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…
An inverse problem by boundary element method
Energy Technology Data Exchange (ETDEWEB)
Tran-Cong, T.; Nguyen-Thien, T. [University of Southern Queensland, Toowoomba, QLD (Australia); Graham, A.L. [Los Alamos National Lab., NM (United States)
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
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.
Numerical modelling of solidification process using interval boundary element method
A. Piasecka Belkhayat
2008-01-01
In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM). The interval Gauss elimination m...
Numerical modelling of solidification process using interval boundary element method
Directory of Open Access Journals (Sweden)
A. Piasecka Belkhayat
2008-12-01
Full Text Available In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM. The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.
(Environmental and geophysical modeling, fracture mechanics, and boundary element methods)
Energy Technology Data Exchange (ETDEWEB)
Gray, L.J.
1990-11-09
Technical discussions at the various sites visited centered on application of boundary integral methods for environmental modeling, seismic analysis, and computational fracture mechanics in composite and smart'' materials. The traveler also attended the International Association for Boundary Element Methods Conference at Rome, Italy. While many aspects of boundary element theory and applications were discussed in the papers, the dominant topic was the analysis and application of hypersingular equations. This has been the focus of recent work by the author, and thus the conference was highly relevant to research at ORNL.
Analysis of Dynamic Modeling Method Based on Boundary Element
Directory of Open Access Journals (Sweden)
Xu-Sheng Gan
2013-07-01
Full Text Available The aim of this study was to study an improved dynamic modeling method based on a Boundary Element Method (BEM. The dynamic model was composed of the elements such as the beam element, plate element, joint element, lumped mass and spring element by the BEM. An improved dynamic model of a machine structure was established based on plate-beam element system mainly. As a result, the dynamic characteristics of a machine structure were analyzed and the comparison of computational results and experimental’s showed the modeling method was effective. The analyses indicate that the introduced method inaugurates a good way for analyzing dynamic characteristics of a machine structure efficiently.
Treatment of domain integrals in boundary element methods
Energy Technology Data Exchange (ETDEWEB)
Nintcheu Fata, Sylvain [ORNL
2012-01-01
A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.
Effective and neutral stresses in soils using boundary element methods
Alarcón Álvarez, Enrique; García-Suárez, C.; Reverter, A.
1983-01-01
The evaluation of neutral pressures in soil mechanics problems is a fundamental step to evaluate deformations in soils. In this paper, we present some results obtained by using the boundary element method for plane problems, describing the undrained situation as well as the consolidation problem.
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
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...
A Kind of Boundary Element Methods for Boundary Value Problem of Helmholtz Equation
Institute of Scientific and Technical Information of China (English)
张然; 姜正义; 马富明
2004-01-01
Problems for electromagnetic scattering are of significant importance in many areas of technology. In this paper we discuss the scattering problem of electromagnetic wave incident by using boundary element method associated with splines. The problem is modelled by a boundary value problem for the Helmholtz eouation
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 ...
Institute of Scientific and Technical Information of China (English)
GUZELBEY Ibrahim H.; KANBER Bahattin; AKPOLAT Abdullah
2004-01-01
In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.
Institute of Scientific and Technical Information of China (English)
LIANG Xinhua; ZHU Ping; LIN Zhongqin; ZHANG Yan
2007-01-01
A lightweight automotive prototype using alter- native materials and gauge thickness is studied by a numeri- cal method. The noise, vibration, and harshness (NVH) performance is the main target of this study. In the range of 1-150 Hz, the frequency response function (FRF) of the body structure is calculated by a finite element method (FEM) to get the dynamic behavior of the auto-body structure. The pressure response of the interior acoustic domain is solved by a boundary element method (BEM). To find the most contrib- uting panel to the inner sound pressure, the panel acoustic contribution analysis (PACA) is performed. Finally, the most contributing panel is located and the resulting structural optimization is found to be more efficient.
THE COUPLING OF NATURAL BOUNDARY ELEMENT AND FINITE ELEMENT METHOD FOR 2D HYPERBOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
De-hao Yu; Qi-kui Du
2003-01-01
In this paper, we investigate the coupling of natural boundary element and finite ele-ment methods of exterior initial boundary value problems for hyperbolic equations. Thegoverning equation is first discretized in time, leading to a time-step scheme, where anexterior elliptic problem has to be solved in each time step. Second, a circular artifi-in an unbounded domain is transformed into the nonlocal boundary value problem in abounded subdomain. And the natural integral equation and the Poisson integral formulaare obtained in the infinite domain Ω2 outside circle of radius R. The coupled variationalformulation is given. Only the function itself, not its normal derivative at artificial bound-and the boundary element stiffness matrix has a few different elements. Such a coupledmethod is superior to the one based on direct boundary element method. This paper dis-cusses finite element discretization for variational problem and its corresponding numericaltechnique, and the convergence for the numerical solutions. Finally, the numerical exampleis presented to illustrate feasibility and efficiency of this method.
Numerical Improvement of The Three-dimensional Boundary Element Method
Ortiz-Aleman, C.; Gil-Zepeda, A.; SÃ¡nchez-Sesma, F. J.; Luzon-Martinez, F.
2001-12-01
Boundary element methods have been applied to calculate the seismic response of various types of geological structures. Dimensionality reduction and a relatively easy fulfillment of radiation conditions at infinity are recognized advantages over domain approaches. Indirect Boundary Element Method (IBEM) formulations give rise to large systems of equations, and the considerable amount of operations required for solving them suggest the possibility of getting some benefit from exploitation of sparsity patterns. In this article, a brief study on the structure of the linear systems derived from the IBEM method is carried out. Applicability of a matrix static condensation algorithm to the inversion of the IBEM coefficient matrix is explored, in order to optimize the numerical burden of such method. Seismic response of a 3-D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzon (1995), was computed and comparisons on time consumption and memory allocation are established. An alternative way to deal with those linear systems is the use of threshold criteria for the truncation of the coefficient matrix, which implies the solution of sparse approximations instead of the original full IBEM systems (Ortiz-Aleman et al., 1998). Performance of this optimized approach is evaluated on its application to the case of a three-dimensional alluvial basin with irregular shape. Transfer functions were calculated for the frequency range from 0 to 1.25 Hz. Inversion of linear systems by using this algorithm lead to significant saving on computer time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
Boundary element method approach to magnetostatic wave problems
Yashiro, K.; Ohkawa, S.; Miyazaki, M.
1985-03-01
In this paper, the technique for application of the boundary element method (BEM) to analysis of magnetostatic waves (MSWs) is established. To show the availability of the technique, two types of waveguides for the MSW are studied; one is a waveguide constituting a YIG slab shielded with metal plates and the other is a waveguide consisting of an unshielded YIG slab. With the former structure the results obtained by the present technique are compared with the analytical solutions, and with the latter the BEM is compared with Marcatili's approximate method since there is no analytical solution in this case. Those comparisons are performed successfully for both cases. The paper concludes that the BEM is useful and effective for analysis of a wide range of MSW problems.
Comparison of boundary element and finite element methods in two-dimensional inelastic analysis
International Nuclear Information System (INIS)
The finite element method has been commonly used to solve boundary value problems in inelastic deformation of metallic structures. Recently, Mukherjee and his coworkers applied the boundary element method to such problems. Planar time-dependent inelasticity problems were considered and a constitutive model with state variables was used to describe material behavior. The accuracy and computational efficiency of these two methods are compared for certain selected planar problems. In order to make the comparison as meaningful as possible, in house computer codes developed by the same group at Cornell, are used
Substantive provisions of Numeral-analytical boundary elements method
Directory of Open Access Journals (Sweden)
V.F. Orobey
2011-06-01
Full Text Available Substantive propositions of the new method of design calculation, that got the name "Numeral-analytical of boundary elements method", offered by authors, are brought. A method consists of development of the fundamental system of decisions (analytically and Green functions (also analytically for every examined task.For the account of certain border terms, or terms of contact between the separate modules (the separate element of the system is so named the small system of linear algebraic equalizations, that must be decided numeral, is made.Discretisation only of border of the area occupied by an object, sharply diminishes the order of the system of resolvent equalizations; there is possibility of decline of regularity of the decided task. A method is strictly reasonable mathematically, as uses the fundamental decisions of differential equalizations, and, means, within the framework of the accepted hypotheses allows to get the exact meaning of parameters of task (efforts, moving, tensions, currents, frequencies of eigentones, critical forces of loss of stability et cetera into an area.Simplicity of logic of algorithm, good convergence of decision, high stability and small accumulation of errors at numeral operations, are marked also.
Submarine Magnetic Field Extrapolation Based on Boundary Element Method
Institute of Scientific and Technical Information of China (English)
GAO Jun-ji; LIU Da-ming; YAO Qiong-hui; ZHOU Guo-hua; YAN Hui
2007-01-01
In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine, a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method (BEM). An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine. The data in differentheights above the model submarine are obtained by use of tri-axial magnetometers. The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data. Moreover, the model can reflect the submarine magnetic field distribution in the air exactly, and is valuable in practical engineering.
A new simple multidomain fast multipole boundary element method
Huang, S.; Liu, Y. J.
2016-09-01
A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.
Comparison of boundary element and finite element methods in spur gear root stress analysis
Sun, H.; Mavriplis, D.; Huston, R. L.; Oswald, F. B.
1989-01-01
The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.
Three-dimensional shape optimization using the boundary element method
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1994-06-01
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod.
Three-dimensional shape optimization using boundary element method
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1993-04-01
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then, the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity shape in a cube and a connecting rod.
NUMERICAL SIMULATION OF 2D FIBER-REINFORCED COMPOSITES USING BOUNDARY ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
KONG Fan-zhong; ZHENG Xiao-ping; YAO Zhen-han
2005-01-01
The boundary element method was improved for the 2D elastic composites with randomly distributed inclusions. This problem can be reduced to a boundary integral equation for a multi-connected domain. Further, considering the matrices of the tractions and displacements for each group of the identical inclusion were the same, an effective computational scheme was designed, since the orders of the resulting matrix equations can be greatly reduced. Numerical examples indicate that this boundary element method scheme is more effective than the conventional multi-domain boundary element method for such a problem. The present scheme can be used to investigate the effective mechanical properties of the fiber-reinforced composites.
Two simple finite element methods for Reissner--Mindlin plates with clamped boundary condition
Bishnu P. Lamichhane
2013-01-01
We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite element techniques. We prove optimal a priori error estimates for both methods.
Energy Technology Data Exchange (ETDEWEB)
Itagaki, M. (Japan Atomic Energy Research Inst., Dept. of Nuclear Ship Engineering, Aza-Kitasekine, Oaza-Sekine, Mutsu, Aomori 035 (JP)); Brebbia, C.A. (Computational Mechanics Inst., Ashurst Lodge, Ashurst, Southampton SO4 2AA (GB))
1991-03-01
This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations.
Seybert, A. F.; Wu, T. W.; Wu, X. F.
1994-01-01
This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
A practical guide to boundary element methods with the software library BEMLIB
Pozrikidis, C
2002-01-01
LAPLACE'S EQUATION IN ONE DIMENSIONGreen's First and Second Identities and the Reciprocal Relation Green's FunctionsBoundary-Value Representation Boundary-Value EquationLAPLACE'S EQUATION IN TWO DIMENSIONS Green's First and Second Identities and the Reciprocal RelationGreen's Functions Integral Representation Integral Equations Hypersingular Integrals Irrotational FlowGeneralized Single- and Double-Layer Representations BOUNDARY-ELEMENT METHODS FOR LAPLACE'S EQUATION IN TWO DIMENSIONSBoundary Element Discretization .Discretization of
An interpolating boundary element-free method (IBEFM) for elasticity problems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.
Institute of Scientific and Technical Information of China (English)
Sheng Zhang; Dehao Yu
2007-01-01
In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.
A Boundary Element Method for Steady Infiltration from Periodic Channels.
Azis, Moh. Ivan; Clements, D. L.; Lobo, M
2003-01-01
The matric flux potential and horizontal and vertical flux distributions are obtained for periodic irrigation channels by using boundary integral equation techniques. Numerical results are given for the special cases of semicircular and rectangular channels and the results compared with those of Batu [Soil Science Society of America Journal, 42:545??? 549, 1978] and Warrick and Lomen [Soil Science Society of America Journal, 40:639???643, 1976] for a flat strip. The re...
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)...
Boundary Element Method Solution in the Time Domain For a Moving Time-Dependent Force
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Kirkegaard, Poul Henning; Rasmussen, K. M.
2001-01-01
The problem of a moving time dependent concentrated force on the surface of an elastic halfspace is of interest in the analysis of traffic generated noise. The Boundary element method (BEM) is superior to the finite element method (FEM) in solving such problems due to its inherent ability so...
Plasma boundary identification in HL-2A by means of the finite current element method
Institute of Scientific and Technical Information of China (English)
You Tian-Xue; Yuan Bao-Shan; Liu Li; Li Fang-Zhu
2005-01-01
In this paper, the finite current element(FCE)method used in HL-2A is described. The calculation and test results show that the error of the reconsturcted boundary given by the FCE method(<3mm)is smaller than that obtained by the current filament medthod used before(<6mm).Even if some current elements are Iocated out of the plasma boundary,the FCE method can also identify the plasma boundary successfully.If the location of the finite current elements is changed is a certain area, the error of the reconstructed boundary is always very small. By employing a conventional PC(Pentium 4 2.4 GHz),the calculation time of one set of plasma discharge parameters does nto exceed 1ms. Thus, the FCM method can identify the diverted plamma configuration quickly and accurately.This is essential and important for real-time shape control in IIL-2A.
A study of applicability of soil-structure interaction analysis method using boundary element method
Energy Technology Data Exchange (ETDEWEB)
Kim, M. K. [KAERI, Taejon (Korea, Republic of); Kim, M. K. [Yonsei University, Seoul (Korea, Republic of)
2003-07-01
In this study, a numerical method for Soil-Structure Interaction (SSI) analysis using FE-BE coupling method is developed. The total system is divided into two parts so called far field and near field. The far field is modeled by boundary element formulation using the multi-layered dynamic fundamental solution and coupled with near field modeled by finite elements. In order to verify the seismic response analysis, the results are compared with those of other commercial code. Finally, several SSI analyses which induced seismic loading are performed to examine the dynamic behavior of the system. As a result, it is shown that the developed method can be an efficient numerical method for solving the SSI analysis.
Murat Ünal
2002-01-01
In this study, a two-dimensional software was developed by using the boundary element method, in order to model and solve the rock mechanics problems encountered in surface and underground excavations. Stability of rock wedges formed at the roof of underground excavations were investigated in detail by using this software. The behaviour of the symmetric wedge on different joint stiffnesses was studied using a modified boundary element software. Then the results obtained were discussed and com...
Boundary Element Method with Non—overlapping Domain Decomposition for Diffusion Equation
Institute of Scientific and Technical Information of China (English)
ZHUJialin; ZHANGTaiping
2002-01-01
A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented.The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integratioin process always restarts from the initial time condition.The process of replacing the interface values,which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel parallel iterative procedure,Numerical experiments demonstrate that the implementation of the present alogrithm is efficient.
CALCULATION OF MILL RIGIDITY BY THREE DIMENSION CONTACT BOUNDARY ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Vertical rigidity of the space self-adaptive 530 high rigidity mill is calculated by applying the boundary element method (BEM) of three-dimension elastic contact problem,which can update the existed deforming separation calculating theory and corresponding methods of material mechanics,elastic mechanics and finite element method.The method has less hypotheses and stronger synthesis in contact-type calculating model.The advantages of the method are high calculating rate,high calculating accuracy,etc..
On the numerical accuracy of the boundary element method [EEG application
Meijs, Jan W.H.; Weier, Onno W.; Peters, Maria J.; Oosterom, van Adriaan
1989-01-01
The numerical accuracy of the boundary element (BE) method used to solve the volume conduction problem of nested compartments, each having a homogeneous conductivity, is studied. The following techniques for improving this accuracy are discussed: the handling of the auto solid angle element ¿ii, the
DEFF Research Database (Denmark)
Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.
2007-01-01
A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...
An introductory study of the convergence of the direct boundary element method
DEFF Research Database (Denmark)
Juhl, Peter Møller
1997-01-01
Although boundary element methods have been used for three decades for the numerical solution of acoustic problems, the issue of convergence is not well known among acoustic engineers. In this paper the concept of convergence is introduced in an intuitive and empirical style. The convergence...... of an axisymmetric boundary element formulation is studied using linear, quadratic or superparametric elements. It is demonstrated that the rate of convergence of these formulations is reduced for calculations involving bodies with edges (geometric singularities). Two methods for improving the rate of convergence...
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
International Nuclear Information System (INIS)
The basic principles of the boundary element method numerical treatment of the radial flow heat diffusion equation are presented. The algorithm copes the time dependent Dirichlet and Neumann boundary conditions, temperature dependent material properties and regions from different materials in thermal contact. It is verified on the several analytically obtained test cases. The developed method is used for the modelling of unsteady radial heat flow in pressurized water reactor fuel rod. (author)
E-coil: an inverse boundary element method for a quasi-static problem
Energy Technology Data Exchange (ETDEWEB)
Sanchez, Clemente Cobos; Garcia, Salvador Gonzalez [Depto. Electromagnetismo y F. de la Materia Facultad de Ciencias University of Granada Avda. Fuentenueva E-18071 (Spain); Power, Henry, E-mail: ccobos@ugr.e [School of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham, Nottingham Park, Nottingham NG7 2RD (United Kingdom)
2010-06-07
Boundary element methods represent a valuable approach for designing gradient coils; these methods are based on meshing the current carrying surface into an array of boundary elements. The temporally varying magnetic fields produced by gradient coils induce electric currents in conducting tissues and so the exposure of human subjects to these magnetic fields has become a safety concern, especially with the increase in the strength of the field gradients used in magnetic resonance imaging. Here we present a boundary element method for the design of coils that minimize the electric field induced in prescribed conducting systems. This work also details some numerical examples of the application of this coil design method. The reduction of the electric field induced in a prescribed region inside the coils is also evaluated.
Energy Technology Data Exchange (ETDEWEB)
GHARAKHANI,ADRIN; WOLFE,WALTER P.
1999-10-01
The prediction of potential flow about zero thickness membranes by the boundary element method constitutes an integral component of the Lagrangian vortex-boundary element simulation of flow about parachutes. To this end, the vortex loop (or the panel) method has been used, for some time now, in the aerospace industry with relative success [1, 2]. Vortex loops (with constant circulation) are equivalent to boundary elements with piecewise constant variation of the potential jump. In this case, extending the analysis in [3], the near field potential velocity evaluations can be shown to be {Omicron}(1). The accurate evaluation of the potential velocity field very near the parachute surface is particularly critical to the overall accuracy and stability of the vortex-boundary element simulations. As we will demonstrate in Section 3, the boundary integral singularities, which arise due to the application of low order boundary elements, may lead to severely spiked potential velocities at vortex element centers that are near the boundary. The spikes in turn cause the erratic motion of the vortex elements, and the eventual loss of smoothness of the vorticity field and possible numerical blow up. In light of the arguments above, the application of boundary elements with (at least) a linear variation of the potential jump--or, equivalently, piecewise constant vortex sheets--would appear to be more appropriate for vortex-boundary element simulations. For this case, two strategies are possible for obtaining the potential flow field. The first option is to solve the integral equations for the (unknown) strengths of the surface vortex sheets. As we will discuss in Section 2.1, the challenge in this case is to devise a consistent system of equations that imposes the solenoidality of the locally 2-D vortex sheets. The second approach is to solve for the unknown potential jump distribution. In this case, for commonly used C{sup o} shape functions, the boundary integral is singular at
Analysis of 3-D Frictional Contact Mechanics Problems by a Boundary Element Method
Institute of Scientific and Technical Information of China (English)
KEUM Bangyong; LIU Yijun
2005-01-01
The development of two boundary element algorithms for solving 3-D, frictional, and linear elastostatic contact problems is reported in this paper. The algorithms employ nonconforming discretizations for solving 3-D boundary element models, which provide much needed flexibility in the boundary element modeling for 3-D contact problems. These algorithms are implemented in a new 3-D boundary element code and verified using several examples. For the numerical examples studied, the results using the new boundary element algorithms match very well with the results using a commercial finite element code, and clearly demonstrate the feasibility of the new boundary element approach for 3-D contact analysis.
AN EFFECTIVE BOUNDARY ELEMENT METHOD FOR ANALYSIS OF CRACK PROBLEMS IN A PLANE ELASTIC PLATE
Institute of Scientific and Technical Information of China (English)
YAN Xiang-qiao
2005-01-01
A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples ( i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.
Contact position controlling for two-dimensional motion bodies by the boundary element method
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
An algorithm is presented for controlling two-dimensional motion contact bodies with conforming discretization. Since a kind of special boundary element is utilized in the algorithm, the displacement compatibility and traction equilibrium conditions at nodes can be satisfied simultaneously in arbitrary locations of the contact interface. In addition, a method is also proposed in which the contact boundary location can be moved flexibly on the possible contact boundary. This method is effective to deal with moving and rolling contact problems on a possible larger moving or rolling contact region. Numerical examples show effectiveness of the presented scheme.
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 simulation method of combinding boundary element method with generalized Langevin dynamics
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new simulation approach to incorporate hydration force into generalized Langevin dynamics (GLD) is developed in this note. The hydration force determined by the boundary element method (BEM) is taken into account as the mean force terms of solvent including Coulombic interactions with the induced surface charge and the surface pressure of solvent. The exponential model is taken for the friction kernel. A simulation study has been performed on the cyclic undecapeptide cyclosporin A (CPA). The results obtained from the new method (GLDBEM) have been analyzed and compared with that obtained from the molecular dynamics (MD) simulation and the conventional stochastic dynamics (SD) simulation. We have found that the results obtained from GLDBEM show the obvious improvement over the SD simulation technique in the study of molecular structure and dynamic properties.
Pai, Ravindra
1991-01-01
A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface bo...
BOUNDARY ELEMENT METHOD FOR MOVING AND ROLLING CONTACT OF 2D ELASTIC BODIES WITH DEFECTS
Institute of Scientific and Technical Information of China (English)
姚振汉; 蒲军平; 金哲植
2001-01-01
A scheme of boundary element method for moving contact of two dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.
A finite element-boundary integral method for cavities in a circular cylinder
Kempel, Leo C.; Volakis, John L.
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.
Anton, I.; Carte, I. N.; Ludescher, H.; Iosif, A.
1990-04-01
The application of the boundary element method to the analysis of axisymmetric motions is examined with particular reference to turbomachines. A procedure for determining the hydrodynamic field in the meridian plane of turbomachine blading using the boundary element method is presented. The method is applied to a Francis turbine impeller with lateral boundaries of the Bovet type. The results obtained are compared with calculations by the finite element method.
A comparison of inverse boundary element method and near-field acoustical holography
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Hald, Jørgen; Saemann, E.-U.
1999-01-01
An inverse boundary element method (IBEM) is used to estimate the surface velocity of a rolling tyre from measurements of the near-field pressure. Subsequently, the sound pressure is calculated over a finite plane surface next to the tyre from the reconstructed velocity field on the tyre surface...
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 expres...
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...
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.
A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
Smith, David J
2010-01-01
A boundary element implementation of the regularised Stokeslet method of Cortez is applied to cilia and flagella-driven flows in biology. Previously-published approaches implicitly combine the force discretisation and the numerical quadrature used to evaluate boundary integrals. By contrast, a boundary element method can be implemented by discretising the force using basis functions, and calculating integrals using accurate numerical or analytic integration. This substantially weakens the coupling of the mesh size for the force and the regularisation parameter, and greatly reduces the number of degrees of freedom required. When modelling a cilium or flagellum as a one-dimensional filament, the regularisation parameter can be considered a proxy for the body radius, as opposed to being a parameter used to minimise numerical errors. Modelling a patch of cilia, it is found that: (1) For a fixed number of cilia, reducing cilia spacing reduces transport. (2) For fixed patch dimension, increasing cilia number increa...
Coupling finite and boundary element methods for 2-D elasticity problems
Krishnamurthy, T.; Raju, I. S.; Sistla, R.
1993-01-01
A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.
Boundary element method for the solution of the diffusion equation in cylindrical symmetry
International Nuclear Information System (INIS)
Equations for the solution of the diffusion equation in plane Cartesian geometry with the Boundary Element method was derived. The equation for the axi-symmetric case were set and included in the computer program. The results were compared to those obtained by the Finite Difference method. Comparing the results some advantages of the proposed method can be observed, with implications on the multidimensional problems. (author)
Institute of Scientific and Technical Information of China (English)
Habib Ammari; Gang Bao
2008-01-01
Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.
Li, Yuan; Dang, HuaYang; Xu, GuangTao; Fan, CuiYing; Zhao, MingHao
2016-08-01
The extended displacement discontinuity boundary integral equation (EDDBIE) and boundary element method is developed for the analysis of planar cracks of arbitrary shape in the isotropic plane of three-dimensional (3D) transversely isotropic thermo-magneto-electro-elastic (TMEE) media. The extended displacement discontinuities (EDDs) include conventional displacement discontinuity, electric potential discontinuity, magnetic potential discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, magnetic induction and heat flux. Employing a Hankel transformation, the fundamental solutions for unit point EDDs in 3D transversely isotropic TMEE media are derived. The EDDBIEs for a planar crack of arbitrary shape in the isotropic plane of a 3D transversely isotropic TMEE medium are then established. Using the boundary integral equation method, the singularities of near-crack border fields are obtained and the extended stress field intensity factors are expressed in terms of the EDDs on crack faces. According to the analogy between the EDDBIEs for an isotropic thermoelastic material and TMEE medium, an analogical solution method for crack problems of a TMEE medium is proposed for coupled multi-field loadings. Employing constant triangular elements, the EDDBIEs are discretized and numerically solved. As an application, the problems of an elliptical crack subjected to combined mechanical-electric-magnetic-thermal loadings are investigated.
Practical application of inverse boundary element method to sound field studies of tyres
DEFF Research Database (Denmark)
Schuhmacher, Andreas
1999-01-01
An approach based on boundary element modelling of sound sources and regularisation techniques was compared with Near-field Acoustical Holography in a study of vibration patterns on a rolling tyre [1]. In the present paper, a further investigation of this Inverse Boundary Element Method (IBEM) is......) is done. Emphasis is put on the regularisation process and how to choose an appropriate regularisation parameter in conjunction with the Tikhonov regularisation. This choice is of vital importance when solving a discrete ill-posed problem and a useful solution is sought. Another aspect...... of the reconstruction process is to feed our model of the problem with as much a priori knowledge as possible, e.g. in the sense of known velocity data on some surfaces. In the modelling of the tyre this can be done by imposing a boundary condition to the nodes belonging to the rim structure, where the normal surface...
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
According to the electric potential of oblique multi-needle electrodes (OMNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from multi-needle electrodes to conductive biological tissues was imaged by solving a set of linear equa- tions. Then, the electric field and potential generated by OMNE in biological tissues at any point may be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced sig- nificance for computing the field and the potential generated by OMNE in bio-tissue, which is a fast, effective and accurate computing method.
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 in...... with mesh definition, geometrical singularities and treatment of closed cavities. These issues are specific of the BEM with losses. Using examples, some strategies are presented that can alleviate shortcomings and improve performance....
Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method
Layton, Simon K.; Barba, Lorena A.
2015-01-01
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, $p$. We take advantage of a unique property of Krylov iterations that allow lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing $p$. ...
A finite element-boundary integral method for conformal antenna arrays on a circular cylinder
Kempel, Leo C.; Volakis, John L.
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.
Institute of Scientific and Technical Information of China (English)
Chang-Jun Zheng; Hai-Bo Chen; Lei-Lei Chen
2013-01-01
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
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 ...
Coupling finite and boundary element methods for two-dimensional potential problems
Krishnamurthy, T.; Raju, I. S.
1992-01-01
A finite element-boundary element (FE-BE) coupling method based on a weighted residual variational method is presented for potential problems, governed by either the Laplace or the Poisson equations. In this method, a portion of the domain of interest is modeled by finite elements (FE) and the remainder of the region by boundary elements (BE). Because the BE fundamental solutions are valid for infinite domains, a procedure that limits the effects of the BE fundamental solution to a small region adjacent to the FE region, called the transition region (TR), is developed. This procedure involves a judicious choice of functions called the transition (T) functions that have unit values on the BE-TR interface and zero values on the FE-TR interface. The present FE-BE coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions. Therefore, transition regions that extend to only one layer of elements between FE and BE regions and the use of simple linear transition functions work well.
ELECTRO-MECHANICAL COUPLING ANALYSIS OF MEMS STRUCTURES BY BOUNDARY ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
Zhang Kai; Cui Yunjun; Xiong Chunyang; Wang Congshun; Fang Jing
2004-01-01
In this paper, we present the applications of Boundary Element Method (BEM)to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems (MEMS).The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics. Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples.
FLUID BOUNDARY ELEMENT METHOD AND ORTHOGONAL TRANSFORM OF DOUBLE COMPLEX VARIABLES
Institute of Scientific and Technical Information of China (English)
罗义银
2003-01-01
A concept of orthogonal double function and its complex variables space was putforward. Its corresponding operation rules, the concept of analytic function and conformaltransform are established. And using this concept discussed its foreground for application offluid boundary element method. In results, this concept and special marks may be toenlarge the plane complex into three-dimensional space, and then extensive application maybe obtained in physics and mathematics.
Application of scaled boundary finite element method in static and dynamic fracture problems
Institute of Scientific and Technical Information of China (English)
Zhenjun Yang
2006-01-01
The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM)and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion.F0r dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.
