-03-14
We present an algorithm for solving the heat equation on irregular time-dependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (J. Comput. Phys. 147(2):60--85) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative. This leads to a method that is second-order accurate in space and time. For the case where the boundary is moving, we convert the moving-boundary problem to a sequence of fixed-boundary problems, combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves. We find that, in the moving boundary case, the use of Crank--Nicolson time discretization is unstable, requiring us to use the L{sub 0}-stable implicit Runge--Kutta method of Twizell, Gumel, and Arigu.
Immersed Boundary Methods for Optimization of Strongly Coupled Fluid-Structure Systems
Jenkins, Nicholas J.
Conventional methods for design of tightly coupled multidisciplinary systems, such as fluid-structure interaction (FSI) problems, traditionally rely on manual revisions informed by a loosely coupled linearized analysis. These approaches are both inaccurate for a multitude of applications, and they require an intimate understanding of the assumptions and limitations of the procedure in order to soundly optimize the design. Computational optimization, in particular topology optimization, has been shown to yield remarkable results for problems in solid mechanics using density interpolations schemes. In the context of FSI, however, well defined boundaries play a key role in both the design problem and the mechanical model. Density methods neither accurately represent the material boundary, nor provide a suitable platform to apply appropriate interface conditions. This thesis presents a new framework for shape and topology optimization of FSI problems that uses for the design problem the Level Set method (LSM) to describe the geometry evolution in the optimization process. The Extended Finite Element method (XFEM) is combined with a fictitiously deforming fluid domain (stationary arbitrary Lagrangian-Eulerian method) to predict the FSI response. The novelty of the proposed approach lies in the fact that the XFEM explicitly captures the material boundary defined by the level set iso-surface. Moreover, the XFEM provides a means to discretize the governing equations, and weak immersed boundary conditions are applied with Nitsche's Method to couple the fields. The flow is predicted by the incompressible Navier-Stokes equations, and a finite-deformation solid model is developed and tested for both hyperelastic and linear elastic problems. Transient and stationary numerical examples are presented to validate the FSI model and numerical solver approach. Pertaining to the optimization of FSI problems, the parameters of the discretized level set function are defined as explicit
A Boundary Element Solution to the Problem of Interacting AC Fields in Parallel Conductors
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Einar M. Rønquist
1984-04-01
Full Text Available The ac fields in electrically insulated conductors will interact through the surrounding electromagnetic fields. The pertinent field equations reduce to the Helmholtz equation inside each conductor (interior problem, and to the Laplace equation outside the conductors (exterior problem. These equations are transformed to integral equations, with the magnetic vector potential and its normal derivative on the boundaries as unknowns. The integral equations are then approximated by sets of algebraic equations. The interior problem involves only unknowns on the boundary of each conductor, while the exterior problem couples unknowns from several conductors. The interior and the exterior problem are coupled through the field continuity conditions. The full set of equations is solved by standard Gaussian elimination. We also show how the total current and the dissipated power within each conductor can be expressed as boundary integrals. Finally, computational results for a sample problem are compared with a finite difference solution.
A new type of shooting method for nonlinear boundary value problems
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Muhammad Ahsan
2013-12-01
Full Text Available In this article we introduce a new type of iterative method for initial value problems (IVPs. We enhance this method by using shooting techniques and interpolation for the boundary value problems. Our method is more accurate and applicable than built in methods used in different software packages. We solved several examples for initial value problems and linear and non-linear boundary value problems and compared results to those obtained using MATLAB.
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...
The reconstruction of sound speed in the Marmousi model by the boundary control method
Ivanov, I B; Semenov, V S
2016-01-01
We present the results on numerical testing of the Boundary Control Method in the sound speed determination for the acoustic equation on semiplane. This method for solving multidimensional inverse problems requires no a priory information about the parameters under reconstruction. The application to the realistic Marmousi model demonstrates that the boundary control method is workable in the case of complicated and irregular field of acoustic rays. By the use of the chosen boundary controls, an `averaged' profile of the sound speed is recovered (the relative error is about $10-15\\%$). Such a profile can be further utilized as a starting approximation for high resolution iterative reconstruction methods.
Caicedo, Vanessa; Rappenglück, Bernhard; Lefer, Barry; Morris, Gary; Toledo, Daniel; Delgado, Ruben
2017-04-01
Three algorithms for estimating the boundary layer heights are assessed: an aerosol gradient method, a cluster analysis method, and a Haar wavelet method. Over 40 daytime clear-sky radiosonde profiles are used to compare aerosol backscatter boundary layer heights retrieved by a Vaisala CL31 ceilometer. Overall good agreement between radiosonde- and aerosol-derived boundary layer heights was found for all methods. The cluster method was found to be particularly sensitive to noise in ceilometer signals and lofted aerosol layers (48.8 % of comparisons), while the gradient method showed limitations in low-aerosol-backscatter conditions. The Haar wavelet method was demonstrated to be the most robust, only showing limitations in 22.5 % of all observations. Occasional differences between thermodynamically and aerosol-derived boundary layer heights were observed.
Ground water modeling applications using the analytic element method.
Hunt, Randall J
2006-01-01
Though powerful and easy to use, applications of the analytic element method are not as widespread as finite-difference or finite-element models due in part to their relative youth. Although reviews that focus primarily on the mathematical development of the method have appeared in the literature, a systematic review of applications of the method is not available. An overview of the general types of applications of analytic elements in ground water modeling is provided in this paper. While not fully encompassing, the applications described here cover areas where the method has been historically applied (regional, two-dimensional steady-state models, analyses of ground water-surface water interaction, quick analyses and screening models, wellhead protection studies) as well as more recent applications (grid sensitivity analyses, estimating effective conductivity and dispersion in highly heterogeneous systems). The review of applications also illustrates areas where more method development is needed (three-dimensional and transient simulations).
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.
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
2015-01-01
SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355
Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J
2014-06-01
Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. Copyright © 2014 John Wiley & Sons, Ltd.
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Jin, B.
2014-05-30
© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
A finite element-analytical method for modeling a structure in an infinite fluid
Zarda, P. R.
1976-01-01
A method is described from which the interaction of an elastic structure with an infinite acoustic fluid is determined. The displacements of the structure and the pressure field of the immediate surrounding fluid are modeled by finite elements, and the remaining pressure field of the infinite fluid region is given by an analytical expression. This method yields a frequency dependent boundary condition for the outer fluid boundary when applied to the frequency response of an elastic beam in contact with an acoustic fluid. The frequency response of the beam is determined using NASTRAN, and compares favorably to the exact solution which is also presented. The effect of the fluid on the response of the structure at low and high frequencies is due to added mass and damping characteristics, respectively.
Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
Jin, Bangti
2013-01-01
We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.
A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow
Toose, E.M.; Geurts, Bernardus J.; Kuerten, Johannes G.M.
1995-01-01
A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra
On one method for solving transient heat conduction problems with asymmetric boundary conditions
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Igor V. Kudinov
2016-06-01
Full Text Available Using additional boundary conditions and additional required function in integral method of heat-transfer we obtain approximate analytical solution of transient heat conduction problem for an infinite plate with asymmetric boundary conditions of the first kind. This solution has a simple form of trigonometric polynomial with coefficients exponentially stabilizing in time. With the increase in the count of terms of a polynomial the obtained solution is approaching the exact solution. The introduction of a time-dependent additional required function, setting in the one (point of the boundary points, allows to reduce solving of differential equation in partial derivatives to integration of ordinary differential equation. The additional boundary conditions are found in the form that the required solution would implement the additional boundary conditions and that implementation would be equivalent to executing the original differential equation in boundary points. In this article it is noted that the execution of the original equation at the boundaries of the area only (via the implementation of the additional boundary conditions leads to the execution of the original equation also inside that area. The absence of direct integration of the original equation on the spatial variable allows to apply this method to solving the nonlinear boundary value problems with variable initial conditions and variable physical properties of the environment, etc.
Multibody Finite Element Method and Application in Hydraulic Structure Analysis
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Chao Su
2015-01-01
Full Text Available Multibody finite element method is proposed for analysis of contact problems in hydraulic structure. This method is based on the block theory of discontinuous deformation analysis (DDA method and combines advantages of finite element method (FEM and the displacement compatibility equation in classical elastic mechanics. Each single block is analyzed using FEM in corresponding local coordinate system and all contacting blocks need to satisfy the displacement compatibility requirement between any two blocks in a blocky system. It is proved that this method is very efficient and practical to overcome the limitations in DDA method when tackling contact problems, such as the overlap problem and the equal strain assumption. In this paper, detailed theoretical basis and formulations are given. Two numerical examples are performed to verify the proposed method successfully. Furthermore, this method is adopted to study the stability issues of underground houses of a large hydropower station.
Modal analysis of double-walled carbon nanocones using the finite element method
Rouhi, S.; Ansari, R.; Nickabadi, S.
2017-12-01
The vibrational properties of double-walled carbon nanocones are investigated herein. The double-walled carbon nanocones with different geometries including apex angles and lengths are considered. The simply supported-simply supported, clamped-free and clamped-clamped boundary conditions are applied on the nanocones. A linear elastic beam-based finite element method is employed to obtain the frequencies of the double-walled carbon nanocones. Elastic beam elements are used to model the carbon-carbon bond in the structure of the nanocones. Besides, the spring elements are employed to describe the nonbonding van der Waals interactions between different layers. Natural frequencies and mode shapes of the double-walled carbon nanocones are extracted by solving the eigenvalue problem. It is observed that increasing the disclination angle of nanocones increases their natural frequency. However, increasing the nanocone’s height leads to decreasing the frequency.
SOLUTION OF TRANSIENT HEAT CONDUCTION PROBLEM BY THE FINITE ELEMENT METHOD
Directory of Open Access Journals (Sweden)
Süleyman TAŞGETİREN
1995-01-01
Full Text Available Determination of temperature distribution is generally the first step in the design of machine elements subjected to ubnormal temperatures in their service life and for selection of materials. During this heat transfer analysis, the boundary and enviromental conditions must be modeled realistically and the geometry must be well represented. A variety of materials deviating from simple constant property isotropic material to composit materials having different properties according to direction of reinforcements are to be analysed. Then, the finite element method finds a large application area due to its use of same notation in heat transfer analysis and mechanical analysis of elements. In this study, the general formulation of two dimensional transient heat conduction is developed and a sample solution is given for arectangular bar subjected to convection baundary condition.