Modeling the 3D Terrain Effect on MT by the Boundary Element Method
Institute of Scientific and Technical Information of China (English)
Ruan Baiyao; Xu Shizhe; Xu Zhifeng
2006-01-01
A numerical method is put forward in this paper, using the boundary element method(BEM) to model 3D terrain effects on magnetotelluric (MT) surveys. Using vector integral theory and electromagnetic field boundary conditions, the boundary problem of two electromagnetic fields in the upper half space (air) and lower half space (earth medium) was transformed into two vector integral equations just related to the topography: one magnetic equation for computing the magnetic field and the other electrical equation for computing the electrical field. The topography integral is decomposed into a series of integrals in a triangle element. For the integral in a triangle element, we suppose that the electromagnetic field in it is the stack of the electromagnetic field in the homogeneous earth and the topography response which is a constant; so the computation becomes simple, convenient and highly accurate. By decomposition and computation, each vector integral equation can be calculated by solving three linear equations that are related to the three Cartesian directions. The matrix of these linear equations is diagonally dominant and can be solved using the Symmetric Successive Over-Relaxation (SSOR) method. The apparent resistivity curve of MT on two 3D terrains calculated by BEM is shown in this paper.
Quantum corrected model for plasmonic nanoparticles: A boundary element method implementation
Hohenester, Ulrich
2015-05-01
We present a variant of the recently developed quantum corrected model (QCM) for plasmonic nanoparticles [Nat. Commun. 3, 825 (2012), 10.1038/ncomms1806] using nonlocal boundary conditions. The QCM accounts for electron tunneling in narrow gap regions of coupled metallic nanoparticles, leading to the appearance of new charge-transfer plasmons. Our approach has the advantages that it emphasizes the nonlocal nature of tunneling and introduces only contact resistance, but not ohmic losses through tunneling. Additionally, it can be implemented much more easily in boundary element method (BEM) approaches. We develop the methodology for the QCM using nonlocal boundary conditions and present simulation results of our BEM implementation, which are in good agreement with those of the original QCM.
Institute of Scientific and Technical Information of China (English)
Xiao Tang; Yuzhi Zhanga; Meng Liu; Yan Li
2009-01-01
A numerical analysis of galvanic corrosion of hot-dip galvanized steel immersed in seawater was presented.The analysis was based on the boundary element methods (BEMs) coupled with Newton-Raphson iterative technique to treat the nonlinear boundary conditions, which were determined by the experimental polarization curves. Results showed that galvanic current density concentrates on the boundary of steel substrate and zinc coating, and the sacrificial protection of zinc coating to steel substrate results in overprotection of steel cathode. Not only oxygen reduction but also hydrogen reduction could occur as cathode reactions, which probably led up to the adsorption and absorption of hydrogen atoms. Flat galvanized steel tensile sample shows a brittle behavior similar to hydrogen embrittlement according to the SSRT (show strain rate test) in seawater.
Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods
Marburg, Steffen
2008-01-01
Among numerical methods applied in acoustics, the Finite Element Method (FEM) is normally favored for interior problems whereas the Boundary Element Method (BEM) is quite popular for exterior ones. That is why this valuable reference provides a complete survey of methods for computational acoustics, namely FEM and BEM. It demonstrates that both methods can be effectively used in the complementary cases. The chapters by well-known authors are evenly balanced: 10 chapters on FEM and 10 on BEM. An initial conceptual chapter describes the derivation of the wave equation and supplies a unified approach to FEM and BEM for the harmonic case. A categorization of the remaining chapters and a personal outlook complete this introduction. In what follows, both FEM and BEM are discussed in the context of very different problems. Firstly, this comprises numerical issues, e.g. convergence, multi-frequency solutions and highly efficient methods; and secondly, solutions techniques for the particular difficulties that arise wi...
Stenroos, M; Mäntynen, V; Nenonen, J
2007-12-01
The boundary element method (BEM) is commonly used in the modeling of bioelectromagnetic phenomena. The Matlab language is increasingly popular among students and researchers, but there is no free, easy-to-use Matlab library for boundary element computations. We present a hands-on, freely available Matlab BEM source code for solving bioelectromagnetic volume conduction problems and any (quasi-)static potential problems that obey the Laplace equation. The basic principle of the BEM is presented and discretization of the surface integral equation for electric potential is worked through in detail. Contents and design of the library are described, and results of example computations in spherical volume conductors are validated against analytical solutions. Three application examples are also presented. Further information, source code for application examples, and information on obtaining the library are available in the WWW-page of the library: (http://biomed.tkk.fi/BEM).
Perton, Mathieu; Contreras-Zazueta, Marcial A.; Sánchez-Sesma, Francisco J.
2016-06-01
A new implementation of indirect boundary element method allows simulating the elastic wave propagation in complex configurations made of embedded regions that are homogeneous with irregular boundaries or flat layers. In an older implementation, each layer of a flat layered region would have been treated as a separated homogeneous region without taking into account the flat boundary information. For both types of regions, the scattered field results from fictitious sources positioned along their boundaries. For the homogeneous regions, the fictitious sources emit as in a full-space and the wave field is given by analytical Green's functions. For flat layered regions, fictitious sources emit as in an unbounded flat layered region and the wave field is given by Green's functions obtained from the discrete wavenumber (DWN) method. The new implementation allows then reducing the length of the discretized boundaries but DWN Green's functions require much more computation time than the full-space Green's functions. Several optimization steps are then implemented and commented. Validations are presented for 2-D and 3-D problems. Higher efficiency is achieved in 3-D.
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
A fast multipole boundary element method for three dimensional potential flow problems
Institute of Scientific and Technical Information of China (English)
TENG Bin; NING Dezhi; GOU Ying
2004-01-01
A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost and memory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for threedimensional potential flow problems. The algorithm based on mixed multipole expansion and numerical integration is implemented in combination with an iterative solver. Numerical examinations, on Dirichlet and Neumann problems,are carried out to demonstrate the capability and accuracy of the present method. It has been shown that the method has evident advantages in saving memory and computing time when used to solve huge-scale problems which may be prohibitive for the traditional BEM implementation.
Dynamic-stiffness matrix of embedded and pile foundations by indirect boundary-element method
Energy Technology Data Exchange (ETDEWEB)
Wolf, J.P.; Darbre, G.R. (Electrowatt Engineering Services Ltd., Zurich (Switzerland))
1984-08-01
The boundary-integral equation method is well suited for the calculation of the dynamic-stiffness matrix of foundations embedded in a layered visco-elastic halfspace (or a transmitting boundary of arbitrary shape), which represents an unbounded domain. It also allows pile groups to be analyzed, taking pile-soil-pile interaction into account. The discretization of this boundary-element method is restricted to the structure-soil interface. All trial functions satisfy exactly the field equations and the radiation condition at infinity. In the indirect boundary-element method distributed source loads of initially unknown intensities act on a source line located in the excavated part of the soil and are determined such that the prescribed boundary conditions on the structure-soil interface are satisfied in an average sense. In the two-dimensional case the variables are expanded in a Fourier integral in the wave number domain, while in three dimensions, Fourier series in the circumferential direction and Bessel functions of the wave number domain, while in three dimensions, Fourier series in the circumferential direction and Bessel functions of the wave number in the radial direction are selected. Accurate results arise with a small number of parameters of the loads acting on a source line which should coincide with the structure-soil interface. In a parametric study the dynamic-stiffness matrices of rectangular foundations of various aspect ratios embedded in a halfplane and in a layer built-in at its base are calculated. For the halfplane, the spring coefficients for the translational directions hardly depend on the embedment, while the corresponding damping coefficients increase for larger embedments, this tendency being more pronounced in the horizontal direction.
Shakedown Analysis of 3-D Structures Using the Boundary Element Method Based on the Static Theorem
Institute of Scientific and Technical Information of China (English)
张晓峰; 刘应华; 岑章志
2003-01-01
The static shakedown theorem was reformulated for the boundary element method (BEM) rather than the finite element method with Melan's theorem, then used to develop a numerical solution procedure for shakedown analysis. The self-equilibrium stress field was constructed by a linear combination of several basis self-equilibrium stress fields with undetermined parameters. These basis self-equilibrium stress fields were expressed as elastic responses of the body to imposed permanent strains obtained using a 3-D BEM elastic-plastic incremental analysis. The lower bound for the shakedown load was obtained from a series of nonlinear mathematical programming problems solved using the Complex method. Numerical examples verified the precision of the present method.
2-D Numerical Wave Tank by Boundary Element Method Using Different Numerical Techniques
Directory of Open Access Journals (Sweden)
Farid Habashi Aliabadi
2013-03-01
Full Text Available In this article, numerical modeling of a 2-D wave tank has been investigated by applying completely nonlinear condition for water surface elevation. This has been accomplished based on potential theory, the combined Eulerian-Lagrangian scheme for time marching and using boundary element method. Other physical and numerical attributes of the current work are: physical modeling in time domain, time integration by 4th order Runge-Kutta method, implementation of appropriate condition at the entrance boundary for wave generation, application of artificial dampers at the exit part of the wave tank, and ultimately numerical smoothing of the resulting free surface by using interpolation through spline functions. At the end, effective parameters on the generated wave have been analyzed and the generated wave has also been validated against the result of the linear wave theory.
A direct mixed-body boundary element method for packed silencers.
Wu, T W; Cheng, C Y R; Zhang, P
2002-06-01
Bulk-reacting sound absorbing materials are often used in packed silencers to reduce broadband noise. A bulk-reacting material is characterized by a complex mean density and a complex speed of sound. These two material properties can be measured by the two-cavity method or calculated by empirical formulas. Modeling the entire silencer domain with a bulk-reacting lining will involve two different acoustic media, air and the bulk-reacting material. Traditionally, the interior silencer domain is divided into different zones and a multi-domain boundary element method (BEM) may be applied to solve the problem. However, defining different zones and matching the elements along each interface is tedious, especially when the zones are intricately connected. In this paper, a direct mixed-body boundary element method is used to model a packed silencer without subdividing it into different zones. This is achieved by summing up all the integral equations in different zones and then adding the hypersingular integral equations at interfaces. Several test cases, including a packed expansion chamber with and without an absorbing center bullet, and a parallel baffle silencer, are studied. Numerical results for the prediction of transmission loss (TL) are compared to experimental data.
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)
An iterative Rankine boundary element method for wave diffraction of a ship with forward speed
Institute of Scientific and Technical Information of China (English)
何广华
2014-01-01
A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.
A study on scattered fields analysis of ultrasonic SH-wave by boundary element method
International Nuclear Information System (INIS)
In this paper, the SH-wave scattering by multi-defects and inclusion using Boundary Element Method is studied. The effects of shape and distance of defects on transmitted and reflected fields are considered. The interaction of multi-defects in SH-wave scattering is also investigated. Numerical calculations by the BEM have been carried out to predict near field solution of scattered fields of ultrasonic SH-wave. The presented results can be used to improve the detection sensitivity and pursue quantitative nondestructive evaluation for inverse problem.
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...
Elasto-viscoplastic consistent tangent operator concept-based implicit boundary element methods
Institute of Scientific and Technical Information of China (English)
刘勇; 梁利华; GlaucioH.Paulino
2000-01-01
An elasto-viscoplastic consistent tangent operator (CTO) concept-based implicit algorithm for nonlinear boundary element methods is presented. Both kinematic and isotropic strain hardening are considered. The elasto-viscoplastic radial return algorithm (RRA) and the elasto-viscoplastic CTO and its related scheme are developed. In addition, the limit cases (e.g. elastoplastic problem) of vis-coplastic RRA and CTO are discussed. Finally, numerical examples, which are compared with the latest FEM results of Ibrahimbegovic et al. and ABAQUS results, are provided.
Elasto-viscoplastic consistent tangent operator concept-based implicit boundary element methods
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
An elasto-viscoplastic consistent tangent operator (CTO) concept-based implicit algorithm for nonlinear boundary element methods is presented. Both kinematic and isotropic strain hardening are considered. The elasto-viscoplastic radial return algorithm (RRA) and the elasto-viscoplastic CTO and its related scheme are developed. In addition, the limit cases (e.g. elastoplastic problem) of viscoplastic RRA and CTO are discussed. Finally, numerical examples, which are compared with the latest FEM results of Ibrahimbegovic et al. and ABAQUS results, are provided.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.
Accurate computation of Galerkin double surface integrals in the 3-D boundary element method
Adelman, Ross; Duraiswami, Ramani
2015-01-01
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations. Integral equation formulations lead to more compact, but dense linear systems. These dense systems are often solved iteratively via Krylov subspace methods, which may be accelerated via the fast multipole method. There are advantages to Galerkin formulations for such integral equations, as they treat problems associated with kernel singularity, and lead to symmetric and better conditioned matrices. However, the Galerkin method requires each entry in the system matrix to be created via the computation of a double surface integral over one or more pairs of triangles. There are a number of semi-analytical methods to treat these integrals, which all have some issues, and are discussed in this paper. We present novel methods to compute all the integrals that arise in Galerkin fo...
The boundary element method for the solution of the multidimensional inverse heat conduction problem
International Nuclear Information System (INIS)
This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author)
A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.
Shi, Fan; Choi, Wonjae; Skelton, Elizabeth A; Lowe, Michael J S; Craster, Richard V
2014-12-01
A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed. PMID:25474780
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.
The boundary element method for light scattering by ice crystals and its implementation in BEM++
Groth, S. P.; Baran, A. J.; Betcke, T.; Havemann, S.; Śmigaj, W.
2015-12-01
A number of methods exist for solving the problem of electromagnetic scattering by atmospheric ice crystals. Amongst these methods, only a few are used to generate "benchmark" results in the atmospheric science community. Most notably, the T-matrix method, Discrete Dipole Approximation, and the Finite-Difference Time-Domain method. The Boundary Element Method (BEM), however, has received considerably less attention in this community despite its extensive use and development in other areas of applied mathematics and engineering. Recently the group of Betcke et al. (2015 [1]) at University College London has released a high performance open source boundary element library called BEM++. In this paper, we employ BEM++ to calculate the scattering properties of hexagonal ice columns of fixed orientation, as well as more complicated particles such as hollow columns and bullet-rosettes. The results for hexagonal columns are compared to those obtained using a highly accurate and well-established T-matrix method (Baran et al., 2001 [2]) for a range of different wavelengths and size parameters. It is shown that the results are in excellent agreement and that BEM++ is a fast alternative to the T-matrix method and others for generating benchmark results. However, the large memory requirements of BEM++ cause it to be limited to size parameters ~15 on a standard desktop PC if an accuracy of roughly 1% is required. The main advantages of BEM++ over many other methods are its flexibility to be applied to homogeneous dielectric particles of arbitrarily complex shape, and its open availability. This flexibility is illustrated by the application of BEM++ to scattering by hollow columns with different cavity types, as well as bullet-rosettes with 2-6 branches.
Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method
Layton, Simon K
2015-01-01
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, $p$. We take advantage of a unique property of Krylov iterations that allow lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing $p$. Via extensive numerical tests, we show that the relaxed Krylov iterations converge with speed-ups of between 2x and 4x for Laplace problems and between 3.5x and 4.5x for Stokes problems. We include an application to Stokes flow around red blood cells, computing with up to 64 cells and problem size up to 131k boundary elements and nearly 400k unknowns. The study was done with an in-house multi-threaded C++ code, on a quad-core CPU.
Boundary elements method for microfluidic two-phase flows in shallow channels
Nagel, Mathias
2014-01-01
In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-on-a-Chip devices and characterized by low Reynolds and low capillary numbers. Assuming that these channels are homogeneous in height and have a large aspect ratio, we use depth-averaged equations to describe these two-phase flows using the Brinkman equation, which constitutes a refinement of Darcy's law. These partial differential equations are discretized and solved numerically using the boundary element method, where a stabilization scheme is applied to the surface tension terms, allowing for a less restrictive time step at low capillary numbers. The convergence of the numerical algorithm is checked against a static analytical solution and on a dynamic test case. Finally the algorithm is applied to the non-linear development of the Saffman-Taylor instability and compared to expe...
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
2015-03-01
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.
Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey
2015-09-01
The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.
Directory of Open Access Journals (Sweden)
Igumnov Leonid
2015-01-01
Full Text Available The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.
Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method
Directory of Open Access Journals (Sweden)
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.
A coupled finite-element, boundary-integral method for simulating ultrasonic flowmeters.
Bezdĕk, Michal; Landes, Hermann; Rieder, Alfred; Lerch, Reinhard
2007-03-01
Today's most popular technology of ultrasonic flow measurement is based on the transit-time principle. In this paper, a numerical simulation technique applicable to the analysis of transit-time flowmeters is presented. A flowmeter represents a large simulation problem that also requires computation of acoustic fields in moving media. For this purpose, a novel boundary integral method, the Helmholtz integral-ray tracing method (HIRM), is derived and validated. HIRM is applicable to acoustic radiation problems in arbitrary mean flows at low Mach numbers and significantly reduces the memory demands in comparison with the finite-element method (FEM). It relies on an approximate free-space Green's function which makes use of the ray tracing technique. For simulation of practical acoustic devices, a hybrid simulation scheme consisting of FEM and HIRM is proposed. The coupling of FEM and HIRM is facilitated by means of absorbing boundaries in combination with a new, reflection-free, acoustic-source formulation. Using the coupled FEM-HIRM scheme, a full three-dimensional (3-D) simulation of a complete transit-time flowmeter is performed for the first time. The obtained simulation results are in good agreement with measurements both at zero flow and under flow conditions. PMID:17375833
Energy Technology Data Exchange (ETDEWEB)
Schmid, G.; Wang, S.; Chouw, N.
1991-04-01
SSI-FEBEM is a computer program for dynamic soil-structure (or structure-soil-structure) interaction analysis in the frequency domain. The program SAP IV (FEM) and the program SSI 2D/3D (BEM) have been integrated into a new program, which allows a coupling of finite and boundary elements. It is applicable to two- and three-dimensional problems. In this manual, the theoretical concept for both FEM and BEM, as used in the program, are briefly introduced. Details of the coupling of FE and BE, are also discussed. However, emphasis is directed towards the use of the computer program concerning data input and output. Finally, several examples on soil-structure interaction (SSI) and structure-soil-structure interaction (SSSI), together with their data are presented. (orig.). [Deutsch] SSI-FEBEM ist ein Programm zur Berechnung der dynamischen Antwort eines Systems Bauwerk-Boden (oder Bauwerk-Boden-Bauwerk) im Frequenzbereich. Das Programm besteht aus dem Programm SAP IV (FEM) und dem Programm SSI 2D/3D (BEM) und koppelt Finite Elemente und Randelemente. Zwei- und dreidimensionale Probleme koennen damit behandelt werden. In dem vorliegenden Bericht werden die theoretischen Grundlagen der angewendeten Methode der Finiten Elemente und der Randelemente kurz vorgestellt und deren Kopplung beschrieben. Der Bericht ist als Benutzerhandbuch anzusehen. Er beinhaltet auch Beispiele der Wechselwirkung zwischen Bauwerk und Baugrund (SSI) und zwischen Bauwerk-Boden-Bauwerk (SSSI). (orig.).
A fast boundary element method for the scattering analysis of high-intensity focused ultrasound.
van 't Wout, Elwin; Gélat, Pierre; Betcke, Timo; Arridge, Simon
2015-11-01
High-intensity focused ultrasound (HIFU) techniques are promising modalities for the non-invasive treatment of cancer. For HIFU therapies of, e.g., liver cancer, one of the main challenges is the accurate focusing of the acoustic field inside a ribcage. Computational methods can play an important role in the patient-specific planning of these transcostal HIFU treatments. This requires the accurate modeling of acoustic scattering at ribcages. The use of a boundary element method (BEM) is an effective approach for this purpose because only the boundaries of the ribs have to be discretized instead of the standard approach to model the entire volume around the ribcage. This paper combines fast algorithms that improve the efficiency of BEM specifically for the high-frequency range necessary for transcostal HIFU applications. That is, a Galerkin discretized Burton-Miller formulation is used in combination with preconditioning and matrix compression techniques. In particular, quick convergence is achieved with the operator preconditioner that has been designed with on-surface radiation conditions for the high-frequency approximation of the Neumann-to-Dirichlet map. Realistic computations of acoustic scattering at 1 MHz on a human ribcage model demonstrate the effectiveness of this dedicated BEM algorithm for HIFU scattering analysis. PMID:26627749
Directory of Open Access Journals (Sweden)
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.
Research on the cyclostationary nearfield acoustic holography based on boundary element method
Institute of Scientific and Technical Information of China (English)
ZHANG Haibin; WAN Quan; JIANG Weikang
2009-01-01
Cyclostationary sound field is a special kind of nonstationary sound field, in which the pressure signal is modulated seriously and sidebands exist in its spectrum. The reconstructed sound field can't figure the cyclostationary features in conventional Nearfield Acoustic Holography (NAH) procedure. On the basis of planar cyclostationary NAH, the cyclostationary NAH based on boundary element method is proposed which can be utilized to analyze radiators with complicated surface. Replacing the Fourier's transform with the second-order cyclic statistics, the Cyclic Spectral Density (CSD) functions is used as the reconstructed physical quantity in the proposed NAH technique, instead of the spectrum or power spectral density of pressure signal. By virtue of the demodulation ability of CSD function, the reconstructed CSD can effectively express the information of modulating and carrier wave respectively. The simulation and experiment illustrate that the validity and accuracy of this cyclostationary NAH technique satisfy the request of engineering.
Noise simulation of aircraft engine fans by the boundary element method
Pyatunin, K. R.; Arkharova, N. V.; Remizov, A. E.
2016-07-01
Numerical simulation results of the civil aircraft engine fan stage noise in the far field are presented. Non-steady-state rotor-stator interaction is calculated the commercial software that solves the Navier-Stokes equations using differentturbulence models. Noise propagation to the far acoustic field is calculated by the boundary element method using acoustic Lighthill analogies without taking into account the mean current in the air inlet duct. The calculated sound pressure levels at points 50 m from the engine are presented, and the directional patterns of the acoustic radiation are shown. The use of the eddy resolving turbulence model to calculate rotor-stator interaction increases the accuracy in predicting fan stage noise.
Institute of Scientific and Technical Information of China (English)
王同科
2002-01-01
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs fromthe high order generalized difference methods. It is proved that the method has optimal order er-ror estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.
Seismic site effects in a deep alluvial basin: numerical analysis by the boundary element method
Semblat, Jean-François; Dangla, Patrick; 10.1016/S0266-352X(02)00017-4
2009-01-01
The main purpose of the paper is the numerical analysis of seismic site effects in Caracas (Venezuela). The analysis is performed considering the boundary element method in the frequency domain. A numerical model including a part of the local topography is considered, it involves a deep alluvial deposit on an elastic bedrock. The amplification of seismic motion (SH-waves, weak motion) is analyzed in terms of level, occurring frequency and location. In this specific site of Caracas, the amplification factor is found to reach a maximum value of 25. Site effects occur in the thickest part of the basin for low frequencies (below 1.0 Hz) and in two intermediate thinner areas for frequencies above 1.0 Hz. The influence of both incidence and shear wave velocities is also investigated. A comparison with microtremor recordings is presented afterwards. The results of both numerical and experimental approaches are in good agreement in terms of fundamental frequencies in the deepest part of the basin. The boundary elemen...
Contreras Zazueta, M. A.; Perton, M.; Sanchez-Sesma, F. J.; Sánchez-Alvaro, E.
2013-12-01
The seismic hazard assessment of extended developments, such as a dam, a bridge or a pipeline, needs the strong ground motion simulation taking into account the effects of surface geology. In many cases the incoming wave field can be obtained from attenuation relations or simulations for layered media using Discrete Wave Number (DWN). Sometimes there is a need to include in simulations the seismic source as well. A number of methods to solve these problems have been developed. Among them the Finite Element and Finite Difference Methods (FEM and FDM) are generally preferred because of the facility of use. Nevertheless, the analysis of realistic dynamic loading induced by earthquakes requires a thinner mesh of the entire domain to consider high frequencies. Consequently this may imply a high computational cost. The Indirect Boundary Element Method (IBEM) can also be employed. Here it is used to study the response of a site to historical seismic activity. This method is particularly suited to model wave propagation through wide areas as it requires only the meshing of boundaries. Moreover, it is well suited to represent finely the diffraction that can occur on a fault. However, the IBEM has been applied mainly to simple geometrical configurations. In this communication significant refinements of the formulation are presented. Using IBEM we can simulate wave propagation in complex geometrical configurations such as a stratified medium crossed by thin faults or having a complex topography. Two main developments are here described; one integrates the DWN method inside the IBEM in order to represent the Green's functions of stratified media with relatively low computational cost but assuming unbounded parallel flat layers, and the other is the extension of IBEM to deal with multi-regions in contact which allows more versatility with a higher computational cost compared to the first one but still minor to an equivalent FEM formulation. The two approaches are fully
Institute of Scientific and Technical Information of China (English)
So Gu Kim
2013-01-01
On March 26, 2010 an underwater explosion (UWE) led to the sinking of the ROKS Cheonan. The official Multinational Civilian-Military Joint Investigation Group (MCMJIG) report concluded that the cause of the underwater explosion was a 250 kg net explosive weight (NEW) detonation at a depth of 6−9 m from a DPRK “CHT-02D” torpedo. Kim and Gitterman (2012a) determined the NEW and seismic magnitude as 136 kg at a depth of approximately 8m and 2.04, respectively using basic hydrodynamics based on theoretical and experimental methods as well as spectral analysis and seismic methods. The purpose of this study was to clarify the cause of the UWE via more detailed methods using bubble dynamics and simulation of propellers as well as forensic seismology. Regarding the observed bubble pulse period of 0.990 s, 0.976 s and 1.030 s were found in case of a 136 NEW at a detonation depth of 8 m using the boundary element method (BEM) and 3D bubble shape simulations derived for a 136 kg NEW detonation at a depth of 8 m approximately 5 m portside from the hull centerline. Here we show through analytical equations, models and 3D bubble shape simulations that the most probable cause of this underwater explosion was a 136 kg NEW detonation at a depth of 8m attributable to a ROK littoral “land control” mine (LCM).
Igumnov Leonid; Ipatov Aleksandr; Belov Aleksandr; Petrov Andrey
2015-01-01
The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach bound...
Numerical improvement of the three-dimensional indirect boundary element method
Ortiz-Aleman, C.; Gil-Zepeda, S. A.; Luzon, F.; Sanchez-Sesma, F. J.
2003-04-01
In recent years, several numerical techniques for the estimation of the seismic response in complex geologic configurations have been developed. The flexibility and versatility of these techniques have increased along with the improvement of computational systems, and they altogether have allowed the study of 3D geometries to model several sedimentary basins around the world. In this article we study the structure of the linear systems derived from the Indirect Boundary Element Method (IBEM). We apply a LU-sparse decomposition solver to the inversion of the IBEM coefficient matrix in order to optimise the numerical burden of such method. As pointed out before, special emphasis is given to understanding the main features of ground motion in sedimentary basins. We compute the seismic response of a 3D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzón (1995), and we establish comparisons on time consumption and memory allocation. Inversion of linear systems by using this new algorithm lead us to a significant saving on CPU time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
Two-Dimensional Fracture Mechanics Analysis Using a Single-Domain Boundary Element Method
Directory of Open Access Journals (Sweden)
Chien-Chung Ke
2012-01-01
Full Text Available This work calculates the stress intensity factors (SIFs at the crack tips, predicts the crack initiation angles, and simulates the crack propagation path in the two-dimensional cracked anisotropic materials using the single-domain boundary element method (BEM combined with maximum circumferential stress criterion. The BEM formulation, based on the relative displacements of the crack tip, is used to determine the mixed-mode SIFs and simulate the crack propagation behavior. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, degree of material anisotropy, and crack types are presented. Furthermore, the propagation path in Cracked Straight Through Brazilian Disc (CSTBD specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Additionally, the anisotropic rock slope failure initiated by the tensile crack can also be analyzed by the proposed crack propagation simulation technique.
Dumont, Ney Augusto
2008-02-01
The paper briefly outlines the conventional and three variational implementations of the boundary element method, pointing out the conceptual imbrications of their constituent matrices. The nature of fundamental solutions is investigated in terms of the resulting matrix spectral properties, as applied to multiply-connected domains, reentering corners and FGMs.
Institute of Scientific and Technical Information of China (English)
袁益让
1996-01-01
The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. This thesis, from actual conditions such as the effects of gravitation, buoyancy and capillary pressure, puts forward for the two class boundary value problem a kind of characteristic mixed finite element scheme by making use of the change of region, time step modified techniques of handling boundary value condition, negative norm estimate and the theory of prior estimates. Optimal order estimates in L2 norm are derived for the error in approximate solutions. Thus the well-known theoretical problem proposed by J. Douglas, Jr has been thoroughly and completely solved.
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1993-02-01
A design sensitivity calculation technique based on the implicit differentiation method is formulated for isoparametric boundary elements for three-dimensional (3D) shape optimization problems. The practical sensitivity equations for boundary displacements and stresses are derived, and the efficiency and accuracy of the technique are compared with the semi-analytic method by implementing the sensitivity analysis of typical and basic shape design problems numerically. The sensitivity calculation technique is then applied to the minimum weight design problems of 3D bodies under stress constraints, such as the shape optimization of the ellipsoidal cavity in a cube and the connecting rod, where the Taylor series approximation, based on the boundary element sensitivity analysis at current design point, is adopted for the efficient implementation of the optimization.
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.
Noise source localization on tyres using an inverse boundary element method
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Saemann, E-U; Hald, J
1998-01-01
A dominating part of tyre noise is radiated from a region close to the tyre/road contact patch, where it is very difficult to measure both the tyre vibration and the acoustic near field. The approach taken in the present paper is to model the tyre and road surfaces with a Boundary Element Model...... (BEM), with unknown node vibration data on the tyre surface. The BEM model is used to calculate a set of transfer functions from the node vibrations to the sound pressure at a set of microphone positions around the tyre. By approximate inversion of the matrix of transfer functions, the surface...
Crack propagation analysis of welded thin-walled joints using boundary element method
Mashiri, F. R.; Zhao, Xiao-Ling; Grundy, P.
Tube-to-plate nodal joints under cyclic bending are widely used in the road transport and agricultural industry. The square hollow sections (SHS) used in these constructions are thin-walled and cold formed, and they have thicknesses of less than 4mm. Some fatigue failures have been observed. The weld undercut may affect the fatigue life of welded tubular joints especially for thin-walled sections. The undercut dimensions were measured using the silicon imprint technique. Modelling of thin-walled cruciform joints, as a simplification of welded tubular joints, is described in this paper to determine the effect of weld undercut on fatigue propagation life. The Boundary Element Analysis System Software (BEASY) is used. The results of the effect of weld toe undercut from this analysis are compared with results from previous research to determine the comparative reduction in fatigue life between thin-walled joints (T=3mm) and those made of thicker sections (T=20mm). The loss in fatigue strength of the thin-walled joints is found to be relatively more than that for thicker walled joints. A 3D model of a tube to plate T-joint is also modelled using the boundary element software, BEASY. The nodal joint consists of a square hollow section, 50×50×3 SHS, fillet welded to a 10-mm thick plate, and subjected to cyclic bending stress. Fatigue analyses are carried out and the results are compared with the only available S-N design curve.
Institute of Scientific and Technical Information of China (English)
JI Zhen-lin; WANG Xue-ren
2008-01-01
In marine engine exhaust silencing systems,the presence of exhaust gas flow influences the sound propagation inside the systems and the acoustic attenuation performance of silencers.In order to investigate the effects of three-dimensional gas flow and acoustic damping on the acoustic attenuation characteristics of marine engine exhaust silencers,a dual reciprocity boundary element method (DRBEM)was developed.The acoustic governing equation in three-dimensional potential flow was derived first,and then the DRBEM numerical procedure is given.Compared to the conventional boundary elementmethod (CBEM),the DRBEM considers the second order terms of flow Mach number in the acoustic governing equation,so it is suitable for the cases with higher Mach number subsonic flow.For complex exhaust silencers,it is difficult to apply the single-domain boundary element method,so a substructure approach based on the dual reciprocity boundary element method is presented.The experiments for measuring transmission loss of silencers are conducted,and the experimental setup and measurements are explained.The transmission loss of a single expansion chamber silencer with extended inlet and outlet were predicted by DRBEM and compared with the measurements.The good agreements between predictions and measurements are observed,which demonstrated that the derived acoustic governing equation and the DRBEM numerical procedure in the present study are correct.
Li, Jianbo; Liu, Jun; Lin, Gao
2013-12-01
Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method (SBFEM) is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.
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.
Institute of Scientific and Technical Information of China (English)
FENG Bo; ZHENG Yong-hong; YOU Ya-ge; HE Zai-ming
2007-01-01
The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation Method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with those by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.
Reid, M T Homer; White, Jacob K
2013-01-01
We present a generic technique, automated by computer-algebra systems and available as open-source software \\cite{scuff-em}, for efficient numerical evaluation of a large family of singular and nonsingular 4-dimensional integrals over triangle-product domains, such as those arising in the boundary-element method (BEM) of computational electromagnetism. To date, practical implementation of BEM solvers has often required the aggregation of multiple disparate integral-evaluation schemes to treat all of the distinct types of integrals needed for a given BEM formulation; in contrast, our technique allows many different types of integrals to be handled by the \\emph{same} algorithm and the same code implementation. Our method is a significant generalization of the Taylor--Duffy approach \\cite{Taylor2003,Duffy1982}, which was originally presented for just a single type of integrand; in addition to generalizing this technique to a broad class of integrands, we also achieve a significant improvement in its efficiency b...
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
BOUNDARY ELEMENT ANALYSIS OF CONTACT PROBLEMS USING ARTIFICIAL BOUNDARY NODE APPROACH
Institute of Scientific and Technical Information of China (English)
Bahattin KANBER; Ibrahim H. GUZELBEY; Ahmet ERKLI
2003-01-01
An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.
Computation of the transient flow in zoned anisotropic porous media by the boundary element method
Bruch, E.; Grilli, S.
Results on the application of the BEM to transient two-dimensional flows in zoned anisotropic porous media are presented, including the iterative calculation of the free surface seepage position. The classical BEM equations are discretized by linear, quadratic, or cubic elements, employing special singular numerical quadrature rules. The method is improved by the incorporation of a subregion division. The present technique is shown to be very accurate and to avoid previously encountered oscillation problems.
Energy Technology Data Exchange (ETDEWEB)
Hassanein, A.M.
1987-01-01
The time dependent heat conduction equation that is solved in different coordinate systems is solved subject to various boundary conditions. Boundary conditions include surface heat flux, energy to vaporization of target materials, radiation from surface to surrounding, and possible phase change of material. This system of equations is subject to two moving boundaries. One moving boundary being the melt-solid interface because the surface heat flux may result in melting the surface of the exposed material. Another moving boundary is the receding surface as a result of evaporation of the wall material due to the continuous heating of the melted surface. Finite difference and the finite element methods are used and compared in such solution to these problems. Physical applications to these problems include high energy deposition from electron or ion beams interaction with materials for space and weapons applications, plasma disruption and energy dump on the walls or components of a fusion reactor, and high energy laser welding and annealing of materials. 23 refs., 3 figs.
Bhattacharyya, S. K.; Premkumar, R.
2003-12-01
In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger, and Turkel (BGT) boundary dampers, which require a circular cylindrical and spherical truncation boundaries in two-(2D) and three-(3D)-dimensional problems, respectively, have been particularly successful in the analysis of scattering and radiation problems. However, for an elongated body, elliptical (2D) or spheroidal (3D) truncation boundaries have potential to reduce the size of modeling domain and hence computational effort. For harmonic problems, such extensions of the first- and second-order BGT dampers are available in the literature. In this paper, BGT dampers in both elliptical and spheroidal coordinate systems have been developed for transient problems involving acoustic radiation as well as fluid-structure interaction and implemented in the context of finite-element method based upon unsymmetric pressure-displacement formulation. Applications to elongated radiators and shells are reported using several numerical examples with excellent comparisons. It is demonstrated that significant computational economy can be achieved for elongated bodies with the use of these dampers.
A simulation of fatigue crack propagation in a welded T-joint using 3D boundary element method
Energy Technology Data Exchange (ETDEWEB)
Xiang Zhihai; Lie, S.T.; Wang Bo; Cen Zhangzhi
2003-02-01
A general procedure to investigate the fatigue propagation process of a 3D surface crack based on multi-region Boundary Element Method is detailed in this paper. The mesh can be automatically regenerated as the crack propagates. A new formula for estimating the effective stress intensity factor is used to calculate the crack extension. The maximum principal stress criterion is then employed to predict the crack growth direction. Comparison between numerical and experimental results of a welded T-joint shows that the proposed procedure is reliable.
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)
Walston, W. H., Jr.
1986-01-01
The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.
Institute of Scientific and Technical Information of China (English)
Zhang-Rui Li; Lei Sun; Zhi Zong; Jing Dong
2012-01-01
The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method.The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4π rule.The solid angle for the open surface is treated in direct method based on its definition.Several kinds of configurations for the bubbles and free surface have been investigated.The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface.The bubble dynamics and their interactions have close relation with the standoff distances,buoyancy parameters and initial sizes of bubbles.Completely different bubble shapes,free surface motions,jetting patterns and pressure distributions under different parameters can be observed in our model,as demonstrated in our calculation results.
Otsuru, Toru; Tomiku, Reiji; Din, Nazli Bin Che; Okamoto, Noriko; Murakami, Masahiko
2009-06-01
An in-situ measurement technique of a material surface normal impedance is proposed. It includes a concept of "ensemble averaged" surface normal impedance that extends the usage of obtained values to various applications such as architectural acoustics and computational simulations, especially those based on the wave theory. The measurement technique itself is a refinement of a method using a two-microphone technique and environmental anonymous noise, or diffused ambient noise, as proposed by Takahashi et al. [Appl. Acoust. 66, 845-865 (2005)]. Measured impedance can be regarded as time-space averaged normal impedance at the material surface. As a preliminary study using numerical simulations based on the boundary element method, normal incidence and random incidence measurements are compared numerically: results clarify that ensemble averaging is an effective mode of measuring sound absorption characteristics of materials with practical sizes in the lower frequency range of 100-1000 Hz, as confirmed by practical measurements. PMID:19507960
NATURAL BOUNDARY INTEGRAL METHOD AND ITS NEW DEVELOPMENT
Institute of Scientific and Technical Information of China (English)
De-hao Yu
2004-01-01
In this paper, the natural boundary integral method, and some related methods, including coupling method of the natural boundary elements and finite elements, which is also called DtN method or the method with exact artificial boundary conditions, domain decomposition methods based on the natural boundary reduction, and the adaptive boundary element method with hyper-singular a posteriori error estimates, are discussed.
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'. PMID:27185960
Complex variable boundary elements for fluid flow
International Nuclear Information System (INIS)
The Complex Variable Boundary Element Method is a numerical method for solving two-dimensional problems of Laplace or Poisson type. It is based on the theory of analytic functions. This paper resumes the basic facts about the method. Application of the method to the stationary incompressible irrotational flow is carried out after that. At the end, a sample problem of flow through an abrupt area change channel is shown. (author)
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...
Zhang, Chen; Shou, Guo-Fa; Lu, Hong; Hua, Ning; Tang, Xue-Zheng; Xia, Ling; Ma, Ping; Tang, Fa-Kuan
2013-09-01
A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso—cardiac vector model is used for a 12-lead electrocardiographic (ECG) and magneto-cardiogram (MCG) simulation study by using the boundary element method (BEM). Also, we obtain the MCG wave picture using a compound four-channel HTc·SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.
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.
Simplified Boundary Element Method for Kinematic Response of Single Piles in Two-Layer Soil
Fayun Liang; Haibing Chen; Wei Dong Guo
2013-01-01
A simple approach is formulated to predict the elastic, kinematic pile bending during harmonic or transient excitation for a circular pile (rather than a simplified thin strip). The kinematic response of a pile embedded in two-layer soil is resolved in the frequency domain caused by the upward propagation of shear waves from the underlying bedrock. The simplified approach is generally valid to nonhomogeneous soil profiles, in light of the good comparison with the dynamic FE method and BDWF so...
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...
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper,a low-order potential based on surface panel method is used for the analysis of marine propellers in unsteady flow.A linear propeller wake model is employed and its geometry is assumed to be independent of the time.The calculation in time domain is carried out from a moment when the rotation of the propeller becomes steady instead of from the moment when the rotation starts from stationary condition.At every time step a linear algebraic equation established on a key blade is solved numerically combined with the Kutta pressure condition.The calculated results by developed code indicate good convergency and effectiveness of present algorithm for conventional propellers and highly skewed propellers.
Shepherd, Micah R; Fahnline, John B; Dare, Tyler P; Hambric, Stephen A; Campbell, Robert L
2015-11-01
Many structural acoustics problems involve a vibrating structure in a heavy fluid. However, obtaining fluid-loaded natural frequencies and damping experimentally can be difficult and expensive. This paper presents a hybrid experimental-numerical approach to determine the heavy-fluid-loaded resonance frequencies and damping of a structure from in-air measurements. The approach combines in-air experimentally obtained mode shapes with simulated in-water acoustic resistance and reactance matrices computed using boundary element (BE) analysis. The procedure relies on accurate estimates of the mass-normalized, in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting, which are then used as basis modes for the in-water BE analysis. The method is validated on a 4.445 cm (1.75 in.) thick nickel-aluminum-bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in-water measurements. Good agreement is shown for the fluid-loaded natural frequencies and one-third octave loss factors. Finally, the limitations of the hybrid approach are examined. PMID:26627781
Mostafa, Mostafa E.
2009-04-01
The finite cube elements method (FCEM) is a numerical tool designed for modelling gravity anomalies and estimating structural index (SI) of solid and fractal bodies with defined boundaries, tilted or in normal position and with variable density contrast. In this work, we apply FCEM to modelling magnetic anomalies and estimating SI of bodies with non-uniform magnetization having variable magnitude and direction. In magnetics as in gravity, FCEM allows us to study the spatial distribution of SI of the modelled bodies on contour maps and profiles. We believe that this will impact the forward and inverse modelling of potential field data, especially Euler deconvolution. As far as the author knows, this is the first time that gravity and magnetic anomalies, as well as SI, of self similar fractal bodies such as Menger sponges and Sierpinsky triangles are calculated using FCEM. The SI patterns derived from different order sponges and triangles are perfectly overlapped. This is true for bodies having variable property distributions (susceptibility or density contrast) under different field conditions (in case of magnetics) regardless of their orientation and depth of burial. We therefore propose SI as a new universal fractal-order-invariant measure which can be used in addition to the fractal dimensions for formulating potential field theory of fractal objects.
边界元计算中一种新的积分方法%A NEW INTEGRATION APPROACH IN BOUNDARY ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
侯劲松; 王泽毅
1999-01-01
In three dimensional boundary element calculation, the boundaryintegration is the most time-consuming work. In this paper, a newapproach called parameterized integration method is presented. Itcalculates values of a multivariate function instead of traditionalGauss integral and saves integral time.
REDUCING DIMENSIONS OF DOMAIN INTEGRATION IN BOUNDARY ELEMENT METHOD%边界元法中区域积分的降维计算方法
Institute of Scientific and Technical Information of China (English)
袁政强; 祝家麟
2002-01-01
The main advantage of Boundary Element Method (BEM) is reducing the dimensions by one in performing calculation.When inhomogeneous term appears in the governing equation of the problem,the domain integral is inevitable excepting some special cases.The common way to perform the domain integral involves subdividing the domain into a series of subdomains over which a numberical integration formula or an analytical quadrature can be applied.This paper presents an alternative way to transform the domain integral over subdomains into equivalent boundary integrals on the boundary of each subdomain,so that all the integrals are performed on the boundary case.It makes the whole calculation of BEM reduced by one dimension really.
无单元Galerkin方法中周期边界条件的处理%Imposing Periodic Boundary Conditions in Element Free Galerkin Methods
Institute of Scientific and Technical Information of China (English)
王晓东; 欧阳洁; 苏进
2011-01-01
本文研究了无单元Galerkin方法中周期边界条件的处理技术,将Lagrange乘子法用于周期边界条件的处理.数值计算结果表明,该方法具有较高的计算精度.另外,它与无单元Galerkin方法中本质边界条件处理的Lagrange乘子法具有统一性,对于周期、本质混合型边界条件的处理尤为方便.%In this paper, the Lagrange multiplier method has been used to impose periodic boundary conditions in the element free Galerkin method. Numerical results indicate that the method maintains the high accuracy property of the element free Galerkin method in periodic problems. In addition,based on the similarity between the method used in this paper for periodic boundary conditions and the Lagrange multiplier method for essential boundary conditions, it is convenient to impose periodicessential mixed boundary conditions.
International Nuclear Information System (INIS)
SSI 2D/3D is a computer programm to calculate dynamic stiffness matrices for soil-structure-interaction problems in frequency domain. It is applicable to two- or three-dimensional situations. The present report is a detailed manual for the use of the computer code written in FORTRAN 77. In addition it gives a survey of the possibilities of the Boundary Element Method applied to dynamic problems in infinite domains. (orig.)
International Nuclear Information System (INIS)
Wide-area groundwater flow analysis for the geological disposal of nuclear waste is conducted in areas 10 to 100 km square at a depth of several kilometers. In Japan with complex topography and geological environment, numerical analyses by segmentation based on the region including FE analysis as a typical example involve difficulty in modeling. This study therefore aims at improving simplicity and preciseness of modeling using BEM through segmentation based on the boundary. Test analyses are conducted to organize data on precision and the characteristics of modeling. Then, this paper describes that the proposed method is fully applicable. (author)
Highly Efficient Boundary Element Analysis of Whispering Gallery Microcavities
Pan, Leyuan
2014-01-01
We demonstrate that the efficiency of the boundary element whispering gallery microcavity analysis can be improved by orders of magnitude with the inclusion of Fresnel approximation. Using this formulation, simulation of a microdisk with wave-number-radius product as large as $kR\\approx8,000$ was demonstrated in contrast to a previous record of $kR\\approx100$. In addition to its high accuracy on computing the modal field distribution and resonance wavelength, this method yields a relative error of $10%$ in calculating the quality factor as high as $10^{11}$ through a direct root searching method where the conventional boundary element method failed to achieve. Finally, quadrupole shaped cavities and double disks as large as $100 {\\mu}m$ in diameter were modeled by employing as few as $512$ boundary elements whilst the simulation of such large cavities using conventional boundary element method were not reported previously.
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.
Institute of Scientific and Technical Information of China (English)
Wen－QingLu
1993-01-01
A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity and temperature gradients are dliminated.and the complete formulation is written in terms of velocity and temperature,This provides considerable reduction is storage and computational requirements while improving accuracy.The non-linear equation systems of boundary element discretization are solved by the quasi-Nweton iterative scheme with Broyden's update.The streamline maps and the temperature distributions in solitary wave and wavy film flow have been obtained,and the variations of Nusselt numbers along the wall-liquid interface are also given.There are large cross-flow velocities and S-shape temperature distributions in the recirculating region of solitary wave.This special flow and thermal process can be a mechanism to enhance heat transport.
Stochastic Boundary Element Analysis of Concrete Gravity Dam
Institute of Scientific and Technical Information of China (English)
张明; 吴清高
2002-01-01
Stochastic boundary integral equations for analyzing large structures are obtained from the partial derivatives of basic random variables. A stochastic boundary element method based on the equations is developed to solve engineering problems of gravity dams using random factors including material parameters of the dam body and the foundation, the water level in the upper reaches, the anti-slide friction coefficient of the dam base, etc. A numerical example shows that the stochastic boundary element method presented in this paper to calculate the reliability index of large construction projects such as a large concrete gravity dam has the advantages of less input data and more precise computational results.
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...
A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures
Smeltzer, Stanley S.; Klang, Eric C.
2001-01-01
The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.
Directory of Open Access Journals (Sweden)
Shao Yan-Lin
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.
Institute of Scientific and Technical Information of China (English)
WANG Xueren; JI Zhenlin
2008-01-01
The Dual Reciprocity Boundary Element Method(DRBEM)is applied to predict the acoustic characteristics of ducts and silencers with three-dimensional potential flow,and the basic principle and numerical procedure of the proposed method are introduced.Compared to the Conventional Boundary Element Method (CBEM),the DRBEM takes into account the second order terms of flow Mach number in the acoustic governing equation,which is suitable for the situations with higher Mach number subsonic flow.The four-pole parameters of a duct and a varying cross-sectional area expansion chamber are predicted with the DRBEM,and the predictions are compared with the one-dimensional analytical solutions and the CBEM results.The comparisons demonstrated that the present method is valid.Transmission loss of silencers with difierent structures was also calculated with the DRBEM.The results showed that the influence of the three-dimensional flow on the acoustic characteristics of silencers with complex structures is not negligible.
A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method (FEM) and the boundary element method (BEM). The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element (FE-BE) coupling method.
Institute of Scientific and Technical Information of China (English)
林志朋; 刘振祥; 杨栋; 欧阳建明; 杨丽佳
2016-01-01
基于deal．ii编写了电磁轨道炮有限元仿真程序，建立了拉格朗日运动坐标下电磁轨道炮的有限元仿真模型；通过使用有限元边界元耦合方法可以对电磁轨道炮的边界条件进行计算，而无需对轨道炮周边的空气划分网格，是一种处理电磁场边界问题的有效方法；但是，由于边界元方法，使用的是满秩矩阵，在三维情况下计算量大，利用轨道炮的对称性，使用对称边界条件，减少了参与计算的网格数目，从而减少计算量。%This article created finite element program and model for rail launch based on deal.ii in La-grange coordinate frame.By using coupling finite element/boundary element coupling method,we can cal-culate boundary condition without air grid surround rail gun.It is a valid method to handle boundary prob-lems of electromagnetic without the perimeter of the rail gun air mesh.But for boundary element method u-sing full matrix which will cost a lot of calculation in 3D situation,we would better using symmetry condi-tions for rail gun to reduce the grid number and calculation.
Toose, E.M.; Geurts, B.J.; Kuerten, J.G.M.
1999-01-01
The boundary integral formulation of the solution to the Stokes equations is used to describe the deformation of small compound non-Newtonian axisymmetric drops suspended in a Newtonian fluid that is subjected to an axisymmetric flow field. The non-Newtonian stress is treated as a source term in the
P, Kirana Kumara
2013-01-01
In this work, first a Fortran code is developed for three dimensional linear elastostatics using constant boundary elements; the code is based on a MATLAB code developed by the author earlier. Next, the code is parallelized using BLACS, MPI, and ScaLAPACK. Later, the parallelized code is used to demonstrate the usefulness of the Boundary Element Method (BEM) as applied to the realtime computational simulation of biological organs, while focusing on the speed and accuracy offered by BEM. A computer cluster is used in this part of the work. The commercial software package ANSYS is used to obtain the `exact' solution against which the solution from BEM is compared; analytical solutions, wherever available, are also used to establish the accuracy of BEM. A pig liver is the biological organ considered. Next, instead of the computer cluster, a Graphics Processing Unit (GPU) is used as the parallel hardware. Results indicate that BEM is an interesting choice for the simulation of biological organs. Although the use ...
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...
Calculation methods for compressible turbulent boundary layers, 1976
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1977-01-01
Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.
Energy Technology Data Exchange (ETDEWEB)
Olschewski, J.; Stein, E.; Wagner, W.; Wetjen, D.
1981-01-01
This paper is a first step in the development of thermodynamically consistent material equations for inelastic materials, such as polycrystalline rock salt. In this context it is of particular importance to reduce the number and the structure of the internal variables, in order to allow for a fit with available experimental data. As an example this is demonstrated in detail in the case of the so-called dislocation model. As physical non-linearities and in addition also geometrical non-linearities lead to an inhomogeneous deformation - and stress state even in the case of simple samples, boundary value problems have to be studied, in order to test the material equations. For this purpose the finite element method has been used.
Wu, C. S.; Young, D. L.; Chiu, C. L.
2013-12-01
This article aims to develop a Cartesian-grid-based numerical model to study the interaction between free-surface flow and stationary or oscillating immersed obstacle in a viscous fluid. To incorporate the effect of the free surface motion, an arbitrary Lagrangian-Eulerian (ALE) scheme is employed to accurately capture the configuration of free surface. To deal with the complex submerged obstacle in the fluid, a hybrid Cartesian/immersed boundary (HCIB) method is adopted, which allows easy implementation of the solid boundary conditions for a fixed structured grid. The two numerical techniques are combined to study the wave-structure interaction problems. The major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients, while the immersed body can move arbitrarily through the Cartesian grid. The meshes deform smoothly over the solid and free-surface boundaries, especially for representing sharp interface. There is no re-meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation. Some numerical examples are displayed respectively to validate the robustness and accuracy of the HCIB method, the ALE based finite-element scheme and their combinations. In addition, the other two numerical applications are carried out to simulate the wave-structure interaction with stationary and moving immersed body. In case studies some physical characteristics are also discussed for a range of amplitude of free-surface wave, Reynolds numbers and the proximity of structure under the liquid surface. The feasibility of the developed novel numerical model is shown through five numerical experiments.
Calculation methods for compressible turbulent boundary layers
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1976-01-01
Calculation procedures for non-reacting compressible two- and three-dimensional turbulent boundary layers were reviewed. Integral, transformation and correlation methods, as well as finite difference solutions of the complete boundary layer equations summarized. Alternative numerical solution procedures were examined, and both mean field and mean turbulence field closure models were considered. Physics and related calculation problems peculiar to compressible turbulent boundary layers are described. A catalog of available solution procedures of the finite difference, finite element, and method of weighted residuals genre is included. Influence of compressibility, low Reynolds number, wall blowing, and pressure gradient upon mean field closure constants are reported.
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......Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited...
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......Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim of the present work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form...
Marsili, P M; Mounié, G; Granié, M; Morucci, J P
1992-01-01
Optimal control techniques have been combined with Alessandrini's singular perturbation method and Wexler's algorithm to reconstruct images in impedance imaging. We have also considered an integral formulation of the potential problem, which has led us to introduce an array of dipoles whose position, orientation and length can be optimised to model the conductivity discontinuities.
Solving Fluid Structure Interaction Problems with an Immersed Boundary Method
Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.
2016-01-01
An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.
Development of classical boundary element analysis of fracture mechanics in gradient materials
Xiao, HT; Yue, QZQ
2013-01-01
Over the last decade, the authors have extended the classical boundary element methods (BEM) for analysis of the fracture mechanics in functionally gradient materials. This paper introduces the dual boundary element method associated with the generalized Kelvin fundamental solutions of multilayered elastic solids (or Yue’s solution). This dual BEM uses a pair of the displacement and traction boundary integral equations. The former is collocated exclusively on the uncracked boundary, and the l...
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.
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
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......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...
Periodic Boundary Conditions in the ALEGRA Finite Element Code
Energy Technology Data Exchange (ETDEWEB)
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
The representation of boundary currents in a finite element shallow water model
Düben, Peter D
2015-01-01
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element discretization methods offers a higher flexibility compared to finite difference and finite volume methods, that are mainly used in previous publications. This is true for the geometry of the coast lines and for the realization of boundary conditions. For our investigations we simulate steady separation of western boundary currents from idealized and realistic coast lines. The use of grid refinement allows a detailed investigation of boundary separation at reasonable numerical cost.
Adaptive Boundary Elements and Error Estimation for Elastic Problems
Directory of Open Access Journals (Sweden)
Jingguo Qu
2014-02-01
Full Text Available In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze computing results according to diverse precision requirement. Against the malpractice exists in the above process, a new method of error estimation was suggested on H-R adaptive boundary element method in this paper. Based on the discrete meshes that are generated for the process of H-R adaptive refinement, the solution error was estimated by the interpolation residue. In addition, this method is easy to programming, which is carried out in the program by automatically creating new adaptive data files. Then a great deal of fore-disposal and post-disposal can be saved. Its validity and effectiveness have been confirmed by numerical example
Institute of Scientific and Technical Information of China (English)
张义波; 张志勇; 周长江; 郑成龙
2012-01-01
针对某型缝纫机,建立了油盘的实体模型和有限元模型,利用HyperWorks-Optistruct进行模态分析,获得结构的固有频率和振型特性参数.在此基础上,利用MSC.Patran/Nastran进行频响分析,并将仿真结果与实验结果对比,验证了模型的有效性.通过拓扑优化和形貌优化对模型进行优化后,提高了油盘前5阶固有频率,避免了共振,且减小表面振动速度,降低了辐射声功率.通过利用SYSNOISE对油盘进行边界元噪声辐射仿真分析,结果表明油盘辐射噪声值降低.最后,经整机振动噪声测试试验,证明减振降噪效果明显.该研究成果能有效提高油盘的结构刚度和降低振动幅度,最终改善缝纫机整机的结构辐射噪声.%For a certain type of sewing machine, a solid model and a finite element model for its oilpan were built. Modal analysis was conducted with finite element method and the structure's natural frequencies and modal shapes were obtained with HyperWorks-Optistruct software. Then, with MSC Patran/Nastran software, frequency response analysis was performed. The results of simulation and test were compared to verify the validity of the model. The oil pan was improved with topology optimization and morphology optimization. After optimal design, the first five natural frequencies of the oil pan increased. Resonances were avoided and surface vibration velocity was reduced, so the radiated sound power was reduced. Using SYSNOISE, the results of noise radiation simulation based on boundary element analysis showed that the radiated noise of the oil pan decreases. Finally, the vibration and noise reductions increased obviously in vibration and noise tests for the improved sewing machine. It was shown that the study can effectively improve its oil pan's structural stiffness and reduce the vibration amplitude, and ultimately reduce the structural radiated noise of the whole sewing machine.
Sound source reconstruction using inverse boundary element calculations
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo; Hansen, Per Christian
2003-01-01
Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form 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, 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 it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies.
An element by element spectral element method for elastic wave modeling
Institute of Scientific and Technical Information of China (English)
LIN Weijun; WANG Xiuming; ZHANG Hailan
2006-01-01
The spectral element method which combines the advantages of spectral method with those of finite element method,provides an efficient tool in simulating elastic wave equation in complex medium. Based on weak form of elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order Lagrange interpolation, and integration over the element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element technique is introduced in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are presented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and spectral algorithms, this method can be used for complex models, including free surface boundaries and strong heterogeneity.