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
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S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
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...
Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
Jin, Bangti
2014-01-01
© 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...... on the state-space do not in general provide analytical solutions. A widely used numerical approach is the sequential Monte Carlo (SMC) method which relies on stochastic simulations to approximate state densities. For offline analysis, however, accurate smoothed state density and parameter estimation can...
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 ...
Symmetric Matrix Fields in the Finite Element Method
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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.
On angle conditions in the finite element method
Brandts, J.; Hannukainen, A.; Korotov, S.; Krizek, M.
2011-01-01
Abstract Angle conditions play an important role in the analysis of the finite element method. They enable us to derive the optimal interpolation order and prove convergence of this method, to derive various a posteriori error estimates, to perform regular mesh refinements, etc. In 1968, Miloˇs
Different Element Methods in Engineering Practice | Onah | Nigerian ...
African Journals Online (AJOL)
Nigerian Journal of Technology ... general manner so that engineers and scientists who are increasingly, called upon to use element methods to support and check their analyses and/or designs can appreciate the essential dierences and similarities in the various methods and their possible advantages and disadvantages.
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
Convergence of multigrid method for edge-based finite-element method
Watanabe, K.; Igarashi, H.; Honma, T.
2003-01-01
This paper discusses robustness of the multigrid (MG) method against distortion of finite elements. The convergence of MG method becomes considerably worse as the finite elements become flat. It is shown that the smoother used in the MG method cannot effectively eliminate the high-frequency component of the residue for flat elements, and this gives rise to deterioration in the convergence. Moreover, the multigrid method with conjugate gradient (CG) smoother is shown to be more robust against ...
Islam, T.; Z. Chik; M. M. Mustafa; H. Sanusi
2012-01-01
This paper presents an efficient model for estimation of soil electric resistivity with depth and layer thickness in a multilayer earth structure. This model is the improvement of conventional two-layer earth model including Wenner resistivity formulations with boundary conditions. Two-layer soil model shows the limitations in specific soil characterizations of different layers with the interrelationships between soil apparent electrical resistivity (ρ) and several soil physical or chemical p...
Methode des elements finis hybride appliquee aux vibrations des coques spheriques
Menaa, Mohamed
The analysis of spherical shells filled with fluid and subjected to supersonic flow has been the subject of few research. Most of these studies treat the dynamic behaviour of empty shells. Few works have investigated spherical shells filled with fluid or subjected to supersonic flutter. In this thesis, we propose to develop a model to analyse the vibratory behaviour of both empty spherical shells and partially filled with fluid. This model is also applicable to study of the dynamic stability of spherical shells subjected to supersonic flow. The model developed is a combination of finite element method, thin shell theory, potential fluid theory and aerodynamic fluid theory. Different parameters are considered here in this study. In the first part of this study, free vibration analysis of spherical shell is carried out. The structural model is based on a combination of thin shell theory and the classical finite element method. Free vibration equations using the hybrid finite element formulation are derived and solved numerically. The results are validated using numerical and theoretical data available in the literature. The analysis is accomplished for spherical shells of different geometries, boundary conditions and radius to thickness ratios. This proposed hybrid finite element method can be used efficiently for design and analysis of spherical shells employed in high speed aircraft structures. In the second part of the present study, a hybrid finite element method is applied to investigate the free vibration of spherical shell filled with fluid. The structural model is based on a combination of thin shell theory and the classical finite element method. It is assumed that the fluid is incompressible and has no free-surface effect. Fluid is considered as a velocity potential variable at each node of the shell element where its motion is expressed in terms of nodal elastic displacement at the fluid-structure interface. Numerical simulation is done and vibration
The Ritz Method for Boundary Problems with Essential Conditions as Constraints
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Vojin Jovanovic
2016-01-01
Full Text Available We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.
Applying the method of fundamental solutions to harmonic problems with singular boundary conditions
Valtchev, Svilen S.; Alves, Carlos J. S.
2017-07-01
The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.
Three-dimensional simulation of jellyfish by the penalty immersed boundary method
Park, Sung Goon; Chang, Cheng Bong; Sung, Hyung Jin; Flow Control Laboratory Team
2012-11-01
The interaction between the motion of a three-dimensional jellyfish and the surrounding fluid was numerically simulated by the penalty immersed boundary method (pIBM). The effects of the vortex formation and the elastic properties on the kinematics of swimming jellyfish were examined. In order to simulate the incompressible fluid motion, the fractional step method was adopted on the Eulerian domain, while the subdivision finite element method was used to describe the solid motion on the Lagrangian domain. Coupling of the fluid motion and the jellyfish motion was realized in the framework of the pIBM. Our results suggest that the starting and stopping vortices, which are respectively induced from a power stroke and a recovery stroke, were formed in the wake of the swimming jellyfish. These two types of vortex interacted with each other, which made the size of vortex larger and caused the augmentation of thrust. Swimming performance of the jellyfish also depended on the elastic properties such as the tension and bending rigidity. It was found that the center velocity of the jellyfish increases with increasing the tension rigidity.
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.
Spectral element method for elastic and acoustic waves in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)
2016-12-15
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
Spectral element method for elastic and acoustic waves in frequency domain
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei; Liu, Na; Liu, Qing Huo
2016-12-01
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
[Application of finite element method in spinal biomechanics].
Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei
2017-02-25
The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.
Finite Element Method for Capturing Ultra-relativistic Shocks
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Conjugate Gradient Method with Ritz Method for the Solution of Boundary Value Problems
Directory of Open Access Journals (Sweden)
Victor Onomza WAZIRI
2007-01-01
Full Text Available In this paper, we wish to determine the optimal control of a one-variable boundary value problem using the Ritz algorithm. The posed optimal control problem was inadequate to achieve our goal using the Conjugate Gradient Method version developed by (Harsdoff, 1976. It is anticipated that other operators from some given different problems may sustain the application of the algorithm if the approximate solutions terms are properly chosen quadratic functionals. The graphical solution given at the end of section five of the paper, however, shows that our problem can not have an optimal minimum value since the minimum output is not unique. The optimal value obtained using Mathcad program codes may constitute a conjugate gradient approximate numerical value. As observed from the graphical output, Ritz algorithm could give credence for wider horizon in the engineering computational methods for vibrations of mechanical components and simulates.
Spectral element method implementation on GPU for Lamb wave simulation
Kudela, Pawel; Wandowski, Tomasz; Radzienski, Maciej; Ostachowicz, Wieslaw
2017-04-01
Parallel implementation of the time domain spectral element method on GPU (Graphics Processing Unit) is presented. The proposed spectral element method implementation is based on sparse matrix storage of local shape function derivatives calculated at Gauss-Lobatto-Legendre points. The algorithm utilizes two basic operations: multiplication of sparse matrix by vector and element-by-element vectors multiplication. Parallel processing is performed on the degree of freedom level. The assembly of resultant force is done by the aid of a mesh coloring algorithm. The implementation enables considerable computation speedup as well as a simulation of complex structural health monitoring systems based on anomalies of propagating Lamb waves. Hence, the complexity of various models can be tested and compared in order to be as close to reality as possible by using modern computers. A comparative example of a composite laminate modeling by using homogenization of material properties in one layer of 3D brick spectral elements with composite in which each ply is simulated by separate layer of 3D brick spectral elements is described. Consequences of application of each technique are explained. Further analysis is performed for composite laminate with delamination. In each case piezoelectric transducer as well as glue layer between actuator and host structure is modeled.
On Round-off Error for Adaptive Finite Element Methods
Alvarez-Aramberri, J.
2012-06-02
Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.
Strong Superconvergence of Finite Element Methods for Linear Parabolic Problems
Directory of Open Access Journals (Sweden)
Kening Wang
2009-01-01
Full Text Available We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on =Ω×(0,], where Ω is a bounded domain in ℛ(≤4 with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of our model problem in 1,(Ω and ( with 2≤<∞ and the almost two order superconvergence in 1,∞(Ω and ∞(. Results of the =∞ case are also included in two space dimensions (=1 or 2. By applying the interpolated postprocessing technique, similar results are also obtained on the error between the interpolation of the approximate solution and the exact solution.
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.
Automated discrete element method calibration using genetic and optimization algorithms
Do, Huy Q.; Aragón, Alejandro M.; Schott, Dingena L.
2017-06-01
This research aims at developing a universal methodology for automated calibration of microscopic properties of modelled granular materials. The proposed calibrator can be applied for different experimental set-ups. Two optimization approaches: (1) a genetic algorithm and (2) DIRECT optimization, are used to identify discrete element method input model parameters, e.g., coefficients of sliding and rolling friction. The algorithms are used to minimize the objective function characterized by the discrepancy between the experimental macroscopic properties and the associated numerical results. Two test cases highlight the robustness, stability, and reliability of the two algorithms used for automated discrete element method calibration with different set-ups.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
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.
Meshless element-free Galerkin method in NDT applications
Xuan, L.; Zeng, Z.; Shanker, B.; Udpa, L.
2002-05-01
Finite element methods (FEM) are widely used for modeling a variety of problems in Nondestructive Evaluation (NDE). For example, in the modeling of multilayer aircraft geometry with third layer cracks under fasteners, the reliance of FEM on a mesh leads to several problems, particularly when tight cracks have to be introduced into the sample. Furthermore remeshing is often required in handling probe motion can be time consuming. This paper presents a meshless element-free Galerkin method (EFG), where the approximation is entirely constructed in terms of a set of nodes. The model is validated and applied to two dimensional magneto-static and eddy current NDT problems.
Parallel computing for the finite element method in MATLAB
Directory of Open Access Journals (Sweden)
Aurimas Šimkus
2013-09-01
Full Text Available In this research, parallel computing capabilities of MATLAB and the capabilities for the finite element method were analyzed. A program for solving a heat transfer problem by the finite element method was implemented. Three different parallel algorithms using CPU and GPU for solving steady state and transient heat transfer problems were proposed and implemented. A maximal speedup of around 2.3 times for steady state and 2 times for transient problem solving time was achieved by using a quad-core CPU.
Davis, R. B.; Stephens, M. V.
1974-01-01
An approximate method for calculating the longitudinal and torsional natural frequencies and associated modal data of a beamlike, variable cross section multibranch structure is presented. The procedure described is the numerical integration of the first order differential equations that characterize the beam element in longitudinal motion and that satisfy the appropriate boundary conditions.
Simulation of Temperature Distribution In a Rectangular Cavity using Finite Element Method
Naa, Christian
2013-01-01
This paper presents the study and implementation of finite element method to find the temperature distribution in a rectangular cavity which contains a fluid substance. The fluid motion is driven by a sudden temperature difference applied to two opposite side walls of the cavity. The remaining walls were considered adiabatic. Fluid properties were assumed incompressible. The problem has been approached by two-dimensional transient conduction which applied on the heated sidewall and one-dimensional steady state convection-diffusion equation which applied inside the cavity. The parameters which investigated are time and velocity. These parameters were computed together with boundary conditions which result in temperature distribution in the cavity. The implementation of finite element method was resulted in algebraic equation which is in vector and matrix form. Therefore, MATLAB programs used to solve this algebraic equation. The final temperature distribution results were presented in contour map within the re...
Simulation of continuously deforming parabolic problems by Galerkin finite-elements method
Directory of Open Access Journals (Sweden)
Yahia S. Halabi
1986-01-01
Full Text Available A general numerical finite element scheme is described for parabolic problems with phase change wherein the elements of the domain are allowed to deform continuously. The scheme is based on the Galerkin approximation in space, and finite difference approximation for the time derivatives. The numerical scheme is applied to the two-phase Stefan problems associated with the melting and solidification of a substance. Basic functions based on Hermite polynomials are used to allow exact specification of flux-latent heat balance conditions at the phase boundary. Numerical results obtained by this scheme indicates that the method is stable and produces an accurate solutions for the heat conduction problems with phase change; even when large time steps used. The method is quite general and applicable for a variety of problems involving transition zones and deforming regions, and can be applied for one multidimensional problems.
Variational Multiscale Finite Element Method for Flows in Highly Porous Media
Iliev, O.
2011-10-01
We present a two-scale finite element method (FEM) for solving Brinkman\\'s and Darcy\\'s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes\\' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy\\'s equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.
Efficient partial element calculation and the extension to cylindrical elements for the PEEC method
Energy Technology Data Exchange (ETDEWEB)
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)
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.
Shape integral method for magnetospheric shapes. [boundary layer calculations
Michel, F. C.
1979-01-01
A method is developed for calculating the shape of any magnetopause to arbitrarily high precision. The method uses an integral equation which is evaluated for a trial shape. The resulting values of the integral equation as a function of auxiliary variables indicate how close one is to the desired solution. A variational method can then be used to improve the trial shape. Some potential applications are briefly mentioned.
Domain decomposition for a mixed finite element method in three dimensions
Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.
2003-01-01
We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Ultrasonic Method for Deployment Mechanism Bolt Element Preload Verification
Johnson, Eric C.; Kim, Yong M.; Morris, Fred A.; Mitchell, Joel; Pan, Robert B.
2014-01-01
Deployment mechanisms play a pivotal role in mission success. These mechanisms often incorporate bolt elements for which a preload within a specified range is essential for proper operation. A common practice is to torque these bolt elements to a specified value during installation. The resulting preload, however, can vary significantly with applied torque for a number of reasons. The goal of this effort was to investigate ultrasonic methods as an alternative for bolt preload verification in such deployment mechanisms. A family of non-explosive release mechanisms widely used by satellite manufacturers was chosen for the work. A willing contractor permitted measurements on a sampling of bolt elements for these release mechanisms that were installed by a technician following a standard practice. A variation of approximately 50% (+/- 25%) in the resultant preloads was observed. An alternative ultrasonic method to set the preloads was then developed and calibration data was accumulated. The method was demonstrated on bolt elements installed in a fixture instrumented with a calibrated load cell and designed to mimic production practice. The ultrasonic method yielded results within +/- 3% of the load cell reading. The contractor has since adopted the alternative method for its future production. Introduction
Parallelization of a coupled immersed boundary and lattice Boltzmann method for fluid and heat flow
Kasparek, Andrzej; Łapka, Piotr
2017-07-01
The paper presents first approach to the GPU-based parallelization of the coupled Immersed Boundary and Lattice Boltzmann Method. The proposed numerical simulator deals with fluid and heat flow in a domains with complex internal boundaries using Cartesian grid. The solution algorithm was parallelized with the aid of the CUDA architecture. Several heat and fluid flow problems, i.e., heated lid-driven flow and laminar natural convection in square domains without internal obstacles and isothermal flow past stationary cylinder were investigated. Satisfactory accelerations of the solution times were obtained for problems without internal boundaries. For test case with internal boundaries decrease in the parallel computing efficiency was observed as a results of numerical handling of the internal boundaries.
A quantitative method for clustering size distributions of elements
Dillner, Ann M.; Schauer, James J.; Christensen, William F.; Cass, Glen R.
A quantitative method was developed to group similarly shaped size distributions of particle-phase elements in order to ascertain sources of the elements. This method was developed and applied using data from two sites in Houston, TX; one site surrounded by refineries, chemical plants and vehicular and commercial shipping traffic, and the other site, 25 miles inland surrounded by residences, light industrial facilities and vehicular traffic. Twenty-four hour size-segregated (0.056fluid catalytic cracking unit catalysts, fuel oil burning, a coal-fired power plant, and high-temperature metal working. The clustered elements were generally attributed to different sources at the two sites during each sampling day indicating the diversity of local sources that impact heavy metals concentrations in the region.
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...
Development of Efficient Trace Element Quantification Methods in Carbonate Rocks
Kehoe, K. W.; Lonero, A.; Liddell, D.
2016-12-01
This study evaluates the feasibility of using a faster handheld x-ray fluorescence (XRF) method with little to no sample preparation to facilitate the analysis of several important trace elements in carbonate rocks when dealing with large sample quantities. The use of handheld energy-dispersive x-ray fluorescence (ED-XRF) has become popular because it offers nondestructive quantifiable elemental analyses of samples. ED-XRF has been used by geologists in rock core analyses, and has been shown to be capable of producing robust quantifiable results when compared with wavelength-dispersive x-ray fluorescence (WD-XRF) for many elements in pelitic rocks. However, there has been little to no published studies on the use of XRF on carbonate rocks, which may be partly due to the scarcity of internationally accepted trace element reference standards. Trace element abundances of several marine carbonate and carbonatite rocks are presented which have been determined in this study by multiple XRF and inductively coupled plasma mass spectrometry (ICP-MS) methods. Four carbonate standards in development, provided by the USGS, have been characterized with the use of ICP-MS and WD-XRF. Analyses of all samples were performed using different methods by two independent labs at Utah State University and Washington State University. These standards offer the wide elemental ranges necessary to properly quantify geochemical data within the unique matrix of carbonate rocks. A comparison of pressed powder pellets was made between ED-XRF and WD-XRF on carbonate rock samples from the Ordovician Garden City Formation and Pogonip Group of northern and west-central Utah respectively, to determine differences in results between the two methods. Additionally, slabbed hand samples as well as loose powdered samples prepared from the same rock samples were also analyzed and compared with the pressed powder pellets with ED-XRF, to determine if sample preparation had significant effects on sample
Modave, A.; Atle, A.; Chan, J.; Warburton, T.
2017-12-01
Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective boundary treatments to limit the size of the computational domain without losing accuracy or computational efficiency, which remains a challenging task. In this paper, we present a combination of a nodal discontinuous Galerkin method with high-order absorbing boundary conditions (HABCs) for cuboidal computational domains. Compatibility conditions are derived for HABCs intersecting at the edges and the corners of a cuboidal domain. We propose a GPU implementation of the computational procedure, which results in a multidimensional solver with equations to be solved on 0D, 1D, 2D and 3D spatial regions. Numerical results demonstrate both the accuracy and the computational efficiency of our approach.
Kot, V. A.
2017-11-01
The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.
Liska, Sebastian
2016-01-01
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also...
A method to characterize the roughness of 2-D line features: recrystallization boundaries
DEFF Research Database (Denmark)
Sun, Jun; Zhang, Yubin; Dahl, Anders Bjorholm
2017-01-01
A method is presented, which allows quantification of the roughness of nonplanar boundaries of objects for which the neutral plane is not known. The method provides quantitative descriptions of both the local and global characteristics. How the method can be used to estimate the sizes of rough fe...... features and local curvatures is also presented. The potential of the method is illustrated by quantification of the roughness of two recrystallization boundaries in a pure Al specimen characterized by scanning electron microscopy.......A method is presented, which allows quantification of the roughness of nonplanar boundaries of objects for which the neutral plane is not known. The method provides quantitative descriptions of both the local and global characteristics. How the method can be used to estimate the sizes of rough...
A Monte Carlo adapted finite element method for dislocation ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 126; Issue 7. A Monte Carlo adapted finite element method for dislocation ... However, geological features of a fault cannot be measured exactly, and therefore these features and data involve uncertainties. This paper presents a Monte Carlo based random model of ...
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
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...
h-p Spectral element methods for three dimensional elliptic ...
Indian Academy of Sciences (India)
The h-p version of the finite element method for solving three dimensional elliptic problems on non-smooth domains with exponential accuracy was proposed by Guo in [9,. 12]. To overcome the singularities which arise along vertices and edges they used geo- metric meshes which are defined in neighbourhoods of vertices, ...
Review on finite element method | Erhunmwun | Journal of Applied ...
African Journals Online (AJOL)
In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and its future. The eventual intension of using FEM is to determine the nodal solution of a particular problem under study. The power of FEM is its ability to discretize complex problems and analyse it part by part.
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
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 gra...
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
Nonconforming h-p spectral element methods for elliptic problems
Indian Academy of Sciences (India)
of the corners, modified polar coordinates are used and a global coordinate system elsewhere. ... applies to elliptic systems too. A method ... Schur complement. Let M denote the number of corner layers and W denote the number of degrees of freedom in each independent variable of the spectral element functions, which.
Stein, David B.; Guy, Robert D.; Thomases, Becca
2016-01-01
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.
Paxton, Bill; Schwab, Josiah; Bauer, Evan B.; Bildsten, Lars; Blinnikov, Sergei; Duffell, Paul; Farmer, R.; Goldberg, Jared A.; Marchant, Pablo; Sorokina, Elena; Thoul, Anne; Townsend, Richard H. D.; Timmes, F. X.