Institute of Scientific and Technical Information of China (English)
韩玉超; 卢晓平; 王中
2015-01-01
The Boundary Element Method(BEM),as a key numerical method,has been widely applied in many fields. However,the research on the Direct Boundary Element Method(DBEM)for ship hydrody⁃namic numerical calculation problems is still insufficient,especially when it comes to the ship hydrody⁃namic potential flow theory. The general method-‘panel method’- is based on Hess-Smith method, which is an Indirect Boundary Element Method(IBEM)whose major flaws exist in both theory and numeri⁃cal calculation. This paper,based on the ship hydrodynamic potential flow theory,adopts DBEM to calcu⁃late the example of two-dimensional unbounded potential flow around a cylinder,and analyzes the influ⁃ence of the boundary element discrete forms and the numerical integral methods on the calculation accura⁃cy. The results carried out by Matlab clearly indicate that using the constant element and Romberg algo⁃rithm method could yield high calculation speed and accuracy.%边界元法作为一种重要的数值方法已在许多领域得到广泛应用，但在船舶水动力势流理论数值计算方面，有关直接边界元法的研究并不充分，尤其是在船舶兴波阻力势流理论求解方面，以往的“面元法”通常是基于Hess-Smith法的间接法，这类方法在理论和数值计算上都存在着缺陷。针对船舶水动力势流理论计算，采用直接边界元法，对二维势流无界绕流算例进行系统的数值计算，并根据二维势流问题的计算结果详细探讨边界单元离散形式和单元上的数值积分方法对计算精度的影响，各项数值计算均以Matlab软件编程实现。结果表明，采用常数单元和龙贝格积分法能够得到较准确的结果，且计算速度较快。
Three dimensional boundary element solutions for eddy current nondestructive evaluation
Yang, Ming; Song, Jiming; Nakagawa, Norio
2014-02-01
The boundary integral equations (BIE) method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations. It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics. The eddy current problem is formulated by the BIE and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The three dimensional arbitrarily shaped objects are described by a number of triangular patches. The Stratton-Chu formulation is specialized for the conductive medium. The equivalent electric and magnetic surface currents are expanded in terms of Rao-Wilton-Glisson (RWG) vector basis function while the normal component of magnetic field is expanded in terms of the pulse basis function. Also, a low frequency approximation is applied in the external medium. Additionally, we introduce Auld's impedance formulas to calculate impedance variation. There are very good agreements between numerical results and those from theory and/or experiments for a finite cross-section above a wedge.
Turner, R. P.; Villa, M.; Sovani, Y.; Panwisawas, C.; Perumal, B.; Ward, R. M.; Brooks, J. W.; Basoalto, H. C.
2016-02-01
Weld simulation methods have often employed mathematical functions to describe the size and shape of the molten pool of material transiently present in a weld. However, while these functions can sometimes accurately capture the fusion boundary for certain welding parameters in certain materials, they do not necessarily offer a robust methodology for the more intricate weld pool shapes that can be produced in materials with a very low thermal conductivity, such as the titanium alloy Ti-6Al-4V. Cross-sections of steady-state welds can be observed which contain a dramatic narrowing of the pool width at roughly half way in to the depth of the plate of material, and a significant widening again at the base. These effects on the weld pool are likely to do with beam focusing height. However, the resultant intricacy of the pool means that standard formulaic methods to capture the shape may prove relatively unsuccessful. Given how critical the accuracy of pool shape is in determining the mechanical response to the heating, an alternative method is presented. By entering weld pool width measurements for a series of depths in a Cartesian co-ordinate system using FE weld simulation software Sysweld, a more representative weld pool size and shape can be predicted, compared to the standard double ellipsoid method. Results have demonstrated that significant variations in the mid-depth thermal profile are observed between the two, even though the same values for top and bottom pool-widths are entered. Finally, once the benefits of the Cartesian co-ordinate method are demonstrated, the robustness of this approach to predict a variety of weld pool shapes has been demonstrated upon a series of nine weld simulations, where the two key process parameters (welding laser power and travel speed) are explored over a design space ranging from 1.5 to 3 kW and 50 to 200 mm/s. Results suggest that for the faster travel speeds, the more detailed Cartesian co-ordinate method is better, whereas
Boundary element modeling of nondissipative and dissipative waves
Energy Technology Data Exchange (ETDEWEB)
Chen, Genmeng [Univ. of Houston, TX (United States). Allied Geophysical Labs.; Zhou, Huawei [Univ. of Houston, TX (United States). Dept. of Geosciences
1994-01-01
A boundary element (BE) algorithm is developed to compute acoustic or SH-waves in models consisting of limited or unlimited volumes and irregular interfaces. The authors solve the BE system in the frequency domain so that anelasticity can be easily represented by different viscoelastic models, such as the Kelvin-Voigt type. Three illustrative computations are shown. The waveform given by the BE method for a circular inclusion model agrees well with that given by the finite-difference (FD) method. Dissipation of waves at high frequency caused by the presence of multi-cracks in an elastic medium resembles the masking effect of anelasticity. The waveforms for nondissipative and dissipative models containing hexagonal inclusions illustrate some interesting characteristics of the composite media.
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
Energy Technology Data Exchange (ETDEWEB)
St. John, C.M.; Sanjeevan, K. [Agapito (J.F.T.) and Associates, Inc., Grand Junction, CO (United States)
1991-12-01
The HEFF Code combines a simple boundary-element method of stress analysis with the closed form solutions for constant or exponentially decaying heat sources in an infinite elastic body to obtain an approximate method for analysis of underground excavations in a rock mass with heat generation. This manual describes the theoretical basis for the code, the code structure, model preparation, and step taken to assure that the code correctly performs its intended functions. The material contained within the report addresses the Software Quality Assurance Requirements for the Yucca Mountain Site Characterization Project. 13 refs., 26 figs., 14 tabs.
Scaled Boundary Finite Element Analysis of Wave Passing A Submerged Breakwater
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coefficient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method (DBEM), it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coefficient and the transmission coefficient are given in the current study.
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 interaction between membrane structure and wind based on the discontinuous boundary element
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Small disturbance potential theory is widely used in solving aerodynamic problems with low Mach numbers, and it plays an important role in engineering design. Concerning structure wind engineering, the body of the structure is in a low velocity wind field, with a low viscosity of air and thin boundary layer, therefore, the tiny shear stress caused by the boundary layer can be ignored, only wind pressure being considered. In this paper, based on small disturbance potential theory, the fluid-structure interaction between the wind and membrane structure is analyzed by joint utilization of the boundary element method (BEM) and finite element method (FEM) through a loose-coupling procedure. However, the boundary of flow field to be calculated is not fully smooth, corners and edges still exist, so the discontinuous boundary element is introduced. Furthermore, because a large scale boundary element equation set with a nonsymmetrical coefficient matrix must be solved, this paper imports a preconditioning GMRES (the generalized minimum residual) iterative algorithm, which takes full advantage of the boundary element method. Several calculation examples have verified the correctness and soundness of the treatments mentioned above.
Institute of Scientific and Technical Information of China (English)
Ding Rui; Jiang Meiqun; Peng Daping
2005-01-01
The boundary element approximation of the parabolic variational inequalities of the second kind is discussed. First, the parabolic variational inequalities of the second kind can be reduced to an elliptic variational inequality by using semidiscretization and implicit method in time; then the existence and uniqueness for the solution of nonlinear non-differentiable mixed variational inequality is discussed. Its corresponding mixed boundary variational inequality and the existence and uniqueness of its solution are yielded. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.
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...... are solved using extended boundary conditions that account for: i) negligible temperature fluctuations at the boundary, and ii) normal and tangential matching of the boundary’s particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers...... as is the case with the existing Finite Element Method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions....
Natural Elements Method for Free Surface Flow
Darbani, M.; Ouahsine, A.; Villon, P.
2009-09-01
The Natural Element Method (NEM) is used to simulate a 2D shallow water flow in presence of free surface and a varying bathymetry. This meshless method used a fully Lagrangian formulation and natural neighbors, which remain a very striking problem related the boundary conditions. The method was succefully used to simulate dam-break flows by solving the fully nonlinear Shallow Water Equations (SWE) and by using an implicit scheme under a transient flow and the Coriolis effect.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
The BIE (boundary integral equation) method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applyiing the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are most important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods
Institute of Scientific and Technical Information of China (English)
崔晓兵; 季振林
2011-01-01
To solve the large scale sound field problems with multi-domain and multi-absorbing materials, a substructure fast multipole boundary element approach was developed. In view of the fact that the arrangement order of an unknown column vector and the node number affected the speed of convergence, a principle was proposed to compose the whole matrix equation. Additionally, in light of the accuracy effect of multipole expansion computation caused by the complex acoustic parameters, some studies and corrections were conducted on the fast multipole boundary element method (FMBEM). As an example of application, the transmission loss of a dissipative expansion chamber silencer was calculated by using the substructure FMBEM and the conventional boundary element method (CBEM). The results indicate that the present approach and corrections are valid. Compared to the CBEM, the advantage of substructure FMBEM in computational efficiency was more obvious as the number of boundary nodes increased for a given frequency.%为解决大尺度声场中常见的多区域复合及多吸声材料复合问题,提出了一种子结构快速多极子边界元法.鉴于未知量列向量的构建次序及边界节点编号顺序对迭代收敛速度有重要影响,提出了整体矩阵方程的构建原则.此外,针对复数形式声参数对多极子展开式计算准确性的影响,对快速多极子边界元法进行了研究与修正.以膨胀腔阻性消声器为例,应用子结构快速多极子边界元法与传统边界元法计算其传递损失.结果表明,该方法与修正是有效的,而且在某给定频率下,随着边界未知节点数的增大,其相对于传统边界元法在计算效率方面的优势越来越明显.
Rahmouni, Lyes; Cools, Kristof; Andriulli, Francesco P
2016-01-01
In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages in several real case scenarios. Unfortunately however, it is widely reported that the accuracy of standard BEM schemes is limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly discretized EEG forward problems, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several ...
Institute of Scientific and Technical Information of China (English)
岳强; 肖洪天; 邹杰
2009-01-01
In order to study the stress and the displacement of the flexible multi-layer elastic pavement under various loads distributed in arbitrary shape, the boundary element method for the flexible layered pavement was presented using the fundamental solutions multi-layer solids for the analysis.With combination of the generalized Kelvin fundamental solution and the boundary element method, the boundary integral equation was established for the boundary value problem of the flexible layered pavement to explain the singular integral appearing in the kernel function.The method, which does not involve integral of layered material' s interface, can be used to solve the stress and the displacement of the multi-layer elastic media under various loads distributed in arbitrary shape.The analytical result shows that the presented method is of higher precision and can be used for analysis of the flexible pavement which mechanical parameters change along the depth because of using the generalized Kelvin fundamental solutions of layered elastic solids.%为研究任意形状分布的各种荷载作用下柔性多层弹性路面应力和位移的性状分布特点,利用层状材料的广义Kelvin基本解,建立了边界元分析方法.结合广义Kelvin基本解与边界元方法,建立柔性层状路面边值问题的边界积分方程,对于核函数中出现的奇异积分做了解答.该方程中不舍在层状材料交界面上的积分,可求解任意形状分布各种荷载作用下的多层弹性体系应力和位移.算例分析表明:该方法可以获得较高的计算精度;由于采用了层状材料的广义Kelvin基本解,该方法能处理力学参数沿深度方向任意变化的柔性路面.
Institute of Scientific and Technical Information of China (English)
江文成; 张怀新; 孟堃宇
2013-01-01
该文运用无紧致声源假定的边界元法和传统的FW-H方程对水滴型潜艇的流噪声特性进行了数值模拟,将数值模拟得到的水听器处的声压值与试验值进行了对比,并研究了两种方法在求解沿潜艇X轴和Z轴上不同特征点处流噪声时的差异.结果表明,对于水听器处的流噪声声压值,边界元法得到的解更接近干试验值,而对于远场求解,两种方法得到的结果相差不大.%By using boundary element method and traditional method of FW-H equation,numerical simulation on the flow noise of streamlined submarine is done in this research.Numerical simulation results of sound pressure at a point where hydrophone located are compared with experimental data.Further research is done on the flow noise at a series of feature points along X and Z direction by using the above two methods.It can be concluded from this numerical simulation that for the flow noise at the hydrophone located point given in this paper,numerical results from boundary element method are closer to experimental data.Besides,for the sound pressure in far field,numerical simulation results from the two above methods are almost the same.
Institute of Scientific and Technical Information of China (English)
刘俊; 林皋; 李建波
2011-01-01
为精确研究超高压输电线路在复杂工况下的工频电场,采用比例边界有限元方法,在建立相应的电场计算模型基础上,利用变分原理并通过比例边界坐标变换,推导出工频电场的比例边界有限元方程、电位求解公式及电场求解公式,分析了超高压输电线路在穿越较复杂地形时的工频电场,探讨了超高压输电线路下存在介质块对工频电场的影响,并将算例计算结果与其他数值方法进行了比较.结果表明,比例边界有限元方法精度高、计算工作量小.%A scaled boundary finite element method (SBFEM) is developed for precise study of power frequency electric field generated by the EHV transmission lines under complex conditions. The electric field model is established, and variational principle technique and coordinate transformation between scaled and Cartesian coordinate is used to derive the scaled boundary finite element equations. The formulation of calculation of electric potential and field is also obtained.The method is also to solve the power-frequency electric field of EHV transmission lines under condition of complex landscape and media block. Numerical experiment is carried out and compared with other numerical methods. The results show that the proposed method yields excellent results, quick convergence and less amount of computation time.
Ghosh, Somnath; Kubair, Dhirendra V.
2016-10-01
Statistically equivalent representative volume elements or SERVEs are representations of the microstructure that are used for micromechanical simulations to generate homogenized material constitutive responses and properties (Swaminathan et al., 2006a; Ghosh, 2011). Typically, a SERVE is generated from the parent microstructure as a statistically equivalent region, whose size is determined from the requirements of convergence of macroscopic properties. Standard boundary conditions, such as affine transformation-based displacement boundary conditions (ATDBCs), uniform traction boundary conditions (UTBCs) or periodic boundary conditions (PBCs) are conventionally applied on the SERVE boundary for micromechanical simulations. However, when the microstructure is characterized by arbitrary, nonuniform distributions of heterogeneities, these simple boundary conditions do not represent the effect of regions exterior to the SERVE. Improper boundary conditions can result in significantly larger than optimal SERVE domains, needed for converged properties. In an attempt to overcome the limitations of the conventional boundary conditions on the SERVE, this paper explores the effect of boundary conditions that incorporate the statistics of the exterior region on the SERVE of elastic composites. Using Green's function based interaction kernels, coupled with statistical functions of the microstructural characteristics like one-point and two-point correlation functions, a novel exterior statistics-based boundary condition or ESBC is derived for the SERVE. The advantages of the ESBC are established by comparing with results of simulations using conventional boundary conditions. Results of the SERVE simulations subjected to ESBCs are also compared with those from other popular methods like statistical volume element (SVE) and weighted statistical volume element (WSVE). The proposed ESBCs offer significant advantages over other methods in the SERVE-based analysis of heterogeneous
Institute of Scientific and Technical Information of China (English)
Xiushan Sun; Lixin Huang; Yinghua Liu; Zhangzhi Cen; Keren Wang
2005-01-01
Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions.Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.
BOUNDARY ELEMENT ANALYSIS OF INTERACTION BETWEEN AN ELASTIC RECTANGULAR INCLUSION AND A CRACK
Institute of Scientific and Technical Information of China (English)
王银邦
2004-01-01
The interaction between an elastic rectangular inclusion and a kinked crack in an infinite elastic body was considered by using boundary element method. The new complex boundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundary integral equation was obtained on interface and involves only singularity of order l/ r. To verify the validity and effectiveness of the present boundary element method, some typical examples were calculated. The obtained results show that the crack stress intensity factors decrease as the shear modulus of inclusion increases. Thus, the crack propagation is easier near a softer inclusion and the harder inclusion is helpful for crack arrest.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The BIE method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applying the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are more important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referring some of the much broader developmental effort. (Auth.)
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...
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
1977-01-01
This numerical prediction summary indicates the wide variety of such procedures which are available. Most procedures have detailed user manuals, and in many cases the codes are available. Many of the special effects treated by various methods (such as nonequilibrium or equilibrium chemistry, transition, roughness etc.) are indicated.
Boundary integral methods for microfluidic problems
Burbidge, Adam
2015-01-01
Microscale experiments of reduced complexity allow one to tease out and examine some of the interesting phenomena that manifest in large hierarchically structured materials which are of general interest across many industries. Recent advances in high speed imaging techniques and post-processing allow experiments to yield small scale information which was previously unavailable, or extremely difficult to obtain. This additional information provides new challenges in terms of theoretical understanding and prediction that requires new tools. We discuss generalised weighted residual numerical methods as a means of solving physically derived systems of PDEs, using the steady Stokes equation as an example. These formulations require integration of arbitrary functions of submanifolds which often will have a lower dimensionality than the parent manifold, leading to cumbersome calculations of the Jacobian determinant. We provide a tensorial view of the transformation, in which the natural element coordinate system is a non-orthogonal frame, and derive an expression for the Jacobian factor in terms of the contravariant metric tensor gij. This approach has the additional advantage that it can be extended to yield the local surface curvature, which will be essential for correct implementation of free surface boundaries.
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.
Institute of Scientific and Technical Information of China (English)
胡志强; 林皋; 王毅; 刘俊
2011-01-01
The scaled boundary finite element method（SBFEM） is a semi-analytical and semi-numerical solution approach for solving partial differential equation.For problem in elasticity,the governing equations can be obtained by mechanically based formulation,Weighted residual formulation and principle of virtual work based on Scaled-boundary-transformation.These formulations are described in the frame of Lagrange system and the unknowns are displacements.In this paper,the discretization of the SBFEM and the dual system to solve elastic problem proposed by W.X.Zhong are combined to derive the governing equations in the frame of Hamilton system by introducing the dual variables.Then the algebraic Riccati equations of the static boundary stiffness matrix for the bounded and unbounded domain are derived based on the hybrid energy and Hamilton variational principle in the interval.The eigen-vector method and precise integration method can be employed to solve the algebraic Riccati equations for static boundary stiffness matrice.%比例边界有限元方法是求解偏微分方程的一种半解析半数值解法。对于弹性力学问题,可采用基于力学相似性、基于比例坐标相似变换的加权余量法和虚功原理得到以位移为未知量的系统控制方程,属于Lagrange体系。但在求解时,又引入了表面力为未知量,控制方程属于Hamilton体系。因而,本文提出在比例边界有限元离散方法的基础上,利用钟万勰教授提出的弹性力学对偶（辛）体系求解方法,通过引入对偶变量,直接在Hamil-ton体系框架内建立控制方程。再利用区段混合能和对偶方程得到了有限域、无限域边界静力刚度所满足的代数Ri
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.
New Boundary Treatment Methods for Lattice Boltamann Method
Institute of Scientific and Technical Information of China (English)
Cheng; Yong-guang; Suo; Li-sheng
2003-01-01
In practical fluid dynamic simulations, the boundary condition should be treated carefully because it always has crucial influence on the numerical accuracy, stability and efficiency. Two types of boundary treatment methods for lattice Boltzmann method (LBM) are proposed. One is for the treatment of boundaries situated at lattice nodes, and the other is for the approximation of boundaries that are not located at the regular lattice nodes. The first type of boundary treatment method can deal with various dynamic boundaries on complex geometries by using a general set of formulas, which can maintain secon-order accuracy. Based on the fact that the fluid flows simulated by LBM are not far from equilibrium, the unknown distributions at a boundary node are expressed as the analogous froms of their corresponding equilibrium distributions. analogous forms of their corresponding equilibrium distributions. Therefore, the number of unknowns can be reduced and an always-closed set of equations can be obtained for the solutions to pressure, velocity and special boundary conditions on various geometries. The second type of boundary treatment is a complete interpolation scheme to treat curved boundaries. It comes from careful analysis of the relations between distribution functions at boundary nodes and their neighboring lattice nodes. It is stable for all situations and of second-order accuracy. Basic ideas, implementation procedures and verifications with typical examples for the both treatments are presented. Numerical simulations and analyses show that they are accurate, stable,general and efficient for pracitical simulations.
New Boundary Treatment Methods for Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
Cheng Yong-guang; Suo Li-sheng
2003-01-01
In practical fluid dynamic simulations, the boundary condition should be treated carefully because it always has crucial influence on the numerical accuracy, stability and efficiency. Two types of boundary treatment methods for lattice Boltzmann method (LBM) are proposed. One is for the treatment of boundaries situated at lattice nodes, and the other is for the approximation of boundaries that are not located at the regular lattice nodes. The first type of boundary treatment method can deal with various dynamic boundaries on complex geometries by using a general set of formulas, which can maintain second-order accuracy. Based on the fact that the fluid flows simulated by LBM are not far from equilibrium, the unknown distributions at a boundary node are expressed as the analogous forms of their corresponding equilibrium distributions. Therefore, the number of unknowns can be reduced and an always-closed set of equations can be obtained for the solutions to pressure, velocity and special boundary conditions on various geometries. The second type of boundary treatment is a complete interpolation scheme to treat curved boundaries. It comes from careful analysis of the relations between distribution functions at boundary nodes and their neighboring lattice nodes. It is stable for all situations and of second-order accuracy. Basic ideas, implementation procedures and verifications with typical examples for the both treatments are presented. Numerical simulations and analyses show that they are accurate, stable, general and efficient for practical simulations.
THEORY AND METHOD FOR WETLAND BOUNDARY DELINEATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on the analysis of the subjectivity of wetland boundary criteria and their causes at present, this paper suggested that, under the condition that the mechanism of wetland formation process has not been understood,"black box" method of System Theory can be used to delineate wetland boundaries scientifically. After analyzing the difference of system construction among aquatic habitats, wetlands and uplands, the lower limit of rooted plants was chosen as the lower boundary criterion of wetlands. Because soil diagnostic horizon is the result of the long-term interaction among all environments, and it is less responsive than vegetation to short-term change, soil diagnostic horizon was chosen as the indicator to delineate wetland upper boundary, which lies at the thinning-out point of soil diagnostic horizon. Case study indicated that it was feasible using the lower limit of rooted plants and the thinning-out point of soil diagnostic horizon as criteria to delineate the lower and upper boundaries of wetland. In the study area, the thinning-out line of albic horizon was coincident with the 55.74m contour line, the maximum horizonerror was less than lm, and the maximum vertical error less than 0.04m. The problem on wetland definition always arises on the boundaries. Having delineated wetland boundaries, wetlands can be defined as follows: wetlands are the transitional zones between uplands and deepwater habitats, they are a kind of azonal complex that are inundated or saturated by surface or ground water, with the lower boundary lying at the lower limit of rooted plants, and the upper boundary at the thinning-out line of upland soil diagnostic horizon.
Artificial Boundary Method for Calculating Ship Wave Resistance
Institute of Scientific and Technical Information of China (English)
文新; 韩厚德
2003-01-01
The calculation of wave resistance for a ship moving at constant speed near a free surface is considered. This wave resistance is calculated with a linearized steady potential model. To deal with the unboundedness of the physical domain in the potential flow problem, we introduce one vertical side as an artificial upstream boundary and two vertical sides as the artificial downstream boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the potential flow problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. The solution of the variational problem by the finite element method gives the numerical approximation of the potential flow around the ship, which was used to calculate the wave resistance. The numerical examples show the accuracy and efficiency of the proposed numerical scheme.
Boundary element simulation of surface waves on a deformed half-space
Litvinchuk, S. Yu.; Belov, A. A.; Markov, I. P.; Ipatov, A. A.; Petrov, A. N.
2015-11-01
Homogeneous and two-layer half-spaces consisting of an anisotropic elastic, isotropic viscoelastic, or poroelastic material are considered. The Kelvin-Voigt model and the model with the Abel kernel are used as models of the viscoelastic material; the poroelastic material is studied within the framework of the model of the compressible Biot material. The case where the half-space contains a cavity is also considered. Propagation of surface waves is studied by the boundary element method. The numerical solution involves the method of collocations for a regularized boundary integral equation.
Wet Friction-Elements Boundary Friction Mechanism and Friction Coefficient Prediction
Directory of Open Access Journals (Sweden)
WANG Yanzhong
2012-12-01
Full Text Available The friction mechanism for the boundary friction course of friction elements engagement was explicitly expressed. The boundary friction model was built up by the surface topography. The model contained the effect of boundary film, adhesion, plough and lubrication. Based on the model, a coefficient for weakening plough for the lubrication was proposed. The modified model could fit for the working condition of wet friction elements. The friction coefficient as a function curve of rotating speed could be finally obtained by the data k and s/sm. The method provides a well interpretation of friction condition and friction coefficient prediction and the agreement between theoretical and experimental friction coefficients is reasonably good.
The view from the boundary: a new void stacking method
Cautun, Marius; Frenk, Carlos S
2015-01-01
We introduce a new method for stacking voids and deriving their profile that greatly increases the potential of voids as a tool for precision cosmology. Given that voids are highly non-spherical and have most of their mass at their edge, voids are better described relative to their boundary rather than relative to their centre, as in the conventional spherical stacking approach. The boundary profile is obtained by computing the distance of each volume element from the void boundary. Voids can then be stacked and their profiles computed as a function of this boundary distance. This approach enhances the weak lensing signal of voids, both shear and convergence, by a factor of two when compared to the spherical stacking method. It also results in steeper void density profiles that are characterised by a very slow rise inside the void and a pronounced density ridge at the void boundary, in qualitative agreement with theoretical models of expanding spherical underdensities. The resulting boundary density profile i...
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 ...
Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements
Talebi, Hossein; Saputra, Albert; Song, Chongmin
2016-08-01
While dominating the numerical stress analysis of solids, the finite element method requires a mesh to conform to the surface of the geometry. Thus the mesh generation of three dimensional complex structures often require tedious human interventions. In this paper, we present a formulation for arbitrary polyhedral elements based on the scaled boundary finite element method, which reduces the difficulties in automatic mesh generation. We also propose a simple method to generate polyhedral meshes with local refinements. The mesh generation method is based on combining an octree mesh with surfaces defined using signed distance functions. Through several numerical examples, we verify the results, study the convergence behaviour and depict the many advantages and capabilities of the presented method. This contribution is intended to assist us to eventually frame a set of numerical methods and associated tools for the full automation of the engineering analysis where minimal human interaction is needed.
Institute of Scientific and Technical Information of China (English)
Pan Xiaomin; Sheng Xinqing
2008-01-01
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finite-element-boundary-integral-multi-level fast multipole algorithm (FE-BI-MLFMA). Among many algorithms of FE-BI-MLFMA, the decomposition algorithm (DA) is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finite-element method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor-mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.
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.
Application of the Finite Element Method to Rotary Wing Aeroelasticity
Straub, F. K.; Friedmann, P. P.
1982-01-01
A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.
Directory of Open Access Journals (Sweden)
Yichao Gao
2011-01-01
Full Text Available The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB. Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.
A boundary element model for lined circular ducts with uniform flow
DEFF Research Database (Denmark)
Juhl, Peter Møller
1996-01-01
A boundary element method has been developed for predicting the acoustics in a circular duct in which a uniform flow propagates. Such a model may be used to predict the performance of different liner designs for inlets of turbo fan engines, which is important for the aeronautics industry. For thi......A boundary element method has been developed for predicting the acoustics in a circular duct in which a uniform flow propagates. Such a model may be used to predict the performance of different liner designs for inlets of turbo fan engines, which is important for the aeronautics industry....... For this application the prediction of attenuation at very high frequencies (up to ka=30) is important. However, it was found that the computational costs of a three-dimensional model would by far exceed the performance of a normal workstation. Therefore, an axisymmetric model with significantly reduced calculation...
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The need for accuracy and detail, plus the availablity of the high speed computer has led to the development of many new modeling methods ranging from general purpose structural analysis finite element programs to special purpose research programs. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The paper summarizes some advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods. (Auth.)
NEW ALGORITHM OF COUPLING ELEMENT-FREE GALERKIN WITH FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
ZHAO Guang-ming; SONG Shun-cheng
2005-01-01
Through the construction of a new ramp function, the element-free Galerkin method and finite element coupling method were applied to the whole field, and was made fit for the structure of element nodes within the interface regions, both satisfying the essential boundary conditions and deploying meshless nodes and finite elements in a convenient and flexible way, which can meet the requirements of computation for complicated field. The comparison between the results of the present study and the corresponding analytical solutions shows this method is feasible and effective.
Institute of Scientific and Technical Information of China (English)
1998-01-01
The boundary element method in framework is given to evaluate three dimensional frictional contact problems. Elasto-plastic material behavior is taken into account by mean of an initial stress formulation and Von Mises yield criterion. The amount of tangential traction at contact surface is limited by Coulomb's friction law and constant shear rule. From some numerical results of a plate rolling problem, it is demonstrated here that the BEM can be used to efficiently and accurately analyze this class of forming problems.
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. Reasonably...... the photoacoustic signal was demonstrated and good agreement with experiments for the actual resonance frequency and the quality factor of the cell was obtained despite its complicated geometry....
Selective Smoothed Finite Element Method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.
High Order Projection Plane Method for Evaluation of Supersingular Curved Boundary Integrals in BEM
Miao Cui; Wei-zhe Feng; Xiao-wei Gao; Kai Yang
2016-01-01
Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curve...
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
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...
Yang, Zhiguo; Rong, Zhijian; Wang, Bo; Zhang, Baile
2015-01-01
In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in accurate simulation of polygonal invisibility cloaks, concentrators and circular rotators arisen from the field of transformation electromagnetics (TE). In practice, we adopt a transparent boundary condition (TBC) characterized by the Dirichlet-to-Neumann (DtN) map to reduce wave propagation in an unbounded domain to a bounded domain. We then introduce a semi-analytic technique to integrate the global TBC with local curvilinear elements seamlessly, which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global Fourier coefficients on spectral-element grids exactly. From the perspective of TE, an invisibility cloak is devised by a singular coordinate transformation of Maxwell's equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observe...