2018-02-01
We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective-core mass during both hydrogen- and helium-burning phases. Stars with MType II supernova properties. These capabilities are exhibited with exploratory models of pair-instability supernovae, pulsational pair-instability supernovae, and the formation of stellar-mass black holes. The applicability of MESA is now widened by the capability to import multidimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, as well as four new software tools - MESA-Web, MESA-Docker, pyMESA, and mesastar.org - to enhance MESA's education and research impact.
Method for recovering elemental silicon from cutting remains.
Ulset, Torgeir; Julrud, Stein; Cassayre, Laurent; Chamelot, Pierre; Massot, Laurent; Taxil, Pierre
2008-01-01
This invention relates to a method for recovering elemental silicon cutting remains containing silicon particles, wherein the method comprises manufacturing solid anodes from the cutting remains, arranging one or more manufactured anode (s) in an electrolytic cell with a molten salt electrolyte and one or more cathode (s), and applying a potential difference between the one or more anode (s) and cathode (s) to obtain an oxidation of metallic silicon in the one or more anode (s), tran...
Discontinuous Galerkin Finite Element Method for Parabolic Problems
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
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.
Energy Technology Data Exchange (ETDEWEB)
Loewe, Konrad
2016-10-18
The first part of the thesis investigates the diffusion of rare-earth (RE) elements in commercial sintered Nd-Fe-B based permanent magnets. A strong temperature dependence of the diffusion distance and resulting change in magnetic properties were found. A maximum increase in coercivity of ∼+350 kA/m using a Dy diffusion source occurred at the optimum annealing temperature of 900 C. After annealing for 6 h at this temperature, a Dy diffusion distance of about 4 mm has been observed with a scanning Hall probe. Consequently, the maximum thickness of grain boundary diffusion processed magnets with homogeneous properties is also only a few mm. The microstructural changes in the magnets after diffusion were investigated by electron microscopy coupled with electron probe microanalysis. It was found that the diffusion of Dy into sintered Nd-Fe-B permanent magnets occurs along the grain boundary phases, which is in accordance with previous studies. A partial melting of the Nd-Fe-B grains during the annealing process lead to the formation of so - called (Nd,Dy)-Fe-B shells at the outer part of the grains. These shells are μm thick at the immediate surface of the magnet and become thinner with increasing diffusion distance towards the center of the bulk. With scanning transmission electron microscopy coupled with electron probe analysis a Dy content of about 1 at.% was found in a shell located about 1.5 mm away from the surface of the magnet. The evaluation of diffusion speeds of Dy and other RE (Tb, Ce, Gd) in Nd-Fe-B magnets showed that Tb diffuses significantly faster than Dy, and Ce slightly slower than Dy, which is attributed to differences in the respective phase diagrams. The addition of Gd to the grain boundaries has an adverse effect on coercivity. Exemplary of the heavy rare earth element Tb, the nano - scale elemental distribution around the grain boundaries after the diffusion process was visualized with high resolution scanning transmission electron microscopy
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Park, Won Dong; Kim, Ji Hoon; Bahn, Chi Bum [Pusan National University, Busan (Korea, Republic of)
2016-10-15
Welding residual stresses are determined by various factors such as heat input, initial temperature of molten bead, heating time, cooling time, cooling conditions, and boundary conditions. In this study, a sensitivity analysis was performed to find the major factors and reasonable assumptions for simulation. Two-dimensional axisymmetric simulation was conducted by using commercial finite element analysis program ABAQUS, for multi-pass Alloy 82 welds in a 304 Stainless Steel and SA-105 Carbon Steel. The major object is to evaluate effects of the heat input methods and weld bead generation methods on the welding residual stress distribution. Totally four kinds of methods were compared. From the previous results, we could make the following conclusions. 1. Although there are non-negligible differences in HAZ depending on heat input method, welding residual stress distributions have roughly similar trends. However, it is needed to perform the more exact analysis to apply heat energy more carefully into the individual bead. 2. Residual stress distribution were similar for the two weld bead generation technique. However, overlapping was happened when element birth technique was applied. Effects of overlapping could not ignore as deformation increases. However, overlapping problem was avoided when quiet element technique was used. 3. Since existence of inactive bead elements, inaccurate weld residual stresses could be occurred in boundaries of previous and next weld elements in case of quiet element technique.
Coarse-to-fine boundary location with a SOM-like method.
Zeng, Delu; Zhou, Zhiheng; Xie, Shengli
2010-03-01
A coarse-to-fine boundary location with a self-organizing map (SOM)-like method is proposed in this paper. Inspired from the conventional SOM and universal gravitation, given a small quantity of supervision seeds from the desired boundaries, neurons are used to evolve to the desired boundaries in a coarse-to-fine framework. The major components of this framework are the designs of union action and evolving rate. In the course of neuron evolution, the union actions acting on these neurons will offer them the evolving directions. Also controlled by the corresponding referenced gradients, the neurons' evolving rates are adaptively adjusted at different positions. With the union actions and evolving rates, the neurons will evolve with appropriate manners to expand the set of feature points on the desired boundaries. The newly expanded feature points will cause the generation updates for feature points and neurons, and offer new information to guide the new generation of neurons to the boundaries. What is more, the proposed multiround evolution is as well a coarse-to-fine way for boundary location. Experiments and comparisons show that the proposed method performs well in complex long concavities, inhomogeneous and weak boundary location with good initialization flexibility.
Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method
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J. Wu
2012-01-01
Full Text Available A hybrid immersed boundary-lattice Boltzmann method (IB-LBM is presented in this work to simulate the thermal flow problems. In current approach, the flow field is resolved by using our recently developed boundary condition-enforced IB-LBM (Wu and Shu, (2009. The nonslip boundary condition on the solid boundary is enforced in simulation. At the same time, to capture the temperature development, the conventional energy equation is resolved. To model the effect of immersed boundary on temperature field, the heat source term is introduced. Different from previous studies, the heat source term is set as unknown rather than predetermined. Inspired by the idea in (Wu and Shu, (2009, the unknown is calculated in such a way that the temperature at the boundary interpolated from the corrected temperature field accurately satisfies the thermal boundary condition. In addition, based on the resolved temperature correction, an efficient way to compute the local and average Nusselt numbers is also proposed in this work. As compared with traditional implementation, no approximation for temperature gradients is required. To validate the present method, the numerical simulations of forced convection are carried out. The obtained results show good agreement with data in the literature.
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
Energy Technology Data Exchange (ETDEWEB)
Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
Discontinuous Galerkin finite element methods for gradient plasticity.
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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.
Hybrid finite element and Brownian dynamics method for charged particles
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Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
Directory of Open Access Journals (Sweden)
Václav URUBA
2010-12-01
Full Text Available Separation of the turbulent boundary layer (BL on a flat plate under adverse pressure gradient was studied experimentally using Time-Resolved PIV technique. The results of spatio-temporal analysis of flow-field in the separation zone are presented. For this purpose, the POD (Proper Orthogonal Decomposition and its extension BOD (Bi-Orthogonal Decomposition techniques are applied as well as dynamical approach based on POPs (Principal Oscillation Patterns method. The study contributes to understanding physical mechanisms of a boundary layer separation process. The acquired information could be used to improve strategies of a boundary layer separation control.
High-order finite element methods for cardiac monodomain simulations
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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.
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
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. PMID:26300783
Bao, Kai
2012-10-01
In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..
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G Boroni
2017-03-01
Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.
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Hossein Jafari
2014-01-01
Full Text Available We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. We solve the fractional Bratu-type problem as an illustrative example.
Interpolation functions in control volume finite element method
Abbassi, H.; Turki, S.; Nasrallah, S. Ben
The main contribution of this paper is the study of interpolation functions in control volume finite element method used in equal order and applied to an incompressible two-dimensional fluid flow. Especially, the exponential interpolation function expressed in the elemental local coordinate system is compared to the classic linear interpolation function expressed in the global coordinate system. A quantitative comparison is achieved by the application of these two schemes to four flows that we know the analytical solutions. These flows are classified in two groups: flows with privileged direction and flows without. The two interpolation functions are applied to a triangular element of the domain then; a direct comparison of the results given by each interpolation function to the exact value is easily realized. The two functions are also compared when used to solve the discretized equations over the entire domain. Stability of the numerical process and accuracy of solutions are compared.
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Problems and methods for determining reserves of renewable elements
Energy Technology Data Exchange (ETDEWEB)
Dalkowski, T.; Dabrowska, I.
1983-01-01
The effects of spare parts on reliability of mining equipment used in coal surface mining are discussed. The optimum number of spare parts and elements used in equipment repair depends on reliability and service life of each element and on failure rates, which are influenced by local conditions. A method for determining the optimum number of spare parts for mining equipment which treats a machine failure as an event of random character is analyzed. Problems associated with replacing elements removed due to wear or failures as well as problems of repair are investigated. A model of spare part management and repair shop management in a coal surface mine is evaluated. Spare part management in the Belchatow brown coal surface mine is discussed with the example of maintenance and repair of belt conveyors. 10 references.
La Follett, Jon R; Williams, Kevin L; Marston, Philip L
2011-08-01
Backscattering of sound by a solid aluminum cylinder was measured in the free field and with the cylinder near a flat surface. The target was suspended just below the surface of a water tank to simulate some aspects of backscattering when resting on the seabed. Measurements were compared with predictions made by an approximate hybrid approach based on multiple two-dimensional finite element calculations and the use of images. Many of the spectral features present in the tank data were present in the model. Comparing numerical model predictions with experimental data serves to build credibility for the modeling approach and can assist in developing insight into the underlying physical processes.
A domain decomposed finite element method for solving Darcian velocity in heterogeneous porous media
Xie, Yifan; Wu, Jichun; Xue, Yuqun; Xie, Chunhong; Ji, Haifeng
2017-11-01
This paper proposes a domain decomposed finite element method (DDFEM) for groundwater flow velocity simulation, which can effectively and efficiently deal with arbitrarily oriented or intersected material interfaces in heterogeneous porous media. The main idea of this problem is to employ domain decompose technique to break the velocity problem down to subproblems by material interfaces, thereby achieving high accuracy at interface nodes and improving the velocity computation efficiency. By solving the global flow field by FEM before velocity computation, this method can capture the global information of the whole study region so as to ensure the subproblem solution accuracy by Yeh's model. After one subproblem has been solved, the DDFEM employs refraction law to obtain the Dirichlet boundary velocities of the adjacent subdomains. Numerical examples have been done to demonstrate the applicability and accuracy of the proposed method. Comparison between the DDFEM and two classical methods shows that the DDFEM can indeed save much computational cost, while achieving high accuracy.