Coupled Finite Element/Boundary Element Analysis of a Vehicle Moving Along a Railway Track
DEFF Research Database (Denmark)
Andersen, Lars; Nielsen, Søren R. K.
2004-01-01
. In this work, analyses are carried out with the aim of investigating the influence of the track design and properties on the level of ground vibration due to a vehicle moving with subsonic speed. A coupled finite element and boundary element model of the track and subsoil is employed, adopting a formulation......Trains running in build-up areas are a source to ground-borne noise. A careful design of the track structure may be one way of minimizing the vibrations in the surroundings. For example, open or in-filled trenches may be constructed along the track, or the soil underneath the track may be improved...... stiffening?even at low frequencies. However, for high-speed vehicles rubber chip barriers may be a promising means of vibration screening...
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.
Institute of Scientific and Technical Information of China (English)
李绪宣; 于更新; 符力耘; 温书亮; 管西竹
2011-01-01
边界元法对随机起伏的复杂海底界面具有良好的适应性.比较了边界元法与有限差分法对复杂断层模型的模拟精度,并验证了边界元法的有效性.利用边界元法对复杂海底模型进行波场模拟,反映起伏海底界面对地震波传播的影响；利用统计参数描述复杂海底地貌特征,将崎岖海底界面划分为快、慢变化和强、弱起伏等4种特征类型.根据不同统计参数的选择建立崎岖海底理论模型,利用边界元法对不同类型的崎岖海底理论模型进行模拟研究,同时与实际海底资料相对比,分析了复杂海底地震散射特征.此项研究成果可为复杂海底地区目标导向地震观测系统设计和采集参数优化提供理论依据.%The boundary-element method ( BEM) has a good adaptability for simulating irregularly rough and complex seabed. The simulation accuracy of BEM for a complex fault model was compared with that of the finite-difference method, and the effectiveness of BEM was confirmed. BEM can be used to conduct wave simulation of rough seabed models, reflecting the impacts of rough seabed on seismic wave propagation. The statistical parameters were used to describe complex seabed topography, and then four types of rough seabed interface can be identified, i. e. fast lateral change, slow lateral change, strong vertical relief and weak vertical relief. The theoretical models of rough seabed can be build by selecting various statistical parameters, and BEM was used to make simulation of different theoretical models of rough seabed. Simultaneously, some actual seabed data was compared and the seismic scattering characteristics of complex seabed were analyzed. These results will provide some theoretical foundations for the seismic acquisition design of complex seabed and the optimization of seismic acquisition parameters.
Directory of Open Access Journals (Sweden)
Sangita A Chakraborty
Full Text Available Chromatin boundary elements serve as cis-acting regulatory DNA signals required to protect genes from the effects of the neighboring heterochromatin. In the yeast genome, boundary elements act by establishing barriers for heterochromatin spreading and are sufficient to protect a reporter gene from transcriptional silencing when inserted between the silencer and the reporter gene. Here we dissected functional topography of silencers and boundary elements within circular minichromosomes in Saccharomyces cerevisiae. We found that both HML-E and HML-I silencers can efficiently repress the URA3 reporter on a multi-copy yeast minichromosome and we further showed that two distinct heterochromatin boundary elements STAR and TEF2-UASrpg are able to limit the heterochromatin spreading in circular minichromosomes. In surprising contrast to what had been observed in the yeast genome, we found that in minichromosomes the heterochromatin boundary elements inhibit silencing of the reporter gene even when just one boundary element is positioned at the distal end of the URA3 reporter or upstream of the silencer elements. Thus the STAR and TEF2-UASrpg boundary elements inhibit chromatin silencing through an antisilencing activity independently of their position or orientation in S. cerevisiae minichromosomes rather than by creating a position-specific barrier as seen in the genome. We propose that the circular DNA topology facilitates interactions between the boundary and silencing elements in the minichromosomes.
A rigid surface boundary element for soil-structure interaction analysis in the direct time domain
Rizos, D. C.
Many soil-structure interaction problems involve studies of single or multiple rigid bodies of arbitrary shape and soil media. The commonly used boundary element methods implement the equations of the rigid body in a form that depends on the particulars of the geometry and requires partitioning and condensation of the associated algebraic system of equations. The present work employs the direct time domain B-Spline BEM for 3D elastodynamic analysis and presents an efficient implementation of rigid bodies of arbitrary shape in contact with, or embedded in, elastic media. The formulation of a rigid surface boundary element introduced herein is suitable for direct superposition in the BEM system of algebraic equations. Consequently, solutions are computed in a single analysis step, eliminating, thus, the need for partitioning of the system of equations. Computational efficiency is also achieved due to the extremely sparse form of the associated coefficient matrices. The proposed element can be used for the modeling of single or multiple rigid bodies of arbitrary shape within the framework of the BEM method. The efficiency and general nature of the proposed element is demonstrated through applications related to the dynamic analysis of rigid surface and embedded foundations and their interaction with embedded rigid bodies of arbitrary shape.
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.
Immersed boundary methods for viscoelastic particulate flows
Krishnan, Sreenath; Shaqfeh, Eric; Iaccarino, Gianluca
2015-11-01
Viscoelastic particulate suspensions play key roles in many energy applications. Our goal is to develop a simulation-based tool for engineering such suspensions. This study is concerned with fully resolved simulations, wherein all flow scales associated with the particle motion are resolved. The present effort is based on Immersed Boundary methods, in which the domain grids do not conform to particle geometry. In this approach, the conservation of momentum equations, which include both Newtonian and non-Newtonian stresses, are solved over the entire domain including the region occupied by the particles. The particles are defined on a separate Lagrangian mesh that is free to move over an underlying Eulerian grid. The development of an immersed boundary forcing technique for moving bodies within an unstructured-mesh, massively parallel, non-Newtonian flow solver is thus developed and described. The presentation will focus on the numerical algorithm and measures taken to enable efficient parallelization and transfer of information between the underlying fluid grid and the particle mesh. Several validation test cases will be presented including sedimentation under orthogonal shear - a key flow in drilling muds and fracking fluids.
Wet Friction-Elements Boundary Friction Mechanism and Friction Coefficient Prediction
Wang, Yanzhong; Wu, Xiangyu; Wei, Bin
2012-01-01
The friction mechanism for the boundary friction course of friction elements engagement was explicitly expressed. The boundary friction model was built up by the surface topography. The model contained the effect of boundary film, adhesion, plough and lubrication. Based on the model, a coefficient for weakening plough for the lubrication was proposed. The modified model could fit for the working condition of wet friction elements. The friction coefficient as a function curve of rotating speed...
Method of securing filter elements
Energy Technology Data Exchange (ETDEWEB)
Brown, Erik P.; Haslam, Jeffery L.; Mitchell, Mark A.
2016-10-04
A filter securing system including a filter unit body housing; at least one tubular filter element positioned in the filter unit body housing, the tubular filter element having a closed top and an open bottom; a dimple in either the filter unit body housing or the top of the tubular filter element; and a socket in either the filter unit body housing or the top of the tubular filter element that receives the dimple in either the filter unit body housing or the top of the tubular filter element to secure the tubular filter element to the filter unit body housing.
Energy Technology Data Exchange (ETDEWEB)
Shih, H.R. [Jackson State Univ., MS (United States); Duffield, R.C.; Lin, J. [Univ. of Missouri, Columbia, MO (United States)
1996-10-01
An integral equation formulation and a numerical procedure for a boundary-finite element technique are developed for the static analysis of a stiffened plate with eccentric stiffeners. This formulation employs the fundamental solution associated with unstiffened plate bending and plane stress problems. With this approach, the resulting integral equation not only contained integrals along the perimeter of the stiffened but additional integrals along the stiffeners and the interface between the plate and its stiffeners. Thus the domain of the plate has to be divided into zones between the stiffeners. Each zone is modeled by boundary elements and stiffeners by finite elements. In this paper, the boundary element solution procedures for plate bending and in-plane problems are presented. The zone technique which permits coupling of unstiffened plate boundary element with stiffener finite elements is presented as well. Numerical example is given to demonstrate the effectiveness of this approach.
Institute of Scientific and Technical Information of China (English)
陈梦英; 商德江; 李琪; 刘永伟
2011-01-01
提出了一种可实现任意形状的运动结构噪声源识别的声全息方法.通过结合移动框架技术与边界元声全息技术两种算法的特点,提出利用移动框架技术将存在多普勒效应的时域数据转换成边界元声全息所需的双平面全息数据,然后由边界元法声全息公式重构任意结构表面的声学信息,实现运动结构噪声源定位.该方法既具有移动框架技术处理运动问题的快速简便,又具有边界元方法可处理任意形状问题的特点.最后在半消声水池中,对运动速度为9.96cm/s的带帽圆柱壳体进行了试验验证,结果表明:在低速条件下,该方法能够准确反演得到该结构的表面有功声强以及声压等声场信息,从而实现噪声源定位,由于条件有限,高速验证需进一步验证.%A method for realizing noise source identification of the arbitrary shaped moving structure is present. A theoretical model is established, which is a combination of moving frame acoustic holography (MFAH) and acoustic holography based on boundary element method (BEM-based NAH). MFAH can change time-domain data which existing Doppler effects into the dual plane holographic data which is needed in the BEM-based NAH. The surface acoustic information of an arbitrary structure is reconstructed by BEM-based NAH, which can be used for location of noise source. It not only has the MFAH's fast and easy characteristics for dealing with movement problem, but also has the BEM-based NAH characteristics of dealing with arbitrary shape. Finally, an experiment test was conducted by using a moving hooded cylindrical shell which speed is 9.96 cm/s as research object in the semi-anechoic pool. The results showed that: the method can accurately realize the inversion of the structure of the surface of active sound intensity and sound pressure and other information in sound field, thereby achieving noise source location. Because of the condition limited, high
Nonconforming ℎ- Spectral Element Methods for Elliptic Problems
Indian Academy of Sciences (India)
P K Dutt; N Kishore Kumar; C S Upadhyay
2007-02-01
In this paper we show that we can use a modified version of the ℎ- spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. In the neighbourhood of the corners, modified polar coordinates are used and a global coordinate system elsewhere. A stability estimate is derived for the functional which is minimized based on the regularity estimate in [2]. We examine how to parallelize the method and show that the set of common boundary values consists of the values of the function at the corners of the polygonal domain. The method is faster than that proposed in [6,7,14] and the ℎ- finite element method and stronger error estimates are obtained.
CASCADIC MULTIGRID METHODS FOR MORTAR WILSON FINITE ELEMENT METHODS ON PLANAR LINEAR ELASTICITY
Institute of Scientific and Technical Information of China (English)
陈文斌; 汪艳秋
2003-01-01
Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented.
Continuous finite element methods for Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Coupled Boundary and Finite Element Analysis of Vibration from Railway Tunnels
DEFF Research Database (Denmark)
Andersen, Lars; Jones, C.J.C.
2006-01-01
body vibration (about 4 to 80 Hz). A coupled finite element and boundary element scheme is applied in both two and three dimensions. Two tunnel designs are considered: a cut-and-cover tunnel for a double track and a single-track tunnel dug with the New Austrian Tunnelling Method (NATM).......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...
Coupled Boundary and Finite Element Analysis of Vibration from Railway Tunnels
DEFF Research Database (Denmark)
Andersen, Lars; Jones, C. J. C.
2004-01-01
body vibration (about 4 to 80 Hz). A coupled finite element and boundary element scheme is applied in both two and three dimensions. Two tunnel designs are considered: a cut-and-cover tunnel for a double track and a single-track tunnel dug with the New Austrian Tunnelling Method (NATM).......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...
Isogeometric Boundary Element Analysis with elasto-plastic inclusions. Part 1: Plane problems
Beer, Gernot; Zechner, Jürgen; Dünser, Christian; Fries, Thomas-Peter
2015-01-01
In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the inclusion may exhibit inelastic material behavior. In this paper only plane stress/strain problems are considered. In our approach the geometry of the inclusion is described using NURBS basis functions. The advantage over currently used methods is that no discretization into cells is required in order to evaluate the arising volume integrals. The other difference to current approaches is that Kernels of lower singularity are used in the domain term. The implementation is verified on simple finite and infinite domain examples with various boundary conditions. Finally a practical application in geomechanics is presented.
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.
Institute of Scientific and Technical Information of China (English)
龙述尧; 熊渊博
2004-01-01
The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method(GFEM), boundary element method(BEM) and element free Galerkin method(EFGM), and is a truly meshless method possessing wide prospects in engineering applications.The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem.
Institute of Scientific and Technical Information of China (English)
FengYangde; WangYuesheng; ZhangZimao; CuiJunzhi
2003-01-01
A 2D time domain boundary element method (BEM) is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion. Coulomb friction is assumed along the contact interface. The incident wave is assumed strong enough so that localized slip and separation take place along the interface. The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip, separation and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embeddedin an infinite solid.
Flux-conserving finite element methods
Zhang, Shangyou; Zhang, Zhimin; Zou, Qingsong
2012-01-01
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator. We propose two methods, post-processing the finite element solutions locally. The new solutions, remaining as optimal-order solutions, are flux-conserving elementwise. In one of our methods, the processed solution also satisfies the original finite element e...
ELEMENT FUNCTIONS OF DISCRETE OPERATOR DIFFERENCE METHOD
Institute of Scientific and Technical Information of China (English)
田中旭; 唐立民; 刘正兴
2002-01-01
The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.
A boundary element approach to estimate the free surface in stratified two-phase flow
International Nuclear Information System (INIS)
Two-phase flows widely exist in many industries. Measuring the phase distribution in two-phase flow is important for the optimization and control of some industrial processes. Electrical resistance tomography (ERT) is a promising non-intrusive visualization technique for monitoring the two-phase flow. However, due to its nonlinear and ill-posed character, high-quality image reconstruction is difficult and some iterative approach is time consuming. In this paper, a boundary element approach is presented for directly estimating the free-surface in two-phase flow using ERT. The unknown free surface is parameterized by a Bézier curve. Coefficients of its control points are estimated by minimizing a residual function using the iterative Levenberg–Marquardt method. To speed up the estimation process, the physical model of ERT is formulated using a boundary element method. Based on this formulation, the forward problem is fast solved through a small size system matrix and the Jacobian matrix is efficiently calculated using an analytic method. After several numerical experiments, this approach is proved fast and precise and several factors influencing the estimation quality are analyzed based on these simulations. (paper)
Natarajan, Sundararajan; Ooi, Ean Tat; Chiong, Irene; Song, Chongmin
2013-01-01
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed polygonal FEM with simple averaging technique and the scaled boundary polygon formulation. For the purpose of numerical integration, we employ the sub-traingulation for the polygonal FEM and classical Gaussian quadrature for the smoothed FEM an...
Dancette, S.; Browet, A.; Martin, G.; Willemet, M.; Delannay, L.
2016-06-01
A new procedure for microstructure-based finite element modeling of polycrystalline aggregates is presented. The proposed method relies (i) on an efficient graph-based community detection algorithm for crystallographic data segmentation and feature contour extraction and (ii) on the generation of selectively refined meshes conforming to grain boundaries. It constitutes a versatile and close to automatic environment for meshing complex microstructures. The procedure is illustrated with polycrystal microstructures characterized by orientation imaging microscopy. Hot deformation of a Duplex stainless steel is investigated based on ex-situ EBSD measurements performed on the same region of interest before and after deformation. A finite element mesh representing the initial microstructure is generated and then used in a crystal plasticity simulation of the plane strain compression. Simulation results and experiments are in relatively good agreement, confirming a large potential for such directly coupled experimental and modeling analyses, which is facilitated by the present image-based meshing procedure.
ARTIFICIAL BOUNDARY METHOD FOR THE THREE-DIMENSIONAL EXTERIOR PROBLEM OF ELASTICITY
Institute of Scientific and Technical Information of China (English)
Hou-de Han; Chun-xiong Zheng
2005-01-01
The exact boundary condition on a spherical artificial boundary is derived for thethree-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem.In the end, a numerical example is given to demonstrate the performance of the proposed method.
Application of Arnoldi method to boundary layer instability
Zhang, Yong-Ming; Luo, Ji-Sheng
2015-12-01
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien-Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous’ in secondary instability. Project supported by the National Natural Science Foundation of China (Grant Nos. 11202147, 11332007, 11172203, and 91216111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032120007).
Argeso, Hakan; Mengi, Yalcin
2014-02-01
A unified formulation is presented, based on the boundary element method, to perform the interaction analysis for the problems involving poroviscoelastic media. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices at a single step in terms of system matrices of boundary element method without solving any special problem, such as, unit displacement or load problem, as required by conventional methods. It further eliminates the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. The formulation is explained by considering a simple interaction problem involving an inclusion embedded in an infinite poroviscoelastic medium, which is under the influence of a dynamic excitation induced by seismic waves. In the formulation, an impedance relation is established for this interaction problem, suitable for performing the interaction analysis by substructure method, which permits carrying out the analysis for inclusion and its surrounding medium separately. The inclusion is first treated as poroviscoelastic, then viscoelastic and finally rigid, where the formulation in each of these cases is obtained consecutively as a special case of the previous one. It is remarkable to note that, a cavity problem where there is a hole in place of inclusion can be also considered within the framework of the present formulation. The formulation is assessed by applying it to some sample problems. The extension of the formulation to other types of interaction problems, such as, multi-inclusion problems, the analyses of foundations supported by a poroviscoelastic medium, etc., will be the subject of a separate study.
Institute of Scientific and Technical Information of China (English)
刘贵立; 张国英; 李荣德
2003-01-01
The model of dislocations was used to construct the model of grain boundary (GB) with pure rare earths, and rare earth elements and impurities. The influence of the interaction between rare earth elements and impurities on the cohesive properties of 5.3° low angle GB of Fe was investigated by the recursion method. The calculated results of environment sensitive embeding energy(EESE) show that the preferential segregation of rare earth elements towards GBs exists. Calculations of bond order integrals (BOI) show that rare earth elements increase the cohesive strength of low angle GB, and impurities such as S, P weaken the intergranular cohesion of the GB. So rare earth element of proper quantity added in steel not only cleanses other harmful impurities off the GBs, but also enhances the intergranular cohesion. This elucidates the action mechanism of rare earth elements in steel from electronic level and offers theoretical evidence for applications of rare earth elements in steels.
A three dimensional implicit immersed boundary method with application
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Most algorithms of the immersed boundary method originated by Peskin are explicit when it comes to the computation of the elastic forces exerted by the immersed boundary to the fluid. A drawback of such an explicit approach is a severe restriction on the time step size for maintaining numerical stability. An implicit immersed boundary method in two dimensions using the lattice Boltzmann approach has been proposed. This paper reports an extension of the method to three dimensions and its application to simul...
The Finite Element Method An Introduction with Partial Differential Equations
Davies, A J
2011-01-01
The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is alsoexplained. This book is written at an introductory level, developing all the necessary concepts where required. Co
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.
Wireless boundary monitor system and method
International Nuclear Information System (INIS)
A wireless boundary monitor system used to monitor the integrity of a boundary surrounding an area uses at least two housings having at least one transmitting means for emitting ultrasonic pressure waves to a medium. Each of the housings has a plurality of receiving means for sensing the pressure waves in the medium. The transmitting means and the receiving means of each housing are aimable and communicably linked. At least one of the housings is equipped with a local alarm means for emitting a first alarm indication whereby, when the pressure waves propagating from a transmitting means to a receiving means are sufficiently blocked by an object a local alarm means or a remote alarm means or a combination thereof emit respective alarm indications. The system may be reset either manually or automatically. This wireless boundary monitor system has useful applications in both indoor and outdoor environments. 4 figs
A finite element model updating technique for adjustment of parameters near boundaries
Gwinn, Allen Fort, Jr.
Even though there have been many advances in research related to methods of updating finite element models based on measured normal mode vibration characteristics, there is yet to be a widely accepted method that works reliably with a wide range of problems. This dissertation focuses on the specific class of problems having to do with changes in stiffness near the clamped boundary of plate structures. This class of problems is especially important as it relates to the performance of turbine engine blades, where a change in stiffness at the base of the blade can be indicative of structural damage. The method that is presented herein is a new technique for resolving the differences between the physical structure and the finite element model. It is a semi-iterative technique that incorporates a "physical expansion" of the measured eigenvectors along with appropriate scaling of these expanded eigenvectors into an iterative loop that uses the Engel's model modification method to then calculate adjusted stiffness parameters for the finite element model. Three example problems are presented that use eigenvalues and mass normalized eigenvectors that have been calculated from experimentally obtained accelerometer readings. The test articles that were used were all thin plates with one edge fully clamped. They each had a cantilevered length of 8.5 inches and a width of 4 inches. The three plates differed from one another in thickness from 0.100 inches to 0.188 inches. These dimensions were selected in order to approximate a gas turbine engine blade. The semi-iterative modification technique is shown to do an excellent job of calculating the necessary adjustments to the finite element model so that the analytically determined eigenvalues and eigenvectors for the adjusted model match the corresponding values from the experimental data with good agreement. Furthermore, the semi-iterative method is quite robust. For the examples presented here, the method consistently converged
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.
A simple boundary element formulation for shape optimization of 2D continuous structures
International Nuclear Information System (INIS)
For the design of nuclear equipment like pressure vessels, steam generators, and pipelines, among others, it is very important to optimize the shape of the structural systems to withstand prescribed loads such as internal pressures and prescribed or limiting referential values such as stress or strain. In the literature, shape optimization of frame structural systems is commonly found but the same is not true for continuous structural systems. In this work, the Boundary Element Method (BEM) is applied to simple problems of shape optimization of 2D continuous structural systems. The proposed formulation is based on the BEM and on deterministic optimization methods of zero and first order such as Powell's, Conjugate Gradient, and BFGS methods. Optimal characterization for the geometric configuration of 2D structure is obtained with the minimization of an objective function. Such function is written in terms of referential values (such as loads, stresses, strains or deformations) prescribed at few points inside or at the boundary of the structure. The use of the BEM for shape optimization of continuous structures is attractive compared to other methods that discretized the whole continuous. Several numerical examples of the application of the proposed formulation to simple engineering problems are presented. (authors)
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
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.
Nilsson, C.-M.; Jones, C. J. C.; Thompson, D. J.; Ryue, J.
2009-04-01
Engineering methods for modelling the generation of railway rolling noise are well established. However, these necessarily involve some simplifying assumptions to calculate the sound powers radiated by the wheel and the track. For the rail, this involves using an average vibration together with a radiation efficiency determined for a two-dimensional (2D) problem. In this paper, the sound radiation from a rail is calculated using a method based on a combination of waveguide finite elements and wavenumber boundary elements. This new method allows a number of the simplifying assumptions in the established methods to be avoided. It takes advantage of the 2D geometry of a rail to provide an efficient numerical approach but nevertheless takes into account the three-dimensional nature of the vibration and sound field and the infinite extent of the rail. The approach is used to study a conventional 'open' rail as well as an embedded tram rail of the type used for street running. In the former case it is shown that the conventional approach gives correct results and the complexity of the new method is mostly not necessary. However, for the embedded rail it is found that it is important to take into account the radiation from several wave types in the rail and embedding material. The damping effect of the embedding material on the rail vibration is directly taken into account and, for the example shown, causes the embedded rail to radiate less sound than the open rail above about 600 Hz. The free surface of the embedding material amplifies the sound radiation at some frequencies, while at other frequencies it moves out of phase with the rail and reduces the radiation efficiency. At low frequencies the radiation from the embedded rail resembles a line monopole source which produces greater power than the 'open' rail which forms a line dipole.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
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......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...... 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...
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.
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
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. PMID:27442240
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. PMID:27442240
Energy Technology Data Exchange (ETDEWEB)
T.F. Eibert; J.L. Volakis; Y.E. Erdemli
2002-03-03
Hybrid finite element (FE)--boundary integral (BI) analysis of infinite periodic arrays is extended to include planar multilayered Green's functions. In this manner, a portion of the volumetric dielectric region can be modeled via the finite element method whereas uniform multilayered regions can be modeled using a multilayered Green's function. As such, thick uniform substrates can be modeled without loss of efficiency and accuracy. The multilayered Green's function is analytically computed in the spectral domain and the resulting BI matrix-vector products are evaluated via the fast spectral domain algorithm (FSDA). As a result, the computational cost of the matrix-vector products is kept at O(N). Furthermore, the number of Floquet modes in the expansion are kept very few by placing the BI surfaces within the computational unit cell. Examples of frequency selective surface (FSS) arrays are analyzed with this method to demonstrate the accuracy and capability of the approach. One example involves complicated multilayered substrates above and below an inhomogeneous filter element and the other is an optical ring-slot array on a substrate several hundred wavelengths in thickness. Comparisons with measurements are included.
Sigüenza, J.; Mendez, S.; Ambard, D.; Dubois, F.; Jourdan, F.; Mozul, R.; Nicoud, F.
2016-10-01
This paper constitutes an extension of the work of Mendez et al. (2014) [36], for three-dimensional simulations of deformable membranes under flow. An immersed thick boundary method is used, combining the immersed boundary method with a three-dimensional modeling of the structural part. The immersed boundary method is adapted to unstructured grids for the fluid resolution, using the reproducing kernel particle method. An unstructured finite-volume flow solver for the incompressible Navier-Stokes equations is coupled with a finite-element solver for the structure. The validation process relying on a number of test cases proves the efficiency of the method, and its robustness is illustrated when computing the dynamics of a tri-leaflet aortic valve. The proposed immersed thick boundary method is able to tackle applications involving both thin and thick membranes/closed and open membranes, in significantly high Reynolds number flows and highly complex geometries.
Institute of Scientific and Technical Information of China (English)
施明光; 徐艳杰; 张楚汉; 刘钧玉
2016-01-01
Any structural domain can be discretized automatically with a mesh of arbitrary n-sided (n≥3)polygon scaled boundary finite elements (PSBFE)based on Delaunay triangulation background mesh.Compared with previous literatures based on SBFEM,PSBFE retains the characteristics of SBFEM's accurately representing orders of singularities at crack tips it is more general and flexible in modeling complicated structures and their crack propagation.Here,PSBFE was for the first time applied to simulate the dynamic interactions between a crack and inclusions in composite material. The numerical results of stationary cracks under dynamic load were consistent with available data in literatures.Next,a local remeshing scheme was employed to simulate the dynamic crack propagation.The numerical results demonstrated that stiff and soft inclusions have the restraining and amplification effects on the dynamic stress intensity factor of a structure;the sizes and positions of inclusions also affect the dynamic stress intensity factor,the larger the size and the closer the inclusion,the more the effects.%基于三角形背景网格，任意结构可用 n（n≥3）边多边形比例边界有限元（Polygon Scaled Boundary Finite Elements，PSBFE）自动离散。相对以往基于比例边界有限元（SBFEM）的应用，该多边形单元不但继承 SBFEM半解析求解裂纹尖端奇异性的特性，而且在模拟复杂结构的网格生成和裂纹扩展上具有更高的通用性。首次用该单元模拟了动荷载下复合材料裂纹和夹杂相互作用。动荷载稳定裂纹情况下，PSBFE 计算结果同现有文献吻合良好，在此基础上，结合基于拓扑的局部网格重剖分方法，模拟了动荷载下夹杂和扩展裂纹相互作用。结果表明，硬质夹杂和软质夹杂对结构的动力应力强度因子分别起到抑制和放大的作用。夹杂尺寸，夹杂大小也会在一定范围内影响动力应力强度因子，尺寸越大距
A new method to detect the ICMEs boundaries
Dumitrache, Cristiana
2014-01-01
A new method to infer the boundaries of the interplanetary coronal mass ejections is proposed. The local minima of a proton temperature anisotropy are used as potential boundaries of the interplanetary event. The low-beta plasma values are then invoked to detect at least four boundaries, two for the beginning and two for the end of an interplanetary coronal mass ejection (ICME). Intermediate boundaries can be identified, as indicated by other plasma and magnetic field signatures, and mark substructures of an event. Using the algorithm we propose here, we have compiled a list with ICME events boundaries registered by \\emph{Ulysses} spacecraft during 2000-2002. Three magnetic clouds (observed on 23 January 2001, 10 June 2001 and 24 August 2001) are analysed with details. This method provides premises for an alternative way of automatic detection of the ICMEs boundaries.
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)
An improved optimal elemental method for updating finite element models
Institute of Scientific and Technical Information of China (English)
Duan Zhongdong(段忠东); Spencer B.F.; Yan Guirong(闫桂荣); Ou Jinping(欧进萍)
2004-01-01
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures,the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.Thc example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
Institute of Scientific and Technical Information of China (English)
陈海兵; 梁发云
2014-01-01
在水平振动或地震作用下，建立圆形桩与土的动力相互作用简化边界元模型，采用动力相互作用因子对群桩基础顶部的惯性响应和运动响应进行分析。桩身运动方程考虑了群桩动力相互作用以及由土体位移引起的被动桩效应，得到了频域内固定群桩基础顶部的水平动力响应的弹性解答。结果表明，简化边界元模型通过土体位移系数，考虑了沿桩身长度方向的土体相互作用，较为准确地得到了桩身运动弯矩，将其运用到群桩基础的计算中，可以用于评估动力作用下群桩基础的桩顶水平阻抗和桩土运动响应。%A simple boundary element approach for the system of circular piles and soils is formulated to predict the lateral impedance and kinematic seismic responses of fixed-head pile groups during the lateral vibration or seismic excitation. The dynamic interaction of piles in a group and the passive pile effect are considered in the dynamic equilibrium of a pile foundation. The elastic solution to the lateral impedance and kinematic seismic responses of the massless pile cap, restricting against rotation, is obtained in the frequency domain. The results show that the soil-displacement-influence coefficient can be used to consider the pile-soil interaction along a pile and to capture the kinematic bending moment accurately. Meanwhile, the coefficients provide reasonable estimations of the lateral impedance and kinematic seismic response of pile groups.