Directory of Open Access Journals (Sweden)
Yankui Sun
2016-03-01
Full Text Available With the introduction of spectral-domain optical coherence tomography (SD-OCT, much larger image datasets are routinely acquired compared to what was possible using the previous generation of time-domain OCT. Thus, there is a critical need for the development of three-dimensional (3D segmentation methods for processing these data. We present here a novel 3D automatic segmentation method for retinal OCT volume data. Briefly, to segment a boundary surface, two OCT volume datasets are obtained by using a 3D smoothing filter and a 3D differential filter. Their linear combination is then calculated to generate new volume data with an enhanced boundary surface, where pixel intensity, boundary position information, and intensity changes on both sides of the boundary surface are used simultaneously. Next, preliminary discrete boundary points are detected from the A-Scans of the volume data. Finally, surface smoothness constraints and a dynamic threshold are applied to obtain a smoothed boundary surface by correcting a small number of error points. Our method can extract retinal layer boundary surfaces sequentially with a decreasing search region of volume data. We performed automatic segmentation on eight human OCT volume datasets acquired from a commercial Spectralis OCT system, where each volume of datasets contains 97 OCT B-Scan images with a resolution of 496×512 (each B-Scan comprising 512 A-Scans containing 496 pixels; experimental results show that this method can accurately segment seven layer boundary surfaces in normal as well as some abnormal eyes.
A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems
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Mohammed AL-Smadi
2014-01-01
Full Text Available The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.
A Testable Design Method for Memories by Boundary Scan Technique
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Qiao Guo-Hui
2016-01-01
Full Text Available This paper presents a design for test the embedded flash in an object System-on-a-chip (SoC. The feature of the Flash TAP (Test Access Port complies with the IEEE std.1149.1, and it can select different scan chains and other control registers for other test. By the trade-off between the test time and the circuit area, an IST (In System Test circuit is designed in the SoC. Experiment results on the embedded memory have shown that the proposed method costs small testing timing by the use of IST.
Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver
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Ma Yanfeng
2016-10-01
Full Text Available An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.
Implicit extrapolation methods for multilevel finite element computations
Energy Technology Data Exchange (ETDEWEB)
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.
Generalization of mixed multiscale finite element methods with applications
Energy Technology Data Exchange (ETDEWEB)
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
The Iris biometric feature segmentation using finite element method
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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.
Finite element method for time-space-fractional Schrodinger equation
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Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Analysis of Waveguide Junction Discontinuities Using Finite Element Method
Deshpande, Manohar D.
1997-01-01
A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. An H-plane discontinuity, an E-plane ridge discontinuity, and a step discontinuity in a concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained by the present method are in excellent agreement with the earlier published results. The numerical results obtained by the FEM are compared with the numerical results obtained using the Mode Matching Method (MMM) and also with the measured data.
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.
Stochastic Finite Element Method in Geotechnical Engineering. Spectral Approach
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Auvinet-Guichard G.
2013-01-01
Full Text Available This paper presents the mathematical tools in which the formulation of Spectral Stochastic Finite Element Method is based. The usefulness of this method to model the spatial variability of heterogeneous materials, and in particular of soils, is illustrated by a practical example in which the propagation of the uncertainty on the deformation modulus to the computed displacement field is assessed. The influence of the correlation length on the distribution of uncertainty is set forth. Finally, the advantages of the method in geotechnical engineering are evaluated and some conclusions are presented.
Free vibration analysis of dragonfly wings using finite element method
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M Darvizeh
2016-04-01
Full Text Available In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eachmode shape evaluated and the ratio between numerical natural frequencyand experimental natural frequency presented as damping ratio. Theresults obtain from present method are in good agreement with sameexperimental methods.
Unstructured spectral element methods of simulation of turbulent flows
Energy Technology Data Exchange (ETDEWEB)
Henderson, R.D. [California Inst. of Technology, Pasadena, CA (United States); Karniadakis, G.E. [Brown Univ., Providence, RI (United States)
1995-12-01
In this paper we present a spectral element-Fourier algorithm for simulating incompressible turbulent flows in complex geometries using unstructured quadrilateral meshes. To this end, we compare two different interface formulations for extending the conforming spectral element method in order to allow for surgical mesh refinement and still retain spectral accuracy: the Zanolli iterative procedure and variational patching based on auxiliary {open_quotes}mortar{close_quotes} functions. We present an interpretation of the original mortar element method as a patching scheme and develop direct and iterative solution techniques that make the method efficient for simulations of turbulent flows. The properties of the new method are analyzed in detail by studying the eigenspectra of the advection and diffusion operators. We then present numerical results that illustrate the flexibility as well as the exponential convergence of the new algorithm for nonconforming discretizations. We conclude with simulation studies of the turbulent cylinder wake at Re = 1000 (external flow) and turbulent flow over riblets at Re = 3280 (internal flow). 36 refs., 29 figs., 7 tabs.
Practical Aspects of Finite Element Method Applications in Dentistry
Directory of Open Access Journals (Sweden)
Grbović Aleksandar
2017-07-01
Full Text Available The use of numerical methods, such as finite element method (FEM, has been widely adopted in solving structural problems with complex geometry under external loads when analytical solutions are unachievable. Basic idea behind FEM is to divide the complex body geometry into smaller and simpler domains, called finite elements, and then to formulate solution for each element instead of seeking a solution for the entire domain. After finding the solutions for all elements they can be combined to obtain a solution for the whole domain. This numerical method is mostly used in engineering, but it is also useful for studying the biomechanical properties of materials used in medicine and the influence of mechanical forces on the biological systems. Since its introduction in dentistry four decades ago, FEM became powerful tool for the predictions of stress and strain distribution on teeth, dentures, implants and surrounding bone. FEM can indicate aspects of biomaterials and human tissues that can hardly be measured in vivo and can predict the stress distribution in the contact areas which are not accessible, such as areas between the implant and cortical bone, denture and gingiva, or around the apex of the implant in trabecular bone. Aim of this paper is to present - using results of several successful FEM studies - the usefulness of this method in solving dentistry problems, as well as discussing practical aspects of FEM applications in dentistry. Some of the method limitations, such as impossibility of complete replication of clinical conditions and need for simplified assumptions regarding loads and materials modeling, are also presented. However, the emphasis is on FE modelling of teeth, bone, dentures and implants and their modifications according to the requirements. All presented studies have been carried out in commercial software for FE analysis ANSYS Workbench.
Roy, Matthew M D; Rivard, Eric
2017-08-15
N-Heterocyclic olefins (NHOs) have gone from the topic of a few scattered (but important) reports in the early 1990s to very recently being a ligand/reagent of choice in the far-reaching research fields of organocatalysis, olefin and heterocycle polymerization, and low oxidation state main group element chemistry. NHOs are formally derived by appending an alkylidene (CR2) unit onto an N-heterocyclic carbene (NHC), and their pronounced ylidic character leads to high nucleophilicity and soft Lewis basic character at the ligating carbon atom. These olefinic donors can also be structurally derived from imidazole, triazole, and thiazole-based heterocyclic carbenes and, as a result, have highly tunable electronic and steric properties. In this Account, we will focus on various synthetic routes to imidazole-2-ylidene derived NHOs (sometimes referred to as deoxy-Breslow intermediates) followed by a discussion of the electron-donor ability of this structurally tunable ligand group. It should be mentioned that NHOs have a close structural analogy with Breslow-type intermediates, N-heterocyclic ketene aminals, and β-azolium ylides; while these latter species play important roles in advancing synthetic organic chemistry, discussion in this Account will be confined mostly to imidazole-2-ylidene derived NHOs. In addition, we will cover selected examples from the literature where NHOs and their anionic counterparts, N-heterocyclic vinylenes, are used to access reactive main group species not attainable using traditional ligands. Added motivation for these studies comes from the emerging number of low coordinate main group element based compounds that display reactivity once reserved for precious metal complexes (such as H-H and C-H bond activation). Moreover, NHOs are versatile precursors to new mixed element (P/C and N/C), and potentially bidentate, ligand constructs of great potential in catalysis, where various metal oxidation states and coordination environments need to be
Ooi, E. T.; Song, C.; Natarajan, S.
2017-07-01
This manuscript presents an extension of the recently-developed high order complete scaled boundary shape functions to model elasto-static problems in functionally graded materials. Both isotropic and orthotropic functionally graded materials are modelled. The high order complete properties of the shape functions are realized through the introduction of bubble-like functions derived from the equilibrium condition of a polygon subjected to body loads. The bubble functions preserve the displacement compatibility between the elements in the mesh. The heterogeneity resulting from the material gradient introduces additional terms in the polygon stiffness matrix that are integrated analytically. Few numerical benchmarks were used to validate the developed formulation. The high order completeness property of the bubble functions result in superior accuracy and convergence rates for generic elasto-static and fracture problems involving functionally graded materials.
Kou, Wenjun; Griffith, Boyce E.; Pandolfino, John E.; Kahrilas, Peter J.; Patankar, Neelesh A.
2015-11-01
This work extends a fiber-based immersed boundary (IB) model of esophageal transport by incorporating a continuum model of the deformable esophageal wall. The continuum-based esophagus model adopts finite element approach that is capable of describing more complex and realistic material properties and geometries. The leakage from mismatch between Lagrangian and Eulerian meshes resulting from large deformations of the esophageal wall is avoided by careful choice of interaction points. The esophagus model, which is described as a multi-layered, fiber-reinforced nonlinear elastic material, is coupled to bolus and muscle-activation models using the IB approach to form the esophageal transport model. Cases of esophageal transport with different esophagus models are studied. Results on the transport characteristics, including pressure field and esophageal wall kinematics and stress, are analyzed and compared. Support from NIH grant R01 DK56033 and R01 DK079902 is gratefully acknowledged. BEG is supported by NSF award ACI 1460334.
Vibration and Buckling Analysis of Moderately Thick Plates using Natural Element Method
Directory of Open Access Journals (Sweden)
Mohammad Etemadi
2015-07-01
Full Text Available Using natural element method (NEM, the buckling and the free vibration behaviors of moderate thick plates is studied here. The basis of NEM is natural neighbors and Voronoi cells concepts. The shape functions of nodes located in the domain is equal to the proportion of common natural neighbors area divided by area that related by each Voronoi cells. First step in analyzing the moderate thick plates is identification boundaries. This is done by nodes scattering on problem domain. Mindlin/Reissner theory is used to express the equations of moderate thick plate. First and second order shape functions obtained from natural element method are used to discretize differential equations. Using numerical integration on whole discrete equations of domain, stiffness, geometry and mass matrices of plate are obtained. Buckling loads and vibration modes are expressed by substituting these matrices in plate equations of motions. Arbitrary shapes of plate are selected for solution. Comparing the results of the current approach with those obtained by other numerical analytical methods, it is shown that natural element method can solve problems with complex areas accurately.
Formation of the Abundance Boundaries of the Heavier Neutron-capture Elements in Metal-poor Stars
Yang, Guochao; Li, Hongjie; Liu, Nian; Zhang, Lu; Cui, Wenyuan; Liang, Yanchun; Niu, Ping; Zhang, Bo
2017-06-01
The abundance scatter of heavier r-process elements (Z≥slant 56) relative to Fe ([r/Fe]) in metal-poor stars preserves excellent information of the star formation history and provides important insights into the various situations of the Galactic chemical enrichment. In this respect, the upper and lower boundaries of [r/Fe] could present useful clues for investigating the extreme situations of the star formation history and the early Galactic chemical evolution. In this paper, we investigate the formation of the upper and lower boundaries of [r/Fe] for the gas clouds. We find that, for a cloud from which metal-poor stars formed, the formation of the upper limits of [r/Fe] is mainly due to the pollution from a single main r-process event. For a cloud from which metal-poor stars formed, the formation of the lower limits of [r/Fe] is mainly due to the pollution from a single SN II event that ejects primary Fe.
The boundary data immersion method for compressible flows with application to aeroacoustics
Energy Technology Data Exchange (ETDEWEB)
Schlanderer, Stefan C., E-mail: stefan.schlanderer@unimelb.edu.au [Faculty for Engineering and the Environment, University of Southampton, SO17 1BJ Southampton (United Kingdom); Weymouth, Gabriel D., E-mail: G.D.Weymouth@soton.ac.uk [Faculty for Engineering and the Environment, University of Southampton, SO17 1BJ Southampton (United Kingdom); Sandberg, Richard D., E-mail: richard.sandberg@unimelb.edu.au [Department of Mechanical Engineering, University of Melbourne, Melbourne VIC 3010 (Australia)
2017-03-15
This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015), ). The BDIM equations for the compressible Navier–Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step.
Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.
Wu, Yumao; Lu, Ya Yan
2011-06-01
Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.
Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method.
Wu, Yumao; Lu, Ya Yan
2009-11-01
For analyzing diffraction gratings, a new method is developed based on dividing one period of the grating into homogeneous subdomains and computing the Neumann-to-Dirichlet (NtD) maps for these subdomains by boundary integral equations. For a subdomain, the NtD operator maps the normal derivative of the wave field to the wave field on its boundary. The integral operators used in this method are simple to approximate, since they involve only the standard Green's function of the Helmholtz equation in homogeneous media. The method retains the advantages of existing boundary integral equation methods for diffraction gratings but avoids the quasi-periodic Green's functions that are expensive to evaluate.
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.
Introduction to assembly of finite element methods on graphics processors
Cecka, Cristopher; Lew, Adrian; Darve, Eric
2010-06-01
Recently, graphics processing units (GPUs) have had great success in accelerating 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 presented and discussed. 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 achieves speedups of 30x or more in comparison to a well optimized serial implementation on the CPU. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite-element discretization.
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...
Least-squares finite element method for fluid dynamics
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
Application of Finite Element Method to Analyze Inflatable Waveguide Structures
Deshpande, M. D.
1998-01-01
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Method for detection of antibodies for metallic elements
Barrick, Charles W.; Clarke, Sara M.; Nordin, Carl W.
1993-11-30
An apparatus and method for detecting antibodies specific to non-protein antigens. The apparatus is an immunological plate containing a plurality of plastic projections coated with a non-protein material. Assays utilizing the plate are capable of stabilizing the non-protein antigens with detection levels for antibodies specific to the antigens on a nanogram level. A screening assay with the apparatus allows for early detection of exposure to non-protein materials. Specifically metallic elements are detected.
Free vibration analysis of dragonfly wings using finite element method
M Darvizeh; A Darvizeh; H Rajabi; A Rezaei
2016-01-01
In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM) is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eac...
Nguyen, Lam; Stoter, Stein; Baum, Thomas; Kirschke, Jan; Ruess, Martin; Yosibash, Zohar; Schillinger, Dominik
2017-03-11
The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field-based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then used to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, ie, the interface width of the phase field, the voxel spacing, and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body. Copyright © 2017 John Wiley & Sons, Ltd.
A tephrochronologic method based on apatite trace-element chemistry
Sell, Bryan Keith; Samson, Scott Douglas
Geochemical correlation of ash-fall beds with conventional tephrochronologic methods is not feasible when original glass composition is altered. Thus, alternative correlation methods may be required. Initial studies of heavily altered Paleozoic tephra (K-bentonites) have suggested the potential for employing trace-element concentrations in apatite as ash-fall bed discriminators. To further test the utility of apatite trace-element tephrochronology, we analyzed apatite phenocrysts from unaltered volcanic rocks with an electron microprobe: nine samples from rocks erupted during the Quaternary and one sample from a rock erupted during the Paleogene. The resulting apatite trace-element data provide unique bed discriminators despite within-crystal variability. Each of the volcanic rocks studied possesses unique trends in Mg, Cl, Mn, Fe, Ce and Y concentrations in apatite. The results from this study establish an important tephrochronologic method that can be applied to nearly all portions of the Phanerozoic stratigraphic record and greatly assist development of an advanced timescale. In addition to establishing a fingerprint for a particular eruption, apatite chemistry provides useful information about the source magma.
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
Ateş, I.; Zegeling, P. A.|info:eu-repo/dai/nl/073634433
2017-01-01
In this paper we describe the application of the homotopy perturbation method (HPM) to two-point boundary-value problems with fractional-order derivatives of Caputo-type. We show that HPM is equivalent to the semi-analytical Adomian decomposition method when applied to a class of nonlinear
Yousef, Hamood Mohammed; Ismail, Ahmad Izani
2017-11-01
In this paper, Laplace Adomian decomposition method (LADM) was applied to solve Delay differential equations with Boundary Value Problems. The solution is in the form of a convergent series which is easy to compute. This approach is tested on two test problem. The findings obtained exhibit the reliability and efficiency of the proposed method.
Mikhal, Julia Olegivna; Pereira, J.C.F; Sequeira, A.; Lopez Penha, D.J.; Slump, Cornelis H.; Pereira, J.M.C.; Janela, J.; Geurts, Bernardus J.; Borges, L.
A volume-penalizing immersed boundary method is presented that facilitates the computation of incompressible fluid flow in complex flow domains. We apply this method to simulate the flow in cerebral aneurysms, and focus on the accuracy with which the flow field and the corresponding shear stress
Simulating Space Capsule Water Landing with Explicit Finite Element Method
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Application of least-squares spectral element solver methods to incompressible flow problems
M.M.J. Proot; M.I. Gerritsma; M. Nool (Margreet)
2003-01-01
textabstractLeast-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
Directory of Open Access Journals (Sweden)
Zhengnan Li
2016-01-01
Full Text Available To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by using the boundary intersection method and pseudospectral method. The subproblems are solved by nonlinear programming algorithm. In this method, the solution that has been solved is employed as the initial guess for the next subproblem so that the time consumption of the entire multiobjective trajectory optimization problem shortens. The maximal range and minimal peak heat problem is solved by the proposed method. The numerical results demonstrate that the proposed method can obtain the Pareto front of the optimal trajectory, which can provide the reference for the trajectory design of hypersonic glider vehicle.
Directory of Open Access Journals (Sweden)
Zhiqiang Zhou
2017-01-01
Full Text Available We study the pricing of the American options with fractal transmission system under two-state regime switching models. This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs with two free boundaries. Then, the solutions of ODEs are expressed in an explicit form. Consequently the early exercise boundaries and the values for the American option are recovered using the Gaver-Stehfest formula. Numerical comparisons of the methods with the finite difference methods are carried out to verify the efficiency of the methods.
Computational methods for the analysis of primate mobile elements
Cordaux, Richard; Sen, Shurjo K.; Konkel, Miriam K.; Batzer, Mark A.
2010-01-01
Transposable elements (TE), defined as discrete pieces of DNA that can move from site to another site in genomes, represent significant components of eukaryotic genomes, including primates. Comparative genome-wide analyses have revealed the considerable structural and functional impact of TE families on primate genomes. Insights into these questions have come in part from the development of computational methods that allow detailed and reliable identification, annotation and evolutionary analyses of the many TE families that populate primate genomes. Here, we present an overview of these computational methods, and describe efficient data mining strategies for providing a comprehensive picture of TE biology in newly available genome sequences. PMID:20238080
Garai, Anirban; Murman, Scott M.; Madavan, Nateri K.
2016-01-01
used involves modeling the pressure fluctuations as acoustic waves propagating in the far-field relative to a single noise-source inside the buffer region. This approach treats vorticity-induced pressure fluctuations the same as acoustic waves. Another popular approach, often referred to as the "sponge layer," attempts to dampen the flow perturbations by introducing artificial dissipation in the buffer region. Although the artificial dissipation removes all perturbations inside the sponge layer, incoming waves are still reflected from the interface boundary between the computational domain and the sponge layer. The effect of these refkections can be somewhat mitigated by appropriately selecting the artificial dissipation strength and the extent of the sponge layer. One of the most promising variants on the buffer region approach is the Perfectly Matched Layer (PML) technique. The PML technique mitigates spurious reflections from boundaries and interfaces by dampening the perturbation modes inside the buffer region such that their eigenfunctions remain unchanged. The technique was first developed by Berenger for application to problems involving electromagnetic wave propagation. It was later extended to the linearized Euler, Euler and Navier-Stokes equations by Hu and his coauthors. The PML technique ensures the no-reflection property for all waves, irrespective of incidence angle, wavelength, and propagation direction. Although the technique requires the solution of a set of auxiliary equations, the computational overhead is easily justified since it allows smaller domain sizes and can provide better accuracy, stability, and convergence of the numerical solution. In this paper, the PML technique is developed in the context of a high-order spectral-element Discontinuous Galerkin (DG) method. The technique is compared to other approaches to treating the in flow and out flow boundary, such as those based on using characteristic boundary conditions and sponge layers. The
Coupling molecular dynamics with lattice Boltzmann method based on the immersed boundary method
Tan, Jifu; Sinno, Talid; Diamond, Scott
2017-11-01
The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the classic problem of rigid ellipsoid particle orbit in shear flow, blood cell stretching test and effective blood viscosity, and demonstrated essentially linear scaling over 16 cores. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code. NIH 1U01HL131053-01A1.