Prediction of Water Movement in Soil by Finite Element Method
Morii, Toshihiro; 森井,俊広
1999-01-01
A computer program SUSFEM for simulating water movement in two-dimensional or axisymmetric unsaturated, partially saturated, or saturated soil is developed. Richards' potential equation supplemented by appropriate boundary and initial conditions is described and formulated on the basis of Galerkin-type finite element method in conj unction with a fully implicit iterative scheme. SUSFEM calculates sequential and spatial variations of pressure head in soil, h. The saturated water movement is pr...
High Order Projection Plane Method for Evaluation of Supersingular Curved Boundary Integrals in BEM
Directory of Open Access Journals (Sweden)
Miao Cui
2016-01-01
Full Text Available Boundary element method (BEM is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curved line/plane, and unified expressions are obtained for both two-dimensional and three-dimensional problems. For the two-dimensional boundary integrals, analytical expressions for the third-order derivatives are derived and are employed to verify the complex-variable-differentiation method (CVDM which is used to evaluate the high order derivatives for three-dimensional problems. A few numerical examples are given to show the effectiveness and the accuracy of the present method.
A method used to determine the upper thermal boundary of subgrade based on boundary layer theory
Institute of Scientific and Technical Information of China (English)
QingBo Bai; Xu Li; YaHu Tian
2015-01-01
In the numerical simulation of long-term subgrade temperature fields, the daily variation of soil temperature at a certain depthh is negligible. Such phenomenon is called the "boundary layer theory." Depthh is defined as the boundary layer thickness and the soil temperature athis approximately equal to a temperature increment plus the average atmosphere temperature. In the past, the boundary layer thickness and temperature increment were usually extracted from monitored data in the field. In this paper, a method is proposed to determinate the boundary layer thickness and temperature incre-ment. Based on the typical designs of highway or railway, the theoretical solution of boundary layer thickness is inferred and listed. Further, the empirical equation and design chart for determining the temperature increment are given in which the following factors are addressed, including solar radiation, equivalent thermal diffusivity and convective heat-transfer coefficient. Using these equations or design charts, the boundary layer thickness and temperature increment can be easily determined and used in the simulation of long-term subgrade temperature fields. Finally, an example is conducted and used to verify the method. The result shows that the proposed method for determining the upper thermal boundary of subgrade is accurate and practical.
Mitharwal, Rajendra
2015-01-01
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization is obtained by leveraging on an extension of Calderon techniques to rectangular systems leading to well-conditioned problems independent of the discretization density. This enables the use of highly discretized Huygens surfaces that can be consequently placed very near to the radiating source. In addition, the new regularized scheme is hybridized with both surfacic homogeneous and volumetric inhomogeneous forward BEM solvers accelerated with fast matrix-vector multiplication schemes. This allows for rapid and effective dosimetric assessments and permits the use of inhomogeneous and realistic head phantoms. Numerical results corroborate the theory and confirms the practical effectiveness of all newly proposed formulations.
Boundary element simulation of size effect in quasi-brittle aggregate materials
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A nonlinear multi-zone boundary element method is applied to simulate the size effect of a series of geome trically similar three-point-bend specimens. The material in which particles are randomly dispersed in a relatively hard matrix can bo applicable to various aggregate materials as well as unidirectionally reinforced fiber composites in the transverse plane. A single edge macrocrack and interfacial microcracks randomly distributed between particles and ma trix are prescribed as initial defects. The shape, size and location of the fracture process zone (FPZ) are realistically simulated and described. The nominal strength of the material is in agreement with the Bazant size effect law. In addi tion, the results show that microcracking is one of the most important micromechanisms for the size effect in aggregate materials.
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.
THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Sun Haitao; Wang Yuanhan
2007-01-01
A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network (IRBFN) constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations (BIE) can be established while the fundamental solutions to the problems are introduced. The singular value decomposition (SVD) method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available.In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.
Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method
Smith, James P.
1996-01-01
A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.
Modified Differential Transform Method for Two Singular Boundary Values Problems
Directory of Open Access Journals (Sweden)
Yinwei Lin
2014-01-01
Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.
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 element methods: Algorithms and architectures
Fischer, Paul; Ronquist, Einar M.; Dewey, Daniel; Patera, Anthony T.
1988-01-01
Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered: the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.
Spectral element methods - Algorithms and architectures
Fischer, Paul; Ronquist, Einar M.; Dewey, Daniel; Patera, Anthony T.
1988-01-01
Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered; the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.
A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS
Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.
1993-01-01
Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).
A Boundary Element Investigation of Liquid Sloshing in Coupled Horizontal and Vertical Excitation
Directory of Open Access Journals (Sweden)
De-Zhi Ning
2012-01-01
Full Text Available Sloshing flows in a two-dimensional rigid rectangular tank under specified excitations in the coupled horizontal and vertical modes are simulated by using a higher-order boundary element method (BEM. The liquid sloshing is formulated as an initial-boundary-value problem based on the fully nonlinear potential flow theory. And a semi-mixed Eulerian-Lagrangian technique combined with the 4th-order Runge-Kutta scheme is employed to advance the solutions in the time marching process. A smoothing technique is applied to the free surface at every several time steps to avoid the possible numerical instabilities. Numerical results obtained are compared with the available solutions to validate the developed model. The parametric studies are carried out to show the liquid sloshing effects in terms of the slosh frequencies and excitation amplitudes in horizontal and vertical modes, the second-order resonance frequency, a bottom-mounted vertical rigid baffle, free surface displacement, and hydrodynamic forces acting on the tank.
Stenroos, Matti
2016-01-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from standard formulation. The approach and resulting solver are verified in three ways, including comparison to finite element method (FEM). In a two-compartment split-sphere model with two spaced monopoles, the results obtained with high-resolution FEM and the BEMs were almost identical (relative difference < 0.003).
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Vorona Yu.V.; Kara I.D.
2015-01-01
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.
Singular and Regular Implementations of the Hybrid Boundary Node Method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The hybrid boundary node method (HdBNM) combines a modified function with the moving least squares approximation to form a boundary-only truly meshless method. This paper describes two implementations of the HdBNM, the singular hybrid boundary node method (ShBNM) and the regular hybrid boundary node method (RhBNM). The ShBNM and RhBNM were compared with each other, and the parameters that influence their performance were studied in detail. The convergence rates and their applicability to thin structures were also investigated. The ShBNM and RhBNM are found to be very easy to implement and to efficiently obtain numerical solutions to computational mechanics problems.
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.
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.
Discrete mechanics Based on Finite Element Methods
Chen, Jing-Bo; Guo, Han-Ying; Wu, Ke
2002-01-01
Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.
A Cartesian embedded boundary method for hyperbolic conservation laws
Energy Technology Data Exchange (ETDEWEB)
Sjogreen, B; Petersson, N A
2006-12-04
The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.
Simulation of extrudate swell using an extended finite element method
Choi, Young Joon; Hulsen, Martien A.
2011-09-01
An extended finite element method (XFEM) is presented for the simulation of extrudate swell. A temporary arbitrary Lagrangian-Eulerian (ALE) scheme is incorporated to cope with the movement of the free surface. The main advantage of the proposed method is that the movement of the free surface can be simulated on a fixed Eulerian mesh without any need of re-meshing. The swell ratio of an upper-convected Maxwell fluid is compared with those of the moving boundary-fitted mesh problems of the conventional ALE technique, and those of Crochet & Keunings (1980). The proposed XFEM combined with the temporary ALE scheme can provide similar accuracy to the boundary-fitted mesh problems for low Deborah numbers. For high Deborah numbers, the method seems to be more stable for the extrusion problem.
On Hybrid and mixed finite element methods
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre
2013-11-01
A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe no-slip or slip conditions (slip length from zero to infinity) at the fluid-solid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particle-based methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the Navier-Stokes equations subject to spatial-independent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. The authors acknowledge the funding support by the ASCR Program of the Office of Science, U.S. Department of Energy.
A MATLAB Code for Three Dimensional Linear Elastostatics using Constant Boundary Elements
P, Kirana Kumara
2013-01-01
Present work presents a code written in the very simple programming language MATLAB, for three dimensional linear elastostatics, using constant boundary elements. The code, in full or in part, is not a translation or a copy of any of the existing codes. Present paper explains how the code is written, and lists all the formulae used. Code is verified by using the code to solve a simple problem which has the well known approximate analytical solution. Of course, present work does not make any contribution to research on boundary elements, in terms of theory. But the work is justified by the fact that, to the best of author's knowledge, as of now, one cannot find an open access MATLAB code for three dimensional linear elastostatics using constant boundary elements. Author hopes this paper to be of help to beginners who wish to understand how a simple but complete boundary element code works, so that they can build upon and modify the present open access code to solve complex engineering problems quickly and easi...
In this study, gas-phase elemental mercury (Hg0) and related species (including inorganic reactive gaseous mercury (RGM) and particulate mercury (PHg)) were measured at Cheeka Peak Observatory (CPO), Washington State, in the marine boundary layer (MBL) during 2001-2002. Air of...
Institute of Scientific and Technical Information of China (English)
Liguo Tang; Jianchun Cheng
2008-01-01
The method of eigenfunction expansion is one of the most elegant methods for solving elastodynamic problems.The solution obtained from it is more concise than that obtained from the integral transform technique.Traditional eigenfunction expansion method is used for the elastodynamic problems with displacement and traction boundary conditions.In this paper,the method is generalized to study the elastodynamic response of an elastic solid with mixed boundary surfaces,and the exact analytical solution is derived.The dynamic response of a finite-length solid aluminum cylinder with two mixed end boundaries is numerically evaluated.The result com-puted from the analytical solution agrees very well with that obtained from finite element method(FEM).
Accelerated Matrix Element Method with Parallel Computing
Schouten, Doug; Stelzer, Bernd
2014-01-01
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current collider experiments. However, the computational complexity of this method for final states with many particles and degrees of freedom sets it at a disadvantage compared to supervised classification methods such as decision trees, k nearest-neighbour, or neural networks. This note presents a concrete implementation of the matrix element technique using graphics processing units. Due to the intrinsic parallelizability of multidimensional integration, dramatic speedups can be readily achieved, which makes the matrix element technique viable for general usage at collider experiments.
A poroelastic immersed boundary method with applications to cell biology
Strychalski, Wanda; Copos, Calina A.; Lewis, Owen L.; Guy, Robert D.
2015-02-01
The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In the traditional immersed boundary method, the fluid and structure move with the same velocity field. In this work, a model based on the immersed boundary method is presented for simulating poroelastic media in which the fluid permeates a porous, elastic structure of small volume fraction that moves with its own velocity field. Two distinct methods for calculating elastic stresses are presented and compared. The methods are validated on a radially symmetric test problem by comparing with a finite difference solution of the classical equations of poroelasticity. Finally, two applications of the modeling framework to cell biology are provided: cellular blebbing and cell crawling. It is shown that in both examples, poroelastic effects are necessary to explain the relevant mechanics.
Finite cell method compared to h-version finite element method for elasto-plastic problems
Institute of Scientific and Technical Information of China (English)
A.ABEDIAN; J.PARVIZIAN; A.D USTER; E.RANK
2014-01-01
The finite cell method (FCM) combines the high-order finite element method (FEM) with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method (h-FEM). The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.
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.
Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method
Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.
2016-01-01
Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity where more and more complex flow problems can be tackled with this approach. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by a contra-rotating open rotor. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the methodologies of how to apply the immersed boundary method to this moving boundary problem, we will provide a detailed validation of the aeroacoustic analysis approach employing the Launch Ascent and Vehicle Aerodynamics (LAVA) solver. Two free-stream Mach numbers with M=0.2 and M=0.78 are considered in this analysis that are based on the nominally take-off and cruise flow conditions. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. Spectral analysis is used to determine the dominant wave propagation pattern in the acoustic near-field.
Zhang, Hao; Trias, F Xavier; Yu, Aibing; Tan, Yuanqiang; Oliva, Assensi
2015-01-01
In our recent work [H. Zhang, F.X. Trias, A. Oliva, D. Yang, Y. Tan, Y. Sheng. PIBM: Particulate immersed boundary method for fluid-particle interaction problems. Powder Technology. 272(2015), 1-13.], a particulate immersed boundary method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsible for the non-slip velocity and temperature boundary conditions at the particle surface, and the kinematics and trajectory of the solid particles were evaluated by the Discrete Element Method (DEM). Four case studies were implemented to demonstrate the capability of the current coupling scheme. Firstly, numerical simulation of natural convection in a two-dimensional square cavity with an isothermal concentric annulus was...
Simulation of a free-surface and seepage face using boundary-fitted coordinate system method
Lee, Kang-Kun; Leap, Darrell I.
1997-09-01
The boundary-fitted coordinate (BFC) system method is applied to simulate steady groundwater seepage with a free-surface and seepage face using the finite-difference method. The BFC system method eliminates the difficulty of fitting finite-difference grids to a changeable free-surface which is not known a priori but will be obtained as part of a solution. Also, grid generation with this approach is simpler than with the finite-element method. At each iterative sweep, the changeable free-surface becomes a part of the boundary-fitted grid lines, making boundary condition implementation easy and accurate. An example problem demonstrating the simulation procedure and numerical results compares very well with the analytical solution.
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.
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.
Fast multipole boundary element analysis of 2D viscoelastic composites with imperfect interfaces
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.
Solving wave equation with spectral methods and nonreflecting boundary conditions
Novák, J; Novak, Jerome; Bonazzola, Silvano
2002-01-01
A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics $(Y_l^m(\\theta, \\phi))$ for the angular dependence and of Chebyshev polynomials $T_n(x)$ for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius $R$ at which boundary conditions are imposed. Time derivatives are estimated using standard finite-differences second order schemes, which are chosen to be implicit to allow for (almost) any size of time-step. Emphasis is put on the implementation of absorbing boundary conditions that allow for the numerical boundary to be completely transparent to the physical wave. This is done using a multipolar expansion of an exact boundary condition for outgoing waves, which is truncated at some point. Using an auxiliary function, which is solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary conditi...
Brezzi, Franco; Hughes, T.J.R.; Suli, Endre
2001-01-01
We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.
Application of Natural Element Method in Numerical Simulation of Crack Propagation
Shanshan Gai; Gang Cheng; Dunfu Zhang; Wang Weidong
2013-01-01
The properties of interpolation of nodal data, ease of imposing essential boundary conditions, and the computational efficiency are some of the most important advantages of natural element method based on the non-Sibsonian interpolation over other meshless methods based on the moving least squares approximants. Accurate imposition of essential boundary conditions is accomplished directly by constructing vector of the displacement field by using non-Sibsonian interpolation method, which is bas...
Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case
Institute of Scientific and Technical Information of China (English)
BAI Yong-Qiang; LIU Zhen; PEI Ming; ZHENG Zhu-Jun
2003-01-01
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.
CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Dan-hui Hong
2005-01-01
In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optimal complexity.
Mixed finite element-finite volume methods
Zine Dine, Khadija; Achtaich, Naceur; Chagdali, Mohamed
2010-01-01
This paper is devoted to present a numerical methods for a model of incompressible and miscible flow in porous media. We analyze a numerical scheme combining a mixed finite element method (MFE) and finite volume scheme (FV) for solving a coupled system includes an elliptic equation (pressure and velocity) and a linear convection-diffusion equation (concentration). The (FV) scheme considered is "vertex centered" type semi implicit. We show that this scheme is $L^{\\infty...
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Efficient Matrix Product State Method for periodic boundary conditions
Pippan, Peter; White, Steven R.; Evertz, Hans Gerd
2008-01-01
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ ...
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
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
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...
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
2015-01-01
This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The authors are both mathematicians (pure and applied) and engineers, and bring together a large number of interesting ideas. The wide variety of topics treated in the contributions provides an excellent overview of current research into the theory and numerical solution of problems involving boundary and interior layers. .
Effective beam method for element concentrations
Energy Technology Data Exchange (ETDEWEB)
Tolhurst, Thomas; Barbi, Mauricio, E-mail: barbi@uregina.ca [University of Regina (Canada); Tokaryk, Tim [Royal Saskatchewan Museum (Canada)
2015-01-29
A method to evaluate chemical element concentrations in samples by generating an effective polychromatic beam using as initial input real monochromatic beam data is presented. There is a great diversity of research being conducted at synchrotron facilities around the world and a diverse set of beamlines to accommodate this research. Time is a precious commodity at synchrotron facilities; therefore, methods that can maximize the time spent collecting data are of value. At the same time the incident radiation spectrum, necessary for some research, may not be known on a given beamline. A preliminary presentation of a method applicable to X-ray fluorescence spectrocopic analyses that overcomes the lack of information about the incident beam spectrum that addresses both of these concerns is given here. The method is equally applicable for other X-ray sources so long as local conditions are considered. It relies on replacing the polychromatic spectrum in a standard fundamental parameters analysis with a set of effective monochromatic photon beams. A beam is associated with each element and can be described by an analytical function allowing extension to elements not included in the necessary calibration measurement(s)
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.
Payette, G. S.; Reddy, J. N.
2011-05-01
In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L2 norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier-Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.
A spectral boundary integral equation method for the 2D Helmholtz equation
International Nuclear Information System (INIS)
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the non-smoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the non-smoothness of the integral kernels in the spectral implementation. The present method is robust for a general smooth boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. Numerical examples of wave scattering are given in which the exponential accuracy of the present numerical method is demonstrated. 15 refs., 3 figs., 4 tabs
Multiphase Transformer Modelling using Finite Element Method
Directory of Open Access Journals (Sweden)
Nor Azizah Mohd Yusoff
2015-03-01
Full Text Available In the year of 1970 saw the starting invention of the five-phase motor as the milestone in advanced electric motor. Through the years, there are many researchers, which passionately worked towards developing for multiphase drive system. They developed a static transformation system to obtain a multiphase supply from the available three-phase supply. This idea gives an influence for further development in electric machines as an example; an efficient solution for bulk power transfer. This paper highlighted the detail descriptions that lead to five-phase supply with fixed voltage and frequency by using Finite-Element Method (FEM. Identifying of specification on a real transformer had been done before applied into software modeling. Therefore, Finite-Element Method provides clearly understandable in terms of visualize the geometry modeling, connection scheme and output waveform.
Immersed boundary-finite element model of fluid-structure interaction in the aortic root
Flamini, Vittoria; DeAnda, Abe; Griffith, Boyce E.
2016-04-01
It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin's immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.
Finite element methods for sea ice modeling
Lietaer, Olivier
2011-01-01
In order to study and understand the behavior of sea ice, numerical sea ice models have been developed since the early seventies and have traditionally been based on structured grids and finite difference schemes. This doctoral research is part of the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM) project whose objective is to bring to oceanography modern numerical techniques. The motivation for this thesis is therefore to investigate the potential of finite element methods and uns...
Widyatmanti, Wirastuti; Wicaksono, Ikhsan; Dinta Rahma Syam, Prima
2016-06-01
Dense vegetation that covers most landscapes in Indonesia becomes a common limitation in mapping the landforms in tropical region. This paper aims to examine the use of radar interferometry for landform mapping in tropical region; to examine the application of segmentation method to develop landform type boundaries; and to identify the topographic elements composition for each type of landform. Using Idrisi® and “eCognition ®” softwares, toposhape analysis, segmentation and multi-spectral classification were applied to identify the composition of topographic elements i.e. the types of land-cover from Landsat 8, elevation, slope, relief intensity and curvatures from SRTM (DEM). Visual interpretation on DEM and land-cover fusion imagery was conducted to derive basic control maps of landform and land-cover. The result shows that in segmentation method, shape and compactness levels are essential in obtaining land-cover, elevation, and slope class units to determine the most accurate class borders of each element. Despite a complex procedure applied in determining landform classification, the combination of topographic elements segmentation result presents a distinct border of each landform class. The comparison between landform maps derived from segmentation process and visual interpretation method demonstrates slight dissimilarities, meaning that multi-stage segmentation approach can improve and provide more effective digital landform mapping method in tropical region. Topographic elements on each type of landforms show distinctive composition key containing the percentage of each curvature elements per area unit. Supported by GIS programming and modeling in the future, this finding is significant in reducing effort in landform mapping using visual interpretation method for a very large coverage but in detail scale level.
Description to wear debris boundaries by radar graph fractal method
Institute of Scientific and Technical Information of China (English)
LIU HongTao; GE ShiRong
2007-01-01
In this paper, radar graph fractal method is introduced to describe wear debris boundaries.Research results show that it is a nice way to describe wear debris boundaries.Since the longest axis is selected as the first coordinate axis, its center point selected as the center point of the radar graph, and the coordinate value of wear debris boundary selected as the measure parameter, the limitations existing in Yard fractal measure method can be avoided.For any wear debris, its radar graph fractal dimension value is one and only, and as the wear debris shape changes from round to strip, the radar graph fractal dimension value also changes from low to high, showing strong uniqueness and independence.Due to the fact that the researched wear debris is gotten in different wear states, the results also prove that radar graph fractal dimension value is correlated with frictional pairs work condition and wear state.Radar graph fractal method is compared with Yard fractal measure methods, and results show that radar graph fractal dimension values gotten from different wear debris have enough value grads to avoid effect of errors, and provide higher sensitivity for wear debris shape.This paper also discusses the influencing factors for radar graph fractal method.With the increase of the decomposing degree value, the radar graph fractal dimension tends to keep stable at one certain value, showing the typical characteristic of the fractal theory.All this proves that radar graph fractal method is an effective description method for wear debris boundaries.
Incipient sediment transport for non-cohesive landforms by the discrete element method (DEM)
Bravo, R.; Ortiz Rossini, Pablo; Pérez Aparicio, José Luis
2014-01-01
We introduce a numerical method for incipient sediment transport past bedforms. The approach is based on the discrete element method (DEM) [1], simulating the micro-mechanics of the landform as an aggregate of rigid spheres interacting by contact and friction. A continuous finite element approximation [2] predicts the boundary shear stress field due to the fluid flow, resulting in drag and lift forces acting over the particles. Numerical experiments verify the method by reproducing results by...
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...... accuracy and computing resources. We also discuss preconditioning and parallelization of the multilevel fast multipole method, and propose higher-order basis functions for curvilinear quadrilaterals and volumetric basis functions for curvilinear hexahedra. The latter have the desirable property of...
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.
Combined radioactivation methods in determining trace elements
International Nuclear Information System (INIS)
The authors have devised a method of radioactivation analysis (RAA) for determining 32 elements by NAA, proton-activation analysis (PAA), and emission spectral analysis (ESA). Here they examine element distributions in certain plants by NAA, PAA, and DAA (deuteron activation analysis) as described elsewhere. The results are compared with those from activation analysis (AA) and ESA. The authors used five species of medicinal plant: Plantago Major L, Salvia officinalis L., Artemisia absinthium L., Alhagi Persarum, and Eremurus. They used referenced methods for preparing the samples, irradiating them in the reactor or cyclotron, and measuring the radioactivity. The γ-ray spectra for the activated samples from all the plants gave peaks representing 24Na, 42K, 56Mn, 140La, 82Br, 124Sb, 46Sc, 59Fe, 198Au, 139Ce, 153Sm, 86Rb, 65Zn, 60Co, and 147MSn. The concentrations of Fe, Sb, Sn, Zn, Rb, Co were determined when the irradiated samples have been kept for 10 days. To determine Ca, Fe, Ti, Cu, Zn, and Sr, ash disks were irradiated by proton and deuteron beams in a cyclotron, where they recorded radiation from the 48Sc, 56Co, 48V, 65Zn, 67Ga, 88Y. The conclusions are that all these plants and the parts of them accumulate the elements in different ways
Apparatus and method for assembling fuel elements
International Nuclear Information System (INIS)
A nuclear fuel element assembling method and apparatus is preferably operable under programmed control unit to receive fuel rods from storage, arrange them into axially aligned stacks of closely monitored length, and transfer the stacks of fuel rods to a loading device for insertion into longitudinal passages in the fuel elements. In order to handle large numbers of one or more classifications of fuel rods or other cylindrical parts, the assembling apparatus includes at least two feed troughs each formed by a pair of screw members with a movable table having a plurality of stacking troughs for alignment with the feed troughs and with a conveyor for delivering the stacks to the loading device, the fuel rods being moved along the stacking troughs upon a fluid cushion. 23 claims, 6 figures
Computational structural analysis and finite element methods
Kaveh, A
2014-01-01
Graph theory gained initial prominence in science and engineering through its strong links with matrix algebra and computer science. Moreover, the structure of the mathematics is well suited to that of engineering problems in analysis and design. The methods of analysis in this book employ matrix algebra, graph theory and meta-heuristic algorithms, which are ideally suited for modern computational mechanics. Efficient methods are presented that lead to highly sparse and banded structural matrices. The main features of the book include: application of graph theory for efficient analysis; extension of the force method to finite element analysis; application of meta-heuristic algorithms to ordering and decomposition (sparse matrix technology); efficient use of symmetry and regularity in the force method; and simultaneous analysis and design of structures.
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 Advanced Boundary Element Formulation for Acoustic Radiation and Scattering in Three Dimensions.
Soenarko, Benjamin
A computational method is presented for determining acoustic fields produced by arbitrary shaped three-dimensional bodies. The formulation includes both radiation and scattering problems. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the body are represented by second order shape functions within the local coordinate system. A general result for the surface velocity potential and the exterior field is derived. This result is applicable to non-smooth bodies, i.e. it includes the case where the surface may have a non-unique normal (e.g. at the edge of a cube). Test cases are shown involving spherical, cylindrical and cubical geometry for both radiation and scattering problems. The present formulation is also extended to include half-space problems in which the effect of the reflected wave from an infinite plane is taken into account. By selecting an appropriate Green's function, the surface integral over the plane is nullified; thus all the computational efforts can be performed only on the radiating or scattering body at issue and thereby greatly simplify the solution. A special formulation involving axisymmetric bodies and boundary conditions is also presented. For this special case, the surface integrals are reduced to line integrals and an integral over the angle of revolution. The integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using simple Gaussian quadrature formula. Since the rest of the integrals involve only line integrals along the generator of the body, any discretization scheme can be easily obtained to achieve a desired degree of accuracy in evaluating these integrals.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The behavior of rare earth element Ce in 2090 Al-Li alloys was studied by the method of low frequency internal friction.The results showed that rare earth element Ce can increase the activation energy of grain boundary and improve the grain boundary strength of alloys.Rare earth element Ce can decrease the tendency of softening of elastic modulus of 2090 Al-Li alloys after heat cycle and keep high elastic modulus of initial state.
Ma, Zhibo; Li, Mo; Roy, Sharmila; Liu, Kevin J; Romine, Matthew L; Lane, Derrick C; Patel, Sapna K; Cai, Haini N
2016-01-01
The three-dimensional (3D) organization of the eukaryotic genome is critical for its proper function. Evidence suggests that extensive chromatin loops form the building blocks of the genomic architecture, separating genes and gene clusters into distinct functional domains. These loops are anchored in part by a special type of DNA elements called chromatin boundary elements (CBEs). CBEs were originally found to insulate neighboring genes by blocking influences of transcriptional enhancers or the spread of silent chromatin. However, recent results show that chromatin loops can also play a positive role in gene regulation by looping out intervening DNA and “delivering” remote enhancers to gene promoters. In addition, studies from human and model organisms indicate that the configuration of chromatin loops, many of which are tethered by CBEs, is dynamically regulated during cell differentiation. In particular, a recent work by Li et al has shown that the SF1 boundary, located in the Drosophila Hox cluster, regulates local genes by tethering different subsets of chromatin loops: One subset enclose a neighboring gene ftz, limiting its access by the surrounding Scr enhancers and restrict the spread of repressive histones during early embryogenesis; and the other loops subdivide the Scr regulatory region into independent domains of enhancer accessibility. The enhancer-blocking activity of these CBE elements varies greatly in strength and tissue distribution. Further, tandem pairing of SF1 and SF2 facilitate the bypass of distal enhancers in transgenic flies, providing a mechanism for endogenous enhancers to circumvent genomic interruptions resulting from chromosomal rearrangement. This study demonstrates how a network of chromatin boundaries, centrally organized by SF1, can remodel the 3D genome to facilitate gene regulation during development.