A review is presented of the heat (and or component mass transfer boundary layer concept. The review included the following: Basic Equations, Partial...Methods, Series Methods for Wedge Flows, and Spalding’s Methods; Extension of Nickel’s Estimation Method to Heat and Mass Transfer , Estimation Theorem...for Heat and Mass Transfer , Application of Nickel’s Estimation Theorem, Discussion on Bracketing Unknown Exact Solutions with Lower and Upper Bounds
Development of a coupled level set and immersed boundary method for predicting dam break flows
Yu, C. H.; Sheu, Tony W. H.
2017-12-01
Dam-break flow over an immersed stationary object is investigated using a coupled level set (LS)/immersed boundary (IB) method developed in Cartesian grids. This approach adopts an improved interface preserving level set method which includes three solution steps and the differential-based interpolation immersed boundary method to treat fluid-fluid and solid-fluid interfaces, respectively. In the first step of this level set method, the level set function ϕ is advected by a pure advection equation. The intermediate step is performed to obtain a new level set value through a new smoothed Heaviside function. In the final solution step, a mass correction term is added to the re-initialization equation to ensure the new level set is a distance function and to conserve the mass bounded by the interface. For accurately calculating the level set value, the four-point upwinding combined compact difference (UCCD) scheme with three-point boundary combined compact difference scheme is applied to approximate the first-order derivative term shown in the level set equation. For the immersed boundary method, application of the artificial momentum forcing term at points in cells consisting of both fluid and solid allows an imposition of velocity condition to account for the presence of solid object. The incompressible Navier-Stokes solutions are calculated using the projection method. Numerical results show that the coupled LS/IB method can not only predict interface accurately but also preserve the mass conservation excellently for the dam-break flow.
Zhang, Chao; Cheng, Li; Qiu, Jinhao; Wang, Hongyuan
2016-04-01
Metal-core Piezoelectric Fiber (MPF) was shown to have great potential to be a structurally integrated sensor for structural health monitoring (SHM) applications. Compared with the typical foil strain gauge, MPF is more suitable for high frequency strain measurement and can create direct conversion of mechanical energy into electric energy without the need for complex signal conditioners or gauge bridges. In this paper, a MPF-based smart layer is developed as an embedded network of distributed strain sensors that can be surface-mounted on a thin-walled structure. Each pair of the adjacent MPFs divides the entire structure into several "virtual elements (VEs)". By exciting the structure at the natural frequency of the VE, a "weak" formulation of the previously developed Pseudo-excitation (PE) approach based on sparse virtual element boundary measurement (VEBM) is proposed to detect the damage. To validate the effectiveness of the VEBM based approach, experiments are conducted to locate a small crack in a cantilever beam by using a MPF- based smart layer and a Laser Doppler Vibrometer (LDV). Results demonstrate that the proposed VEBM approach not only inherits the enhanced noise immunity capability of the "weak" formulation of the PE approach, but also allows a significant reduction in the number of measurement points as compared to the original version of the PE approach.
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
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.; Bienstman, P.; Vanholme, L.
2004-01-01
Finite element vectorial optical mode solver is used to analyze microstructured waveguides in a relatively small computational domain. The presentation will consider the computational method, as well as the applications of it on a number of waveguides with 2-D cross section where microstructures are
Coupled Boundary and Finite Element Analysis of Vibration from Railway Tunnels
DEFF Research Database (Denmark)
Andersen, Lars; Jones, C.J.C.
2006-01-01
The analysis of vibration from railway tunnels is of growing interest as new and higher-speed railways are built under the ground to address the transport problems of growing modern urban areas around cities. Such analysis can be carried out using numerical methods but models and therefore comput...
Villanueva Perez, Carlos Hernan
Computational design optimization provides designers with automated techniques to develop novel and non-intuitive optimal designs. Topology optimization is a design optimization technique that allows for the evolution of a broad variety of geometries in the optimization process. Traditional density-based topology optimization methods often lack a sufficient resolution of the geometry and physical response, which prevents direct use of the optimized design in manufacturing and the accurate modeling of the physical response of boundary conditions. The goal of this thesis is to introduce a unified topology optimization framework that uses the Level Set Method (LSM) to describe the design geometry and the eXtended Finite Element Method (XFEM) to solve the governing equations and measure the performance of the design. The methodology is presented as an alternative to density-based optimization approaches, and is able to accommodate a broad range of engineering design problems. The framework presents state-of-the-art methods for immersed boundary techniques to stabilize the systems of equations and enforce the boundary conditions, and is studied with applications in 2D and 3D linear elastic structures, incompressible flow, and energy and species transport problems to test the robustness and the characteristics of the method. A comparison of the framework against density-based topology optimization approaches is studied with regards to convergence, performance, and the capability to manufacture the designs. Furthermore, the ability to control the shape of the design to operate within manufacturing constraints is developed and studied. The analysis capability of the framework is validated quantitatively through comparison against previous benchmark studies, and qualitatively through its application to topology optimization problems. The design optimization problems converge to intuitive designs and resembled well the results from previous 2D or density-based studies.
Directory of Open Access Journals (Sweden)
H. Edalati
2016-01-01
Full Text Available Utilizing one of the mesh free methods, the present paper concerns static analysis of thin plates with various geometric shapes based on the mindlin classical plate theories. In this numerical method, the domain of issue is solely expressed through a set of nods and no gridding or element is required. To express the domain of issues with various geometric shapes, first a set of nodes are defined in a standard rectangular domain , then via a three-order map with, these nodes are transferred to the main domain of the original issue; therefore plates of various geometric shapes can be analyzed. Among meshfree numerical methods, Element Free Galerkin method (EFG is utilized here. The method is one of the weak form integral methods that uses MLS shape functions for approximation. Regarding the absence of Delta feature in MLS functions, boundary conditions cannot be imposed directly; hence the Lagrangian method is utilized to impose boundary conditions. At the end, our outputs are compared with those of analytic and finite element methods for plates, in order to validate the exactness of our solution method, and then after reliability is established, a few new examples will be solved.
Solving eighth-order boundary value problems using differential transformation method
Hussin, Che Haziqah Che; Mandangan, Arif
2014-12-01
In this study, we solved linear and nonlinear eighth-order boundary value problems using Differential Transformation Method. Then we calculate the error of DTM and compare the results with other methods such as modified application of the variational iteration method (MVAM), homotopy perturbation method (HPM) and modified Adomian decomposition method (MADM). We compared the errors of each method with exact solutions. We provided several numerical examples in order to show the accuracy and efficiency of present method. The results showed that the DTM is more accurate in comparison with those obtained by other methods.
Boundary layer separation method for recycling of sodium ions from industrial wastewater.
Petho, Dóra; Horváth, Géza; Liszi, János; Tóth, Imre; Paor, Dávid
2010-12-01
The most effective technological solution for waste treatment is recycling. We have developed a new method for the treatment of industrial wastewaters and have called it the boundary layer separation method (BLSM). We have used the phenomenon that, on the surface of an electrically charged electrode, ions can be enriched in the boundary layer, as compared with the inside of the phase. The essence of the method is that, with an appropriately chosen velocity, the boundary layer can be removed from the wastewater, and the boundary layer, which is rich in ions, can be recycled. The BLSM can be executed as a cyclic procedure. The capacitance of the boundary layer was examined. The best mass transport can be achieved with the use of 1000 and 1200 mV polarization potentials in the examined system, with its value being 1200 mg/m2 per cycle. The necessary operation times were determined by the examination of the velocity of the electrochemical processes. When using 1000 mV polarization potential, the necessary adsorption time is at least 25 seconds, and the desorption time at least 300 seconds. The advantage of the procedure is that it does not use dangerous chemicals, only inert electrodes. The drawback is that it is not selective to ions, the achievable separation in one step is low, and the hydrogen that emerges during the electrolysis might be dangerous.
Deniz, Sinan; Bildik, Necdet
2016-06-01
In this paper, we use Adomian Decomposition Method (ADM) to solve the singularly perturbed fourth order boundary value problem. In order to make the calculation process easier, first the given problem is transformed into a system of two second order ODEs, with suitable boundary conditions. Numerical illustrations are given to prove the effectiveness and applicability of this method in solving these kinds of problems. Obtained results shows that this technique provides a sequence of functions which converges rapidly to the accurate solution of the problems.
The Evaluation of the Boundary Vorticity by URANS and LES Methods
Directory of Open Access Journals (Sweden)
Ion MALAEL
2015-12-01
Full Text Available The role of concentrated vorticity in fluid dynamics phenomena, concerning both the vorticity creation at the boundary and the response to the flow field is not wholly understood. The Lighthill describes the vorticity production at a solid boundary as a slow diffusion of the vorticity similar to the Fourier heat conduction. In the paper it is shown that this mechanism associated to URANS method is not applied to the concentrated vorticity case, and the LES method better reproduces the flows involving concentrations vorticity.
Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates
Kitahara, M
1985-01-01
The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro
Mikheev, N. I.; Saushin, I. I.; Goltsman, A. E.
2017-09-01
The results of an experimental evaluation of velocity profiles, turbulent pulsations, generation and dissipation of turbulent energy in a nonequilibrium boundary layer under the adverse pressure gradient are presented. The profiles of characteristics are estimated by means of the field dynamics of the two-component instantaneous velocity vectors measured by the optical method Smoke Image Velocimetry. The opportunities of using the field measurement method SIV to study the spatial evolution of small-scale characteristics in a boundary layer with a pressure gradient have been showed.
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
DEFF Research Database (Denmark)
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
(7). In this paper a reliability-based shape optimization problem is formulated with the total expected cost as objective function and some requirements for the reliability measures (element or systems reliability measures) as constraints, see section 2. As design variables sizing variables......Application of first-order reliability methods FORM (see Madsen, Krenk & Lind [8)) in structural design problems has attracted growing interest in recent years, see e.g. Frangopol [4), Murotsu, Kishi, Okada, Yonezawa & Taguchi [9) and Sørensen [14). In probabilistically based optimal design...... stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...
The nonconforming virtual element method for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications
2018-02-05
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L^{2}-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.
Ardonceau, Pascal
2009-04-01
The Note presents an unconventional computational method for irrotational and incompressible fluid flows over lifting bodies. At first, Laplace's equation for the velocity potential is solved with internal Dirichlet conditions expressed at the nodes of the mesh rather than at smooth surface positions. Continuous distributions of surface normal doublets are used, and obtaining the surface velocity field with such distributions becomes straightforward. Secondly, an original Neumann type formulation of the Kutta conditions is proposed. Expressing the minimization of the velocity flux across the wall shows a significant reduction of the discretization impact upon the computed global efforts when compared to local no-load conditions. The method can be applied to 2 or 3-dimensional flows, steady or not. To cite this article: P. Ardonceau, C. R. Mecanique 337 (2009).
Energy Technology Data Exchange (ETDEWEB)
Del Coz Diaz, J.J.; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown. [Author].
Energy Technology Data Exchange (ETDEWEB)
Diaz del Coz, J.J. [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)]. E-mail: juanjo@constru.uniovi.es; Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Rodriguez, A. Martin [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Martinez-Luengas, A. Lozano [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown.
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.
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.
Li, Ping
2014-05-01
A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens\\' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer\\'s shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.
Hybrid immersed boundary method for airfoils with a trailing-edge flap
DEFF Research Database (Denmark)
Zhu, Wei Jun; Behrens, Tim; Shen, Wen Zhong
2013-01-01
In this paper, a hybrid immersed boundary technique has been developed for simulating turbulent flows past airfoils with moving trailing-edge flaps. Over the main fixed part of the airfoil, the equations are solved using a standard body-fitted finite volume technique, whereas the moving trailing...... boundaries the k-ωturbulence model is modified and adapted to the local conditions associated with the immersed boundary method. The obtained results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing-edge flap and that flow control...... using an adjustable trailing-edge flap is an efficient way to regulate the aerodynamic loading on airfoils. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved....
Fraga Filho, Carlos Alberto Dutra
2017-11-01
The aim of this paper is to present a computational algorithmic implementation of physical reflective boundary conditions and applications, for use in particle methods. It is motivated by the lack of a straightforward study in the literature dedicated to the presentation of this reflective boundary condition, based on Newton's restitution law and the foundations of analytic geometry. Particular attention is given here to the procedures of collision detection and response. The importance of the consistency of input data and an appropriate temporal integration technique for use in the particle method is also discussed. Validation tests are performed, with the results of the algorithm verified using analytical results. Numerical simulations of static and dynamic problems are carried out. The analysis of the numerical results shows that the physical reflective boundary conditions are consistent and that the algorithm has been properly implemented.
Application of the Finite-Element Z-Matrix Method to e-H2 Collisions
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
The present study adapts the Z-matrix formulation using a mixed basis of finite elements and Gaussians. This is a energy-independent basis which allows flexible boundary conditions and is amenable to efficient algorithms for evaluating the necessary matrix elements with molecular targets.
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T.
1987-01-01
A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector.
Methods and framework for visualizing higher-order finite elements.
Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh
2006-01-01
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the
Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations
Iliev, Oleg P.
2010-01-01
We present a two-scale finite element method for solving Brinkman\\'s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy\\'s equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.
Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows
Matin, Rastin; Hernandez-Garcia, Anier; Mathiesen, Joachim
2016-01-01
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.
Safner, T.; Miller, M.P.; McRae, B.H.; Fortin, M.-J.; Manel, S.
2011-01-01
Recently, techniques available for identifying clusters of individuals or boundaries between clusters using genetic data from natural populations have expanded rapidly. Consequently, there is a need to evaluate these different techniques. We used spatially-explicit simulation models to compare three spatial Bayesian clustering programs and two edge detection methods. Spatially-structured populations were simulated where a continuous population was subdivided by barriers. We evaluated the ability of each method to correctly identify boundary locations while varying: (i) time after divergence, (ii) strength of isolation by distance, (iii) level of genetic diversity, and (iv) amount of gene flow across barriers. To further evaluate the methods' effectiveness to detect genetic clusters in natural populations, we used previously published data on North American pumas and a European shrub. Our results show that with simulated and empirical data, the Bayesian spatial clustering algorithms outperformed direct edge detection methods. All methods incorrectly detected boundaries in the presence of strong patterns of isolation by distance. Based on this finding, we support the application of Bayesian spatial clustering algorithms for boundary detection in empirical datasets, with necessary tests for the influence of isolation by distance. ?? 2011 by the authors; licensee MDPI, Basel, Switzerland.
Coupled Boundary and Finite Element Analysis of Vibration from Railway Tunnels
DEFF Research Database (Denmark)
Andersen, Lars; Jones, C. J. C.
2004-01-01
The analysis of vibration from railway tunnels is of growing interest as new and higher-speed railways are built under the ground to address the transport problems of growing modern urban areas around cities. Such analysis can be carried out using numerical methods but models and therefore...... axis, it is useful to evaluate the potential uses of two-dimensional models before committing to much more costly three-dimensional approaches. The vibration forces in the track due to the passage of a train are by nature three-dimensional and a complete analysis undoubtedly requires a model of three......-dimensional wave propagation. The aim of this paper is to investigate the quality of the information that can be gained from a two-dimensional model of a railway tunnel. The vibration transmission from the tunnel floor to the ground surface is analysed for the frequency range relevant to the perception of whole...
A comparison of numerical methods used for finite element modelling of soft tissue deformation
Pathmanathan, P
2009-05-01
Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.
Calculation of Pressure Distribution at Rotary Body Surface with the Vortex Element Method
Directory of Open Access Journals (Sweden)
S. A. Dergachev
2014-01-01
Full Text Available Vortex element method allows to simulate unsteady hydrodynamic processes in incompressible environment, taking into account the evolution of the vortex sheet, including taking into account the deformation or moving of the body or part of construction.For the calculation of the hydrodynamic characteristics of the method based on vortex element software package was developed MVE3D. Vortex element (VE in program is symmetrical Vorton-cut. For satisfying the boundary conditions at the surface used closed frame of vortons.With this software system modeled incompressible flow around a cylindrical body protection elongation L / D = 13 with a front spherical blunt with the angle of attack of 10 °. We analyzed the distribution of the pressure coefficient on the body surface of the top and bottom forming.The calculate results were compared with known Results of experiment.Considered design schemes with different number of Vorton framework. Also varied radius of VE. Calculation make possible to establish the degree of sampling surface needed to produce close to experiment results. It has been shown that an adequate reproducing the pressure distribution in the transition region spherical cylindrical surface, on the windward side requires a high degree of sampling.Based on these results Can be possible need to improve on the design scheme of body's surface, allowing more accurate to describe the flow vorticity in areas with abrupt changes of geometry streamlined body.
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.
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. .
Lamichhane, Bishnu P.
2014-01-01
We present a finite element method for Stokes equations using the Crouzeix-Raviart element for the velocity and the continuous linear element for the pressure. We show that the inf-sup condition is satisfied for this pair. Two numerical experiments are presented to support the theoretical results.
2.5-D frequency-domain viscoelastic wave modelling using finite-element method
Zhao, Jian-guo; Huang, Xing-xing; Liu, Wei-fang; Zhao, Wei-jun; Song, Jian-yong; Xiong, Bin; Wang, Shang-xu
2017-10-01
2-D seismic modelling has notable dynamic information discrepancies with field data because of the implicit line-source assumption, whereas 3-D modelling suffers from a huge computational burden. The 2.5-D approach is able to overcome both of the aforementioned limitations. In general, the earth model is treated as an elastic material, but the real media is viscous. In this study, we develop an accurate and efficient frequency-domain finite-element method (FEM) for modelling 2.5-D viscoelastic wave propagation. To perform the 2.5-D approach, we assume that the 2-D viscoelastic media are based on the Kelvin-Voigt rheological model and a 3-D point source. The viscoelastic wave equation is temporally and spatially Fourier transformed into the frequency-wavenumber domain. Then, we systematically derive the weak form and its spatial discretization of 2.5-D viscoelastic wave equations in the frequency-wavenumber domain through the Galerkin weighted residual method for FEM. Fixing a frequency, the 2-D problem for each wavenumber is solved by FEM. Subsequently, a composite Simpson formula is adopted to estimate the inverse Fourier integration to obtain the 3-D wavefield. We implement the stiffness reduction method (SRM) to suppress artificial boundary reflections. The results show that this absorbing boundary condition is valid and efficient in the frequency-wavenumber domain. Finally, three numerical models, an unbounded homogeneous medium, a half-space layered medium and an undulating topography medium, are established. Numerical results validate the accuracy and stability of 2.5-D solutions and present the adaptability of finite-element method to complicated geographic conditions. The proposed 2.5-D modelling strategy has the potential to address modelling studies on wave propagation in real earth media in an accurate and efficient way.
Flexural Modeling of the Andean System Using Finite Element Method
Sacek, V.; Ussami, N.
2007-05-01
The general equation of flexure of the lithosphere in cartesian coordinates is solved using a numerical Finite Element Method (FEM) with triangular elements in non-structured meshes. This alternative way to model bending of thin elastic plates lying over an inviscid fluid allows taking into account lateral variation of rigidity, plate discontinuities and full 3-D representation of loads. The numerical solution was initially compared with the analytical solution of bending of an elastic plate loaded by an uniformally distributed load. The method was applied to model flexure of a plate due to curved orogenic belts and the results were compared with solutions obtained if a 2-D approximation of plates and loads was considered. The proposed numerical method was applied to study flexural deformation of the western edge of the South American lithospheric plate due to the loads of the Andean mountains, using Te =75 km for both continuous and broken plates. The predicted forebulges agree with the observed distribution of positive gravity anomalies paralleling the negative gravity anomalies associated with the high topography of the Andes. Maximum amplitudes of forebulges correlate with Purus Arch in Solimões basin (W Brazil) and the Chaco Pampeana plain (Argentina), and between these two regions, a saddle point occurs over the Pantanal wetland (SW Brazil).
The Distinct Element Method - Application to Structures in Jointed Rock
Energy Technology Data Exchange (ETDEWEB)
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.