Ma, Zhibo; Li, Mo; Roy, Sharmila; Liu, Kevin J; Romine, Matthew L; Lane, Derrick C; Patel, Sapna K; Cai, Haini N
2016-08-26
The three-dimensional (3D) organization of the eukaryotic genome is critical for its proper function. Evidence suggests that extensive chromatin loops form the building blocks of the genomic architecture, separating genes and gene clusters into distinct functional domains. These loops are anchored in part by a special type of DNA elements called chromatin boundary elements (CBEs). CBEs were originally found to insulate neighboring genes by blocking influences of transcriptional enhancers or the spread of silent chromatin. However, recent results show that chromatin loops can also play a positive role in gene regulation by looping out intervening DNA and "delivering" remote enhancers to gene promoters. In addition, studies from human and model organisms indicate that the configuration of chromatin loops, many of which are tethered by CBEs, is dynamically regulated during cell differentiation. In particular, a recent work by Li et al has shown that the SF1 boundary, located in the Drosophila Hox cluster, regulates local genes by tethering different subsets of chromatin loops: One subset enclose a neighboring gene ftz, limiting its access by the surrounding Scr enhancers and restrict the spread of repressive histones during early embryogenesis; and the other loops subdivide the Scr regulatory region into independent domains of enhancer accessibility. The enhancer-blocking activity of these CBE elements varies greatly in strength and tissue distribution. Further, tandem pairing of SF1 and SF2 facilitate the bypass of distal enhancers in transgenic flies, providing a mechanism for endogenous enhancers to circumvent genomic interruptions resulting from chromosomal rearrangement. This study demonstrates how a network of chromatin boundaries, centrally organized by SF1, can remodel the 3D genome to facilitate gene regulation during development. PMID:27621770
cuIBM -- A GPU-accelerated Immersed Boundary Method
Layton, Simon K; Barba, Lorena A
2011-01-01
A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single CPU core) which reflects the constraints of a bandwidth-dominated problem on the GPU. Nevertheless, GPUs offer the capacity to solve large problems on commodity hardware. This work includes validation and a convergence study of the GPU-accelerated IBM, and various optimizations.
A comparison of boundary correction methods for Strang splitting
Einkemmer, Lukas
2016-01-01
In this paper we consider splitting methods in the presence of non-homogeneous boundary conditions. In particular, we consider the corrections that have been described and analyzed in Einkemmer, Ostermann 2015 and Alonso-Mallo, Cano, Reguera 2016. The latter method is extended to the non-linear case, and a rigorous convergence analysis is provided. We perform numerical simulations for diffusion-reaction, advection-reaction, and dispersion-reaction equations in order to evaluate the relative performance of these two corrections. Furthermore, we introduce an extension of both methods to obtain order three locally and evaluate under what circumstances this is beneficial.
Calculation of Turbulent Boundary Layers Using the Dissipation Integral Method
Institute of Scientific and Technical Information of China (English)
MatthiasBuschmann
1999-01-01
This paper gives an introduction into the dissipation integral method.The general integral equations for the three-dimensional case are derved.It is found that for a practical calculation algorithm the integral monentum equation and the integral energy equation are msot useful.Using Two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown.Test cases for two-and three-dimensional boundary layers are analysed and discussed.The paper concludes with a discussion of the advantages and limits of dissipation integral methods.
Numerical analysis of Weyl's method for integrating boundary layer equations
Najfeld, I.
1982-01-01
A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.
Institute of Scientific and Technical Information of China (English)
Lie-heng Wang
2000-01-01
In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h1-2) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while I.Hlavacek et. al. obtained the error bound O(h ) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]).
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 ...
Effective beam method for element concentrations.
Tolhurst, Thomas; Barbi, Mauricio; Tokaryk, Tim
2015-03-01
There is a great diversity of research being conducted at synchrotron facilities around the world and a diverse set of beamlines to accommodate this research. Time is a precious commodity at synchrotron facilities; therefore, methods that can maximize the time spent collecting data are of value. At the same time the incident radiation spectrum, necessary for some research, may not be known on a given beamline. A preliminary presentation of a method applicable to X-ray fluorescence spectrocopic analyses that overcomes the lack of information about the incident beam spectrum that addresses both of these concerns is given here. The method is equally applicable for other X-ray sources so long as local conditions are considered. It relies on replacing the polychromatic spectrum in a standard fundamental parameters analysis with a set of effective monochromatic photon beams. A beam is associated with each element and can be described by an analytical function allowing extension to elements not included in the necessary calibration measurement(s). PMID:25723941
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
An element-free Galerkin method for ground penetrating radar numerical simulation
Institute of Scientific and Technical Information of China (English)
冯德山; 郭荣文; 王洪华
2015-01-01
An element-free Galerkin method (EFGM) is used to solve the two-dimensional (2D) ground penetrating radar (GPR) modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method (FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.
A Coupling Model of the Discontinuous Deformation Analysis Method and the Finite Element Method
Institute of Scientific and Technical Information of China (English)
ZHANG Ming; YANG Heqing; LI Zhongkui
2005-01-01
Neither the finite element method nor the discontinuous deformation analysis method can solve problems very well in rock mechanics and engineering due to their extreme complexities. A coupling method combining both of them should have wider applicability. Such a model coupling the discontinuous deformation analysis method and the finite element method is proposed in this paper. In the model, so-called line blocks are introduced to deal with the interaction via the common interfacial boundary of the discontinuous deformation analysis domain with the finite element domain. The interfacial conditions during the incremental iteration process are satisfied by means of the line blocks. The requirement of gradual small displacements in each incremental step of this coupling method is met through a displacement control procedure. The model is simple in concept and is easy in numerical implementation. A numerical example is given. The displacement obtained by the coupling method agrees well with those obtained by the finite element method, which shows the rationality of this model and the validity of the implementation scheme.
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.
Energy Technology Data Exchange (ETDEWEB)
Steibler, P.
2000-07-01
The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet
An approximate method to acoustic radiation problems: element radiation superposition method
Institute of Scientific and Technical Information of China (English)
wANG Bin; TANG weilin; FAN Jun
2008-01-01
An approximate method is brought forward to predict the acoustic pressure based on the surface velocity.It is named Element Radiation Superposition Method(ERSM).The study finds that each element in Acoustic Transfer Vector(ATV)equals the acoustic pressure radiated by the corresponding surface element vibrating in unit velocity and other surface elements keep still.that is the acoustic pressure radiated by the corresponding baffled pistonvibrating in unit velocity.So,it utilizes the acoustic pressure radiated by a baffled piston to establish the transfer relationship between the surfaEe velocity and the acoustic pressure.The total acoustic pressure is obtained through summing up the products of the surface velocity and the transfer quantity.It adopts the regular baffle to fit the actual baffle in order to calculate the acoustic pressure radiated by the baffled piston.This approximate method has larger advantage in calculating speed and memory space than Boundary Element Method.Numerical simulations show that this approximate method is reasonable and feasible.
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
Zeng, X.; Scovazzi, G.
2016-06-01
We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce. In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework. The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.
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.
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.
Using boundary methods to compute the Casimir energy
Lombardo, F C; Villar, P I
2010-01-01
We discuss new approaches to compute numerically the Casimir interaction energy for waveguides of arbitrary section, based on the boundary methods traditionally used to compute eigenvalues of the 2D Helmholtz equation. These methods are combined with the Cauchy's theorem in order to perform the sum over modes. As an illustration, we describe a point-matching technique to compute the vacuum energy for waveguides containing media with different permittivities. We present explicit numerical evaluations for perfect conducting surfaces in the case of concentric corrugated cylinders and a circular cylinder inside an elliptic one.
A class of hybrid finite element methods for electromagnetics: A review
Volakis, J. L.; Chatterjee, A.; Gong, J.
1993-01-01
Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.
Cooper, Christopher D; Barba, L A
2013-01-01
The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2%, then the simpler, single-surface model can be used. When calculating b...
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.
Adaptive Finite Element Methods for Continuum Damage Modeling
Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.
1995-01-01
The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.
Bugeanu, Monica; Di Remigio, Roberto; Mozgawa, Krzysztof; Reine, Simen Sommerfelt; Harbrecht, Helmut; Frediani, Luca
2015-12-21
The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the integral equation formulation (IEF) of the polarizable continuum model (PCM), generally lead to working equations which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the IEFPCM with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module PCMSolver and interfaced with LSDalton, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any QC software with minimal effort. PMID:26256401
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.
Hydrodynamic ram modeling with the immersed boundary method
Energy Technology Data Exchange (ETDEWEB)
Lewis, M.W.; Kashiwa, B.A.; Rauenzahn, R.M.
1998-03-01
The authors have modeled a hydrodynamic ram experiment conducted at Wright-Patterson Air Force Base. In the experiment, a projectile traveling at 200 ft/sec impacted and penetrated a simulated airplane wing containing water. The structure consisted of composite panels with stiffeners and rivets, and an aluminum panel. The test included instrumentation to measure strains, accelerations, and pressures. The technique used for modeling this experiment was a multifluid compressible finite volume approach. The solid fields, namely the projectile and the plates which comprised the structure, were represented by a set of discrete, Lagrangian-frame, mass points. These mass points were followed throughout the computation. The contribution of the stress state at each mass point was applied on the grid to determine the stress divergence contribution to the equations of motion and resulting grid based accelerations. This approach has been defined as the immersed boundary method. The immersed boundary method allows the modeling of fluid-structure interaction problems involving material failure. The authors implemented a plate theory to allow the representation of each plate by a surface of mass points. This theory includes bending terms and transverse shear. Arbitrary constitutive models may be used for each plate. Here they describe the immersed boundary method as they have implemented. They then describe the plate theory and its implementation. They discuss the hydrodynamic ram experiment and describe how they modeled it. They compare computed results with test data. They finally conclude with a discussion of benefits and difficulties associated with this modeling approach and possible improvement to it.
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.
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
Boundary integral equation method for added mass in arrays of cylinders
International Nuclear Information System (INIS)
The dynamic behavior of a group of cylinders in fluid, such as heat exchanger tubes and nuclear fuel assemblies, is strongly influenced by the surrounding fluid. Although, the added mass of such clusters of cylinders has been studied by many researchers with various analytical methods and numerical methods, no attempt has been made so far to analyze these problems by the Boundary Integral Equation Method (BIEM). This paper presents a BIEM model simulating the added mass arising when clusters of cylinders vibrate in an inviscid and incompressible fluid. In this model, perturbed fluid pressure is described by a two- dimensional Laplace equation. The primary advantage of this approach compared with other numerical methods, e.g., the finite element method (FEM), is that the integration and discretization of the model are only needed on boundary rather than in whole domain. Therefore, the proposed approach is much more economical than the finite element method. Various numerical examples are subsequently presented in this paper to illustrate the methodology and to demonstrate its accuracy
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.
A NOVEL BOUNDARY INTEGRAL EQUATION METHOD FOR LINEAR ELASTICITY--NATURAL BOUNDARY INTEGRAL EQUATION
Institute of Scientific and Technical Information of China (English)
Niu Zhongrong; Wang Xiuxi; Zhou Huanlin; Zhang Chenli
2001-01-01
The boundary integral equation (BIE) of displacement derivatives is put at a disadvantage for the difficulty involved in the evaluation of the hypersingular integrals. In this paper, the operators δij and εij are used to act on the derivative BIE. The boundary displacements, tractions and displacement derivatives are transformed into a set of new boundary tensors as boundary variables. A new BIE formulation termed natural boundary integral equation (NBIE) is obtained. The NBIE is applied to solving two-dimensional elasticity problems. In the NBIE only the strongly singular integrals are contained. The Cauchy principal value integrals occurring in the NBIE are evaluated. A combination of the NBIE and displacement BIE can be used to directly calculate the boundary stresses. The numerical results of several examples demonstrate the accuracy of the NBIE.
Nuclear analytical methods for platinum group elements
International Nuclear Information System (INIS)
Platinum group elements (PGE) are of special interest for analytical research due to their economic importance like chemical peculiarities as catalysts, medical applications as anticancer drugs, and possible environmental detrimental impact as exhaust from automobile catalyzers. Natural levels of PGE are so low in concentration that most of the current analytical techniques approach their limit of detection capacity. In addition, Ru, Rh, Pd, Re, Os, Ir, and Pt analyses still constitute a challenge in accuracy and precision of quantification in natural matrices. Nuclear analytical techniques, such as neutron activation analysis, X ray fluorescence, or proton-induced X ray emission (PIXE), which are generally considered as reference methods for many analytical problems, are useful as well. However, due to methodological restrictions, they can, in most cases, only be applied after pre-concentration and under special irradiation conditions. This report was prepared following a coordinated research project and a consultants meeting addressing the subject from different viewpoints. The experts involved suggested to discuss the issue according to the (1) application, hence, the concentration levels encountered, and (2) method applied for analysis. Each of the different fields of application needs special consideration for sample preparation, PGE pre-concentration, and determination. Additionally, each analytical method requires special attention regarding the sensitivity and sample type. Quality assurance/quality control aspects are considered towards the end of the report. It is intended to provide the reader of this publication with state-of-the-art information on the various aspects of PGE analysis and to advise which technique might be most suitable for a particular analytical problem related to platinum group elements. In particular, many case studies described in detail from the authors' laboratory experience might help to decide which way to go. As in many cases
Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow
Institute of Scientific and Technical Information of China (English)
Xiang Bo; Mi Xiao; Ji Changming; Luo Qingsong
2007-01-01
In order to improve the finite analytic method's adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor's computed result, the result of this method is more satisfactory.
Stability Estimates for ℎ- Spectral Element Methods for Elliptic Problems
Indian Academy of Sciences (India)
Pravir Dutt; Satyendra Tomar; B V Rathish Kumar
2002-11-01
In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which minimizes a weighted squared norm of the residuals in the partial differential equation and a fractional Sobolev norm of the residuals in the boundary conditions and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in an appropriate fractional Sobolev norm, to the functional being minimized. Since the second derivatives of the actual solution are not square integrable in a neighborhood of the corners we have to multiply the residuals in the partial differential equation by an appropriate power of $r_k$, where $r_k$ measures the distance between the point and the vertex $A_k$ in a sectoral neighborhood of each of these vertices. In each of these sectoral neighborhoods we use a local coordinate system $(_k, _k)$ where $_k = ln r_k$ and $(r_k, _k)$ are polar coordinates with origin at $A_k$, as first proposed by Kondratiev. We then derive differentiability estimates with respect to these new variables and a stability estimate for the functional we minimize. In [6] we will show that we can use the stability estimate to obtain parallel preconditioners and error estimates for the solution of the minimization problem which are nearly optimal as the condition number of the preconditioned system is polylogarithmic in , the number of processors and the number of degrees of freedom in each variable on each element. Moreover if the data is analytic then the error is exponentially small in .
Dutt, Pravir; Tomar, Satyendra
2003-01-01
In this paper we show that the h-p spectral element method developed in [3,8,9] applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska-Brezzi inf-sup conditions are satisfied. We establish basic stability estimates for a no
Mathematical analysis of EEP method for one-dimensional finite element postprocessing
Institute of Scientific and Technical Information of China (English)
ZHAO Qing-hua; ZHOU Shu-zi; ZHU Qi-ding
2007-01-01
For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan's element energy projection (EEP) method has the accuracy O(hmin{2k,k+4}).The theoretical analysis coincides the reported numerical results.
Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria
Figueroa-López, R. N.; Lozada-Cruz, G.
2016-11-01
In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds.
Discrete Finite Elements Method in space-time domain for parabolic linear problems
Directory of Open Access Journals (Sweden)
Maria Morandi Cecchi
1991-11-01
Full Text Available Theory, error-bound and applications of Discrete Finite Element Method is given to solve a class of linear one and two-dimensional parabolic problems on Sobolev space-time domains, with non-homogeneous discontinuous initial data and general boundary conditions.
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....
Simulation of wind effects on tall structures by finite element method
Ebrahimi, Masood
2016-06-01
In the present study finite element method is used to predict the wind forces on a tall structure. The governing equations of mass and momentum with boundary conditions are solved. The κ- ɛ turbulence model is utilized to calculate the turbulence viscosity. The results are independent from the generated mesh. The numerical results are validated with American Society of Civil Engineering standards.
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....
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The present study aims at developing a new method-Random M icrostructure Finite Element Method (RMFEM)for the effective properties of composite materials . In this method, a random microstructure model is used to simulate the microstructure of the real composite materials. The physical fields in such a randm microstructure model under specified boundary and initial conditions are analyzed by finite element method. The effective properties of composite materials can be obtained from the analysis results. As verification, some effective properties of composite materials, such as elastic module,thermal expansion coefficient, thermal conductivity and elastoplastic properties, are investigated by random microstructure finite element method. The numerical results are given together with the experimental data. It i- revealed that the random microstructure finite element method is a very valid method for the determination of the effective properties of composite materials.
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
A Characteristic Non-Reflecting Boundary Treatment in Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
KIM Dehee; KIM Hyung Min; JHON Myung S.; VINAY Ⅲ Stephen J.; BUCHANAN John
2008-01-01
In lattice Boltzmann methods, disturbances develop at the initial stages of the simulation, the decay characteristics depend mainly on boundary treatment methods; open boundary conditions such as equilibrium and bounce-back schemes potentially generate uncontrollable disturbances. Excessive disturbances originate from non-physical reflecting waves at boundaries. Characteristic boundary conditions utilizing the signs of waves at boundaries which suppress these reflecting waves, as well as their implementation in the lattice Boltzmann method, are introduced herein. The performance of our novel boundary treatment method to effectively suppress excessive disturbances is verified by three different numerical experiments.
Enhanced patch test of finite element methods
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.
A method for making an alkaline element
Energy Technology Data Exchange (ETDEWEB)
Obi, F.; Takada, K.
1983-05-11
A mixture of asphalt with polybutene is applied to the contacting surfaces of the body top and the hermetically sealing stuffing. After assembly the element is heated to a temperature which exceeds the softening point of the mixture. The edge of the body is rolled in. The element has high reliability.
Robbins, Joshua; Voth, Thomas E.
2007-12-01
The eXtended Finite Element Method (X-FEM) is a finite-element based discretization technique developed originally to model dynamic crack propagation [1]. Since that time the method has been used for modeling physics ranging from static meso-scale material failure to dendrite growth. Here we adapt the recent advances of Vitali and Benson [2] and Song et al. [3] to model dynamic loading of a polycrystalline material. We use demonstration problems to examine the method's efficacy for modeling the dynamic response of polycrystalline materials at the meso-scale. Specifically, we use the X-FEM to model grain boundaries. This approach allows us to i) eliminate ad-hoc mixture rules for multi-material elements and ii) avoid explicitly meshing grain boundaries.
Directory of Open Access Journals (Sweden)
Javier A. Dottori
2015-01-01
Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.
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.
Boundary integral method applied in chaotic quantum billiards
Li, B; Li, Baowen; Robnik, Marko
1995-01-01
The boundary integral method (BIM) is a formulation of Helmholtz equation in the form of an integral equation suitable for numerical discretization to solve the quantum billiard. This paper is an extensive numerical survey of BIM in a variety of quantum billiards, integrable (circle, rectangle), KAM systems (Robnik billiard) and fully chaotic (ergodic, such as stadium, Sinai billiard and cardioid billiard). On the theoretical side we point out some serious flaws in the derivation of BIM in the literature and show how the final formula (which nevertheless was correct) should be derived in a sound way and we also argue that a simple minded application of BIM in nonconvex geometries presents serious difficulties or even fails. On the numerical side we have analyzed the scaling of the averaged absolute value of the systematic error \\Delta E of the eigenenergy in units of mean level spacing with the density of discretization (b = number of numerical nodes on the boundary within one de Broglie wavelength), and we f...
De Corato, M.; Slot, J. J. M.; Hütter, M.; D'Avino, G.; Maffettone, P. L.; Hulsen, M. A.
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.
Roncal, Julissa; Guyot, Romain; Hamon, Perla; Crouzillat, Dominique; Rigoreau, Michel; Konan, Olivier N'Guessan; Rakotomalala, Jean-Jacques; Nowak, Michael D; Davis, Aaron P; de Kochko, Alexandre
2016-02-01
The completion of the genome assembly for the economically important coffee plant Coffea canephora (Rubiaceae) has allowed the use of bioinformatic tools to identify and characterize a diverse array of transposable elements (TEs), which can be used in evolutionary studies of the genus. An overview of the copy number and location within the C. canephora genome of four TEs is presented. These are tested for their use as molecular markers to unravel the evolutionary history of the Millotii Complex, a group of six wild coffee (Coffea) species native to Madagascar. Two TEs from the Gypsy superfamily successfully recovered some species boundaries and geographic structure among samples, whereas a TE from the Copia superfamily did not. Notably, species occurring in evergreen moist forests of eastern and southeastern Madagascar were divergent with respect to species in other habitats and regions. Our results suggest that the peak of transpositional activity of the Gypsy and Copia TEs occurred, respectively, before and after the speciation events of the tested Madagascan species. We conclude that the utilization of active TEs has considerable potential to unravel the evolutionary history and delimitation of closely related Coffea species. However, the selection of TE needs to be experimentally tested, since each element has its own evolutionary history. Different TEs with similar copy number in a given species can render different dendrograms; thus copy number is not a good selection criterion to attain phylogenetic resolution. PMID:26231981
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.
Simultaneous heat and moisture transfer in porous elements: transfer function method
International Nuclear Information System (INIS)
The presence of moisture in a porous element may strongly affect the transfer of heat through this element due to the processes which occur associated with the phase changes at the boundary surfaces and internally in the wall body. In addition, the structural properties of the element may also be meaningfully affected. The formulation of mathematical models for the simultaneous heat and mass transfer in porous elements results in a pair of nonlinear coupled equations for the temperature and moisture content distributions, in the material. It is supposed, in this work, that the actual variation of the properties of the porous medium is small in the range of variables which describe the specific problem to be analyzed. This enables us to work with linearized equations, making possible the use of linear solution methods. In this context, the present work deals with a linear procedure for the solution of simultaneous heat and moisture transfer problems in porous elements, sujected to arbitrary boundary conditions. This results in a linear relation between the heat and mass flux densities through the boundary surfaces of the elements and their associated potentials. It is shown that the model is consistent in asymptotical limiting cases; the model is then used for analyzing the drying process of a porous element, subjected to ambient actual conditions. (Author)
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
An adaptive version of immersed boundary method for simulating flows with complex stationary and moving boundaries is presented.The method employs a ghost-cell methodology which allows for a sharp representation of the immersed boundary.To simplify the implementation of the methodology,a volume-of-fluid method is introduced to identify the immersed boundary.In addition,the domain is spatially discretized using a tree-based discretization which is relatively simple to implement a fully flexible adaptive refinement strategy.Finally,the methodology is validated by comparing it with numerical and experimental results on three cases:(1) the flow passing a circular cylinder at Re=40 and Re=100,(2) a periodic oscillation of a circular cylinder in fluid at rest and(3) the self-propelled fish-like swimming at Re=6400.
Method and system for processing optical elements using magnetorheological finishing
Menapace, Joseph Arthur; Schaffers, Kathleen Irene; Bayramian, Andrew James; Molander, William A
2012-09-18
A method of finishing an optical element includes mounting the optical element in an optical mount having a plurality of fiducials overlapping with the optical element and obtaining a first metrology map for the optical element and the plurality of fiducials. The method also includes obtaining a second metrology map for the optical element without the plurality of fiducials, forming a difference map between the first metrology map and the second metrology map, and aligning the first metrology map and the second metrology map. The method further includes placing mathematical fiducials onto the second metrology map using the difference map to form a third metrology map and associating the third metrology map to the optical element. Moreover, the method includes mounting the optical element in the fixture in an MRF tool, positioning the optical element in the fixture; removing the plurality of fiducials, and finishing the optical element.
Indian Academy of Sciences (India)
Pravir Dutt; Satyendra Tomar
2003-11-01
In this paper we show that the ℎ- spectral element method developed in [3,8,9] applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska–Brezzi inf-sup conditions are satisfied. We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are continuous only at the vertices of the elements. We obtain a stability estimate when the spectral element functions vanish at the vertices of the elements, which is needed for parallelizing the numerical scheme. Finally, we indicate how the mesh refinement strategy and choice of polynomial degree depends on the regularity of the coefficients of the differential operator, smoothness of the sides of the polygon and the regularity of the data to obtain the maximum accuracy achievable.
Finite element method analysis of elastic wave propagation in 3 dimensional structure
International Nuclear Information System (INIS)
It is known to be very complicated to obtain an efficient solution of elastic wave propagation in a three dimensional structure. In this paper the finite element method has been implemented to evaluate the displacement waveform for elastic wave by modeling for some interacting the three dimensional structure. In this experiment meshing method, time increasement, damping factor, boundary condition and loading condition has been discussed specially. Our FEM results are agreed with the wave form Laser Interferometer Displacement Sensor and the Ray Tracing method simulation. from these results the applicability of finite element method was illustrated.
Institute of Scientific and Technical Information of China (English)
Chen Li; Ma He-Ping; Cheng Yu-Min
2013-01-01
In this paper,the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems.The CVRKP-FE method not only conveniently imposes the essential boundary conditions,but also exploits the advantages of the individual methods while avoiding their disadvantages,then the computational efficiency is higher.A hybrid approximation function is applied to combine the CVRKP method with the FE method,and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme.The corresponding formulations of the CVRKP-FE method are presented in detail.Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.
Institute of Scientific and Technical Information of China (English)
Si YUAN; Yan DU; Qin-yan XING; Kang-sheng YE
2014-01-01
The element energy projection (EEP) method for computation of super-convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton’s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re-sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation (ODE) of second-order as the model problem, this paper describes the related fundamental idea, the imple-mentation strategy, and the computational algorithm. Representative numerical exam-ples are given to show the eﬃciency, stability, versatility, and reliability of the proposed approach.
A method for making a dry element
Energy Technology Data Exchange (ETDEWEB)
Abe, T.; Isikhara, K.; Kimura, T.; Momose, K.; Sakata, Y.
1983-08-11
The agglomerate is coated along the lateral surface by a separator and is enclosed in a zinc cylinder which serves as the anode. A separating plate is installed in the upper part of the agglomerate between the agglomerate and the anode. A current outlead is attached to the anode. The element is inserted into a body, pressing the plate into the agglomerate with a punch which has a recess. A guide cylinder is used for precise installation of the element. The space between the plate and the body in the upper part of the element is filled with wax or another substance. Short circuiting (KZ) between the current outlead and the agglomerate is prevented in the element.
Bhardwaj, Rajneesh; Mittal, Rajat
2011-11-01
The modeling of complex biological phenomena such as cardiac mechanics is challenging. It involves complex three dimensional geometries, moving structure boundaries inside the fluid domain and large flow-induced deformations of the structure. We present a fluid-structure interaction solver (FSI) which couples a sharp-interface immersed boundary method for flow simulation with a powerful finite-element based structure dynamics solver. An implicit partitioned (or segregated) approach is implemented to ensure the stability of the solver. We validate the FSI solver with published benchmark for a configuration which involves a thin elastic plate attached to a rigid cylinder. The frequency and amplitude of the oscillations of the plate are in good agreement with published results and non-linear dynamics of the plate and its coupling with the flow field are discussed. The FSI solver is used to understand left-ventricular hemodynamics and flow-induced dynamics of mitral leaflets during early diastolic filling and results from this study are presented.
Goyal, M.; Bhargava, R.
2014-05-01
This paper deals with the double-diffusive boundary layer flow of non-Newtonian nanofluid over a stretching sheet. In this model, where binary nanofluid is used, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The variational finite element method (FEM) is used to solve these ordinary differential equations. We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, modified Dufour number, viscoelastic parameter, Prandtl number, regular Lewis number, Dufour Lewis number, and nanofluid Lewis number on the flow field and heat transfer characteristics. Graphical display of the numerical examine are performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, reduced Nusselt, reduced Sherwood and reduced nanofluid Sherwood number distributions. The present study has many applications in coating and suspensions, movement of biological fluids, cooling of metallic plate, melt-spinning, heat exchangers technology, and oceanography.
Directory of Open Access Journals (Sweden)
Wei Li
2012-01-01
Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.
Elgeti, Stefanie
2015-01-01
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled with a domain deformation approach. This work reviews five of those approaches: interface tracking using a boundary-conforming mesh and, in the interface capturing context, the level-set method, the volume-of-fluid method, particle methods, as well as the phase-field method. The history of each method is presented in combination with the most recent developments in the field. Particularly, the topics of extended finite elements (XFEM) and NURBS-based methods, such as Isogeometric Analysis (IGA), are addressed. For illustration purposes, two applications have been chosen: two-phase flow involving drops or bubbles and sloshing tanks. The challenges of these applications, such as the geometrically correct representation of the free surface or the incorporation of surface tension ...
Novel high-performance element in the electromagnetic finite-element method--node-edge element
Institute of Scientific and Technical Information of China (English)
Sheng Xinqing; Peng Zhen
2008-01-01
It is known in the computational electromagnetics (CEM) that the node element has a relative well-conditioned matrix,but suffers from the spurious solution problem; whereas the edge element has no spurious solutions,but usually produces an ill-conditioned matrix.Particularly,when the mesh is over dense,the iterative solution of the matrix equation from edge element converges very slowly.Based on the node element and edge element,a node-edge element is presented,which has no spurious solutions and better-conditioned matrix.Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
Institute of Scientific and Technical Information of China (English)
Yun-qing Huang; Shi Shu; Xi-jun Yu
2006-01-01
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
International Nuclear Information System (INIS)
Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- Abstract: A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves
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.
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.
等参谱元方法的研究%RESEARCH OF AN ISOPARAMETRIC SPECTRAL ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
陈雪江; 秦国良; 徐忠
2003-01-01
An isoparametric spectral element method that combines the idea of the isopara-metric element in finite element methods with spectral element methods is pro-posed. The computational domain is broken up into curvilinear quadrangular ele-ments to approach boundaries more specifically and solve the differential equation in complex geometry. By this means both the Helmholtz equations with rect-angular geometry and the Poisson's equations with annular geometry those have analytical solutions are solved. The predicted results are in excellent agreement with the analytical solutions.
Method for inspecting nuclear reactor fuel elements
International Nuclear Information System (INIS)
A technique for disassembling a nuclear reactor fuel element without destroying the individual fuel pins and other structural components from which the element is assembled is described. A traveling bridge and trolley span a water-filled spent fuel storage pool and support a strongback. The strongback is under water and provides a working surface on which the spent fuel element is placed for inspection and for the manipulation that is associated with disassembly and assembly. To remove, in a non-destructive manner, the grids that hold the fuel pins in the proper relative positions within the element, bars are inserted through apertures in the grids with the aid of special tools. These bars are rotated to flex the adjacent grid walls and, in this way relax the physical engagement between protruding portions of the grid walls and the associated fuel pins. With the grid structure so flexed to relax the physical grip on the individual fuel pins, these pins can be withdrawn for inspection or replacement as necessary without imposing a need to destroy fuel element components
Margolis, S. V.; Doehne, E. F.
1988-01-01
Trace element and stable isotope analyses were performed on a series of sediment samples crossing the Cretaceous-Tertiary (K-T) boundary from critical sections at Aumaya and Sopelano, Spain. The aim is to possibly distinguish extraterrestrial vs. volcanic or authigenic concentration of platinum group and other elements in K-T boundary transitional sediments. These sediments also have been shown to contain evidence for step-wise extinction of several groups of marine invertebrates, associated with negative oxygen and carbon isotope excursions occurring during the last million years of the Cretaceous. These isotope excursions have been interpreted to indicate major changes in ocean thermal regime, circulation, and ecosystems that may be related to multiple events during latest Cretaceous time. Results to date on the petrographic and geochemical analyses of the Late Cretaceous and Early Paleocene sediments indicate that diagenesis has obviously affected the trace element geochemistry and stable isotope compositions at Zumaya. Mineralogical and geochemical analysis of K-T boundary sediments at Zumaya suggest that a substantial fraction of anomalous trace elements in the boundary marl are present in specific mineral phases. Platinum and nickel grains perhaps represent the first direct evidence of siderophile-rich minerals at the boundary. The presence of spinels and Ni-rich particles as inclusions in aluminosilicate spherules from Zumaya suggests an original, non-diagenetic origin for the spherules. Similar spherules from southern Spain (Caravaca), show a strong marine authigenic overprint. This research represents a new approach in trying to directly identify the sedimentary mineral components that are responsible for the trace element concentrations associated with the K-T boundary.
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.
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...
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...
Finite volume element method for analysis of unsteady reaction-diffusion problems
Institute of Scientific and Technical Information of China (English)
Sutthisak Phongthanapanich; Pramote Dechaumphai
2009-01-01
A finite volume element method is developed for analyzing unsteady scalar reaction--diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction--diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the highgradient boundary layers.
Hydraulic fracturing with distinct element method
Pruiksma, J.P.; Bezuijen, A.
2002-01-01
In this report, hydraulic fracturing is investigated using the distinct element code PFC2D from Itasca. Special routines were written to be able to model hydraulic fracturing. These include adding fluid flow to PFC2D and updating the fluid flow domains when fractures appear. A brief description of t
A review of flexibility-based finite element method for beam-column elements
Institute of Scientific and Technical Information of China (English)
LI Shuang; ZHAI Changhai; XIE Lili
2009-01-01
For material nonlinear problem, elements derived with the flexibility-based method are more accurate than classical elements derived with the stiffness-based method. A review of the current state of the art of the flexibility-based finite element method is provided to enhance the robustness of structure analysis. The research on beam-column elements is the mainstream in the research on flexibility-based finite element method at present. The original development of flexibility-based finite element method is reviewed, and the further development of this method is then presented in several specific aspects, such as geometrically nonlinear analysis and dynamic analysis. The further research needed to be carried out in the future is finally discussed.
Cai, Jian; Modest, Michael F.
2016-01-01
In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that present the symmetry conditions. In Photon Monte Carlo methods, this is achieved by imposing specular reflective boundary conditions for the radiative intensity. In this work, a similar specular reflective boundary condition is developed for Discrete Ordinate Methods. The effectiveness of the new boundary condition is demonstrated by multiple numerical examples including plane symmetry and axisymmetry.
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...
Analysis of bender element test interpretation using the discrete element method
O’Donovan, J.; O’Sullivan, C.; Marketos, G.; Muir Wood, D.
2015-01-01
While bender element testing is now well-established as a laboratory technique to determine soil stiffness, a robust technique to interpret the data remains elusive. A discrete element method (DEM) model of a face-centred cubic packing of uniform spheres was created to simulate bender element tests
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Uranus, H.P.; Hoekstra, H.J.W.M.
2004-01-01
A finite-element-based vectorial optical mode solver is used to analyze microstructured optical waveguides. By employing 1st-order Bayliss-Gunzburger-Turkel-like transparent boundary conditions, both the real and imaginary part of the modal indices can be calculated in a relatively small computation
Cunefare, K. A.; Koopmann, G. H.
1991-01-01
This paper presents the theoretical development of an approach to active noise control (ANC) applicable to three-dimensional radiators. The active noise control technique, termed ANC Optimization Analysis, is based on minimizing the total radiated power by adding secondary acoustic sources on the primary noise source. ANC Optimization Analysis determines the optimum magnitude and phase at which to drive the secondary control sources in order to achieve the best possible reduction in the total radiated power from the noise source/control source combination. For example, ANC Optimization Analysis predicts a 20 dB reduction in the total power radiated from a sphere of radius at a dimensionless wavenumber ka of 0.125, for a single control source representing 2.5 percent of the total area of the sphere. ANC Optimization Analysis is based on a boundary element formulation of the Helmholtz Integral Equation, and thus, the optimization analysis applies to a single frequency, while multiple frequencies can be treated through repeated analyses.
Wenquan Wang; Rui Yin; Dongwei Hao; Yan Yan
2014-01-01
A self-propelled swimming fish model is established, which can reflect the interaction between fish movement, internal force generated by muscle contraction, and the external force provided by fluid. Using finite element immersed boundary method combined with traditional feedback force method, the self-propelled swimming fish is numerically simulated. Firstly, a self-induced vibration of a cantilever beam immersed in a fluid is one of the benchmarks of fluid-structure interaction, which is us...
Institute of Scientific and Technical Information of China (English)
S.E.SADIQUE; S.; RAMAKRISHNA; S.BASRI; S.M.SAPUAN; M.M.HMEGATAHMED
2001-01-01
The contact characteristics of rigid cylinders lubricated by Newtonian liquids are inves-tigated in this paper using hard elastohydrodynamic lubrication (EHL) theory. Numerical modelingis formulated for the coupled set of generalized pressure and plane strain elasticity equations for afinite plane model and a circular representation of the junction under a pure hard rolling line con-tact using boundary element method (BEM). Also a numerical routine is developed to compute filmthickness and pressure profiles and the results are evaluated for a range of possible dimen-sionless parameters such as speed and load. The hydrodynamic equation is also transformed intoa form of boundary integral equation, which is solved by Simpson’s rule. The elasticity equationwith boundary conditions was solved by constant and quadratic elements based on an iterativeprocedure by assuming an initial film thickness. From the comparative study between the presentNewtonian model and the previously published results proved to be very effective and efficient andhigh precision is easily achieved for such rolling elements as well. The computed results areshown to be amenable to standard boundary element formulation of EHL problem in the contactregion and show that speed and load have influential effects on the lubricating film shape.
Segregation of solute elements at grain boundaries in an ultrafine grained Al-Zn-Mg-Cu alloy
International Nuclear Information System (INIS)
The solute segregation at grain boundaries (GBs) of an ultrafine grained (UFG) Al-Zn-Mg-Cu alloy processed by equal-channel angular pressing (ECAP) at 200 oC was characterised using three-dimensional atom probe. Mg and Cu segregate strongly to the grain boundaries. In contrast, Zn does not always show clear segregation and may even show depletion near the grain boundaries. Trace element Si selectively segregates at some GBs. An increase in the number of ECAP passes leads to a decrease in the grain size but an increase in solute segregation at the boundaries. The significant segregation of alloying elements at the boundaries of ultrafine-grained alloys implies that less solutes will be available in the matrix for precipitation with a decrease in the average grain size. -- Research Highlights: → Atom probe tomography has been employed successfully to reveal unique segregation of solutes at ultrafine grained material. → Mg and Cu elements segregated strongly at the grain boundary of an ultrafine grained Al-Zn-Mg-Cu alloy processed by 4-pass and 8-pass ECAP at 200 oC. Zn frequently depleted at GBs with a Zn depletion region of 7-15 nm in width on one or both sides of the GBs. Only a small fraction (3/13) of GBs were observed with a low level of Zn segregation where the combined Mg and Cu excess is over 3.1 atom/nm2. Si appeared selectively segregated at some of the GBs. → The increase in number of ECAP passes from 4 to 8 correlated with the increase in mean level segregation of Mg and Cu for both solute excess and peak concentration. → The change of plane normal of a grain boundary within 30o only leads to a slight change in the solute segregation level.
Electrodeposition methods in superheavy element chemistry
International Nuclear Information System (INIS)
To prepare electrodeposition experiments with superheavy elements (SHE), their homologs were investigated. In the experiments, various electrode materials and electrolytes were used. Critical potentials (Ecrit) where the electrodeposition starts and potentials for the deposition of 50% of the atoms in solution (E50%) were determined. Underpotential deposition was observed in most cases. An electrolytic cell for a fast electrochemical deposition was developed and the time for the deposition of 50% of the atoms in solution (t50%) was determined. Short lived α-emitting isotopes were produced at Gesellschaft fuer Schwerionenforschung (GSI), Darmstadt, transferred to the aqueous phase with ALOHA (automated liquid online heavy element apparatus), transported to an electrolytic cell and deposited on a palladinated Ni tape. It was shown that the coupling of devices for collection, electrodeposition, and α-spectroscopy is feasible and might be of great use in SHE chemistry. (orig.)
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 this implementation and the modelling of the hydraulic fracturing is given. After the set-up of the hydraulic fracturing simulations has been discussed, with all the main input parameters, several m...
The boundary point method for Reissner′s plates%Reissner型板边界点法
Institute of Scientific and Technical Information of China (English)
吴约; 王左辉
2001-01-01
In this paper, a series of particular solutions are formed by utilizing correspondent Reissher′s plate fundamental solutions. Thus all elements in the coefficient matrix of boundary element equations for plates to be solved will be determined by boundary point method. In the process of solving, interpolation and numerical integration are not needed and numerical treatment for singular integration is avoided, meanwhile, the calculation of physical characteristics of any point does not depend on boundary unknowns to be solved, therefore, the accuracy is excellent. The method presented may be applied to solving the problems of all kinds of plates and shells no matter if the problem is isotropic or anisotropic. But it should be noticed that the matrix of all particular solution field should conform with the fundamental solution of the specific problem.%文章采用Reissner型板基本解来构建一系列特解，再通过边界点法确定边界元方程系效矩阵的全部元素。解算中不涉及具体插值，不用数值积分，避免了奇性处理，而任意点物理量的计算不依赖于待解的边界未知量，算效高，精度好。该法还可用来分析其它各类板壳问题，无论是各向同性还是各向异性的，不同的只是应按各自的基本解来构造全特解场矩阵。
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
Zhang, Shuhai; Oskay, Caglar
2015-04-01
This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global-local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson-Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.
Adjoint Formulation for an Embedded-Boundary Cartesian Method
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
2004-01-01
Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2005-01-01
Why another book on the finite element method? There are currently more than 200 books in print with ""Finite Element Method"" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems.Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral eleme
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.
Continuous Finite Element Methods of Molecular Dynamics Simulations
Directory of Open Access Journals (Sweden)
Qiong Tang
2015-01-01
Full Text Available Molecular dynamics simulations are necessary to perform very long integration times. In this paper, we discuss continuous finite element methods for molecular dynamics simulation problems. Our numerical results about AB diatomic molecular system and A2B triatomic molecules show that linear finite element and quadratic finite element methods can better preserve the motion characteristics of molecular dynamics, that is, properties of energy conservation and long-term stability. So finite element method is also a reliable method to simulate long-time classical trajectory of molecular systems.
Mechanics of a crushable pebble assembly using discrete element method
Energy Technology Data Exchange (ETDEWEB)
Annabattula, R.K., E-mail: ratna.annabattula@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany); Gan, Y., E-mail: yixiang.gan@sydney.edu.au [School of Civil Engineering, University of Sydney, 2006 NSW, Sydney (Australia); Zhao, S. [College of Mechanical and Electronics Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018 (China); Kamlah, M., E-mail: marc.kamlah@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany)
2012-11-15
The influence of crushing of individual pebbles on the overall strength of a pebble assembly is investigated using discrete element method. An assembly comprising of 5000 spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation. Then, the pebble assembly is subjected to uni-axial compression ({epsilon}{sub 33}=1.5%) with periodic boundary conditions. The crushable pebble assembly shows a significant difference in stress-strain response in comparison to a non-crushable pebble assembly. The analysis shows that a ideal plasticity like behaviour (constant stress with increase in strain) is the characteristic of a crushable pebble assembly with sudden damage. The damage accumulation law plays a critical role in determining the critical stress while the critical number of completely failed pebbles at the onset of critical stress is independent of such a damage law. Furthermore, a loosely packed pebble assembly shows a higher crush resistance while the critical stress is insensitive to the packing factor ({eta}) of the assembly.
Response Surface Stochastic Finite Element Method of Composite Structure
Directory of Open Access Journals (Sweden)
Cai Deyong
2016-01-01
Full Text Available Response Surface Method (RSM has been applied to structural reliability problems successfully in many areas. Finite Element Method (FEM is one of the most widely used computational methods, which permit the analysis and design of large-scale engineering systems. In order to obtain a reliability analysis method of composite structure with satisfactory accuracy and computational efficiency, RSM and FEM were combined by secondary development of ABAQUS. Response Surface Stochastic Finite Element Method (RSSFEM which can solve the reliability problems of composite structure was developed. The numerical accuracy and the computational efficiency of the developed method were demonstrated by comparison with Monte-Carlo Stochastic Finite Element Method (MCSFEM.
Spectral element methods for the incompressible Navier-Stokes equations
Maday, Yvon; Patera, Anthony T.
1989-01-01
Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the construction and analysis of optimal-order spectral element discretizations for elliptic and saddle (Stokes) problems, as well as the efficient solution of the resulting discrete equations by rapidly convergent tensor-product-based iterative procedures. Several examples of spectral element simulation of moderate Reynolds number unsteady flow in complex geometry are presented.
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
Multiphysics Finite Element Methods for a Poroelasticity Model
Feng, Xiaobing; Ge, Zhihao; Li, Yukun
2014-01-01
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To better describe the multiphysics process of deformation and diffusion for poro-elastic materials, we first present a reformulation of the original model by introducing two pseudo-pressures, one of them is shown to satisfy a diffusion equation, we then propo...
A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method
Wang, Xiao-Yen J.
2015-01-01
The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.
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.
Simulation of near-fault bedrock strong ground-motion field by explicit finite element method
Institute of Scientific and Technical Information of China (English)
ZHANG Xiao-zhi; HU Jin-jun; XIE Li-li; WANG Hai-yun
2006-01-01
Based on presumed active fault and corresponding model, this paper predicted the near-fault ground motion filed of a scenario earthquake (Mw=6 3/4 ) in an active fault by the explicit finite element method in combination with the source time function with improved transmitting artificial boundary and with high-frequency vibration contained.The results indicate that the improved artificial boundary is stable in numerical computation and the predicted strong ground motion has a consistent characteristic with the observed motion.
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.
Simulating Biofilm Deformation and Detachment with the Immersed Boundary Method
Sudarsan, Rangarajan; Ghosh, Sudeshna; Stockie, John M.; Eberl, Hermann J.
2016-03-01
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 biofilm colony at different stages of growth, we consider a family of four biofilm shapes with varying aspect ratio. Our numerical simulations focus on the behaviour of weak biofilms (with relatively low yield stress threshold) and investigate features of the fluid-structure interaction such as locations of maximum shear and increased drag. The most important conclusion of this work is that the commonly employed detachment strategy in biofilm models based only on interfacial shear stress can lead to incorrect or inaccurate results when applied to the study of shear induced detachment of weak biofilms. Our detachment strategy based on equivalent continuum stresses provides a unified and consistent IB framework that handles both sloughing and erosion modes of biofilm detachment, and is consistent with strategies employed in many other continuum based biofilm models.
Novak, Jerome; Bonazzola, Silvano
2002-01-01
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary condition is simply written as a perturbation of the usual Sommerfeld radiation boundary condition. It is very easily implemented using spectral methods in spherical coordinates. Numer...
A finite element computational method for high Reynolds number laminar flows
Kim, Sang-Wook
1987-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
Energy Technology Data Exchange (ETDEWEB)
Pingenot, J; Jandhyala, V
2007-03-01
This report summarizes the work performed for Lawrence Livermore National Laboratory (LLNL) at the University of Washington between September 2004 and May 2006. This project studied fast solvers and stability for time domain integral equations (TDIE), especially as applied to radiating boundary for a massively parallel FEM solver.
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.
MESHLESS METHOD OF DUAL RECIPROCITY HYBRID RADIAL BOUNDARY NODE METHOD FOR ELASTICITY
Institute of Scientific and Technical Information of China (English)
Fei Yan; Xiating Feng; Hui Zhou
2010-01-01
Combining the radial point interpolation method(RPIM),thedualreciprocitymethod(DRM)and the hybrid boundary node method(HBNM),a dual reciprocity hybrid radial boundary node method(DHRBNM)is proposed for linear elasticity.Compared to DHBNM,RPIM is exploited to replace the moving least square(MLS)in DHRBNM,and it gets rid of the deficiency of MLS approximation,in which shape functions lack the delta function property,the boundary condition can not be applied easily and directly and it's computational expense is high.Besides,different approximate functions are discussed in DRM to get the interpolation property,in which the accuracy and efficiency for different basis functions are compared.Then RPIM is also applied in DRM to replace the conical function interpolation,which can greatly improve the accuracy of the present method.To demonstrate the effectiveness of the present method,DHBNM is applied for comparison,and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.
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.
Study of flow and mass transport in multilayered aquifers using boundary integral method
Energy Technology Data Exchange (ETDEWEB)
Zakikhani, M.
1988-01-01
In recent years, the boundary integral element method (BIEM) has been widely used in the area of ground-water modeling. This method, based on Green's theorem, has a variety of advantages over domain methods. Earlier applications of the BIEM to multilayer aquifer problems were restricted to steady-state flows. In these applications, layered aquifer systems were solved iteratively using the Bessel function as the principal Green function. In this formulation, the argument of the Bessel function is a function of hydraulic properties of the aquifer-aquitard system. Such an approach reduces the efficiency of the computations and yields less accurate numerical results. In the study presented here, a non-iterative boundary integral equation formulation (NIBIEM) for multilayer aquifer systems with or without a well network is developed. In this procedure, the coefficients of the singular points associated with pumping or recharge wells are included in the analysis in an analytic sense. This improves the efficiency and the accuracy of the computation. The formulation presented is developed for three different phases of flow.
Least-squares finite element methods for compressible Euler equations
Jiang, Bo-Nan; Carey, G. F.
1990-01-01
A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
Solution-adaptive finite element method in computational fracture mechanics
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
Effective beam method for element concentrations
Tolhurst, Thomas; Barbi, Mauricio; Tokaryk, Tim
2015-01-01
There is a great diversity of research being conducted at synchrotron facilities around the world and a diverse set of beamlines to accommodate this research. Time is a precious commodity at synchrotron facilities; therefore, methods that can maximize the time spent collecting data are of value. At the same time the incident radiation spectrum, necessary for some research, may not be known on a given beamline. A preliminary presentation of a method applicable to X-ray fluorescence spectrocopi...
SPECTRAL FINITE ELEMENT METHOD FOR A UNSTEADY TRANSPORT EQUATION
Institute of Scientific and Technical Information of China (English)
MeiLiquan
1999-01-01
In this paper,a new numerical method,the coupling method of spherical harmonic function spectral and finite elements,for a unsteady transport equation is dlscussed,and the error analysis of this scheme is proved.
An h-p Taylor-Galerkin finite element method for compressible Euler equations
Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.
1991-01-01
An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.
Kazerani, Tohid
2011-01-01
The study presented in this thesis aims to numerically explore the micro-mechanisms underlying rock fracture and fragmentation under dynamic loading. The approach adopted is based on the Discrete Element Method (DEM) coupled to the Cohesive Process Zone (CPZ) theory. It assumes rock material as assemblage of irregular-sized deformable fragments joining together at their cohesive boundaries. The simulation, which is referred to as Cohesive Fragment Mod...
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.
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.
A new complex variable element-free Galerkin method for two-dimensional potential problems
Institute of Scientific and Technical Information of China (English)
Cheng Yu-Min; Wang Jian-Fei; Bai Fu-Nong
2012-01-01
In this paper,based on the element-free Galerkin (EFG) method and the improved complex variable moving least-square (ICVMLS) approximation,a new meshless method,which is the improved complex variable element-free Galerkin (ICVEFG) method for two-dimensional potential problems,is presented. In the method,the integral weak form of control equations is employed,and the Lagrange multiplier is used to apply the essential boundary conditions.Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained.Compared with the complex variable moving least-square (CVMLS) approximation proposed by Cheng,the functional in the ICVMLS approximation has an explicit physical meaning.Furthermore,the ICVEFG method has greater computational precision and efficiency.Three numerical examples are given to show the validity of the proposed method.
Wing flutter boundary prediction using unsteady Euler aerodynamic method
Lee-Rausch, Elizabeth M.; Batina, John T.
1993-01-01
Modifications to an existing 3D implicit upwind Euler/Navier-Stokes code for the aeroelastic analysis of wings are described. These modifications include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time-integration with the governing flow equations. The paper gives a brief description of these modifications and presents unsteady calculations which check the modifications to the code. Euler flutter results for an isolated 45 deg swept-back wing are compared with experimental data for seven freestream Mach numbers which define the flutter boundary over a range of Mach number from 0.499 to 1.14. These comparisons show good agreement in flutter characteristics for freestream Mach numbers below unity. For freestream Mach numbers above unity, the computed aeroelastic results predict a premature rise in the flutter boundary as compared with the experimental boundary. Steady and unsteady contours of surface Mach number and pressure are included to illustrate the basic flow characteristics of the time-marching flutter calculations and to aid in identifying possible causes for the premature rise in the computational flutter boundary.
Institute of Scientific and Technical Information of China (English)
Shao Yu-Fei; Yang Xin; Zhao Xing; Wang Shao-Qing
2012-01-01
Grain boundary activity in nanocrystalline Al under an indenter is studied by using a multiscale method.It is found that grain boundaries and twin boundaries can be transformed into each other by emitting and absorbing dislocations.The transition processes might result in grain coarsening and refinement events.Dislocation reflection generated by a piece of stable grain boundary is also observed,because of the complex local atomic structure within the nanocrystalline Al.This implies that nanocrystalline metals might improve their internal structural stability with the help of some special local grain boundaries.
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),
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.
Smith, Emily M; Lajoie, Bryan R; Jain, Gaurav; Dekker, Job
2016-01-01
Three-dimensional genome structure plays an important role in gene regulation. Globally, chromosomes are organized into active and inactive compartments while, at the gene level, looping interactions connect promoters to regulatory elements. Topologically associating domains (TADs), typically several hundred kilobases in size, form an intermediate level of organization. Major questions include how TADs are formed and how they are related to looping interactions between genes and regulatory elements. Here we performed a focused 5C analysis of a 2.8 Mb chromosome 7 region surrounding CFTR in a panel of cell types. We find that the same TAD boundaries are present in all cell types, indicating that TADs represent a universal chromosome architecture. Furthermore, we find that these TAD boundaries are present irrespective of the expression and looping of genes located between them. In contrast, looping interactions between promoters and regulatory elements are cell-type specific and occur mostly within TADs. This is exemplified by the CFTR promoter that in different cell types interacts with distinct sets of distal cell-type-specific regulatory elements that are all located within the same TAD. Finally, we find that long-range associations between loci located in different TADs are also detected, but these display much lower interaction frequencies than looping interactions within TADs. Interestingly, interactions between TADs are also highly cell-type-specific and often involve loci clustered around TAD boundaries. These data point to key roles of invariant TAD boundaries in constraining as well as mediating cell-type-specific long-range interactions and gene regulation. PMID:26748519
Mo, Huangrui; Zhang, Fan; Cronin, Duane S
2016-01-01
In this paper, a sharp interface immersed boundary method is developed for efficiently and robustly solving flow with arbitrarily irregular and changing geometries. The proposed method employs a three-step prediction-correction flow reconstruction scheme for boundary treatment and enforces Dirichlet, Neumann, Robin, and Cauchy boundary conditions in a straightforward and consistent manner. Numerical experiments concerning flow of two and three space dimensions, stationary and moving objects, convex and concave geometries, no-slip and slip wall boundary conditions are conducted to demonstrate the proposed method.
Kawai, T.
Among the topics discussed are the application of FEM to nonlinear free surface flow, Navier-Stokes shallow water wave equations, incompressible viscous flows and weather prediction, the mathematical analysis and characteristics of FEM, penalty function FEM, convective, viscous, and high Reynolds number FEM analyses, the solution of time-dependent, three-dimensional and incompressible Navier-Stokes equations, turbulent boundary layer flow, FEM modeling of environmental problems over complex terrain, and FEM's application to thermal convection problems and to the flow of polymeric materials in injection molding processes. Also covered are FEMs for compressible flows, including boundary layer flows and transonic flows, hybrid element approaches for wave hydrodynamic loadings, FEM acoustic field analyses, and FEM treatment of free surface flow, shallow water flow, seepage flow, and sediment transport. Boundary element methods and FEM computational technique topics are also discussed. For individual items see A84-25834 to A84-25896
Abdallah, Ayman Ahmed
1990-01-01
Component mode synthesis (CMS) is a method of dynamic analysis, for structures having a large number of degrees of freedom (DOF). These structures often required lengthy computer CPU time and large computer memory resources, if solved directly by the finite-element method (FEM). In CMS, the structure is divided into independent components in which the DOF are defined by a set of generalized coordinates defined by displacement shapes. The number of the generalized coordinates are much less than the original number of physical DOF, in the component. The displacement shapes are used to transform the component property matrices and any applied external loads, to a reduced system of coordinates. Reduced system property matrices are assembled, and any type of dynamic analysis is carried out in the reduced coordinate system. Any obtained results are back transformed to the original component coordinate systems. In all conventional methods of CMS, the mode shapes used for components are dynamic mode shapes, supplemented by static deflected shapes. Historically, all the dynamic mode shapes used in conventional CMS are the natural modes (eigenvectors) of components. A new method of CMS, namely the boundary flexibility vector method of CMS, is presented. The method provides for the incorporation of a set of static Ritz vectors, referred to as boundary flexibility vectors, as a replacement and/or supplement to conventional eigenvectors, as displacement shapes for components. The generation of these vectors does not require the solution of a costly eigenvalue problem, as in the case of natural modes in conventional CMS, and hence a substantial saving in CPU time can be achieved. The boundary flexibility vectors are generated from flexibility (or stiffness) properties of components. The formulation presented is for both free and fixed-interface components, and for both the free and forced vibration problems. Free and forced vibration numerical examples are presented to verify
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
Variable kinematic plate elements coupled via Arlequin method
GIUNTA, GAETANO; Biscani, Fabio; Carrera, Erasmo
2012-01-01
In this work, plate elements based on different kinematic assumptions and variational principles are combined through the Arlequin method. Computational costs are reduced assuming refined models only in those zones with a quasi-three-dimensional stress field, whereas computationally cheap, low-order elements are used in the remaining parts of the plate. Plate elements are formulated on the basis of a unified formulation (UF). Via UF, higher-order, layer-wise and mixed theories can be easily f...
Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping
2013-05-01
This paper develops a numerical solution to the radiative heat transfer problem coupled with conduction in an absorbing, emitting and isotropically scattering medium with the irregular geometries using the natural element method (NEM). The walls of the enclosures, having temperature and mixed boundary conditions, are considered to be opaque, diffuse as well as gray. The NEM as a meshless method is a new numerical scheme in the field of computational mechanics. Different from most of other meshless methods such as element-free Galerkin method or those based on radial basis functions, the shape functions used in NEM are constructed by the natural neighbor interpolations, which are strictly interpolant and the essential boundary conditions can be imposed directly. The natural element solutions in dealing with the coupled heat transfer problem for the mixed boundary conditions have been validated by comparison with those from Monte Carlo method (MCM) generated by the authors. For the validation of the NEM solution to radiative heat transfer in the semicircular medium with an inner circle, the results by NEM have been compared with those reported in the literatures. For pure radiative transfer, the upwind scheme is employed to overcome the oscillatory behavior of the solutions in some conditions. The steady state and transient heat transfer problem combined with radiation and conduction in the semicircular enclosure with an inner circle are studied. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter and the boundary emissivity are analyzed on the radiative and conductive heat fluxes and transient temperature distributions.
Chung, T. J.; Karr, Gerald R.
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.
Linear-scaling multipole-accelerated Gaussian and finite-element Coulomb method
Watson, Mark A.; Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2008-02-01
A linear-scaling implementation of the Gaussian and finite-element Coulomb (GFC) method is presented for the rapid computation of the electronic Coulomb potential. The current work utilizes the fast multipole method (FMM) for the evaluation of the Poisson equation boundary condition. The FMM affords significant savings for small- and medium-sized systems and overcomes the bottleneck in the GFC method for very large systems. Compared to an exact analytical treatment of the boundary, more than 100-fold speedups are observed for systems with more than 1000 basis functions without any significant loss of accuracy. We present CPU times to demonstrate the effectiveness of the linear-scaling GFC method for both one-dimensional polyalanine chains and the challenging case of three-dimensional diamond fragments.