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).
Boundary element-free method for elastodynamics
Institute of Scientific and Technical Information of China (English)
CHENG; Yumin; PENG; Miaojuan
2005-01-01
The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.
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.
Forward seismic modeling with the use of boundary element method
Energy Technology Data Exchange (ETDEWEB)
Xuejun, L.
1991-01-01
Boundary element method for wave equation boundary value problem involves three steps: the boundary value problem of wave equations is converted into the boundary value problem of Helmholtz's equations by performing the one-dimensional Fourier transform of time variable, the new boundary value problem is converted into an integral equation by using Green's formula; and the integral equation is solved using boundary element method, and the required numerical solution is obtained by using inverse Fourier transform. This paper analyzes the theoretical formulas and application of the method. This method can be applied to forward and inverse seismic problems. In solving integral equation using boundary element method, the adoption of interval truncation division results in less element knots, less internal storage, faster operation and more accurate computation.
(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.
Novel boundary element method for resolving plate bending problems
Institute of Scientific and Technical Information of China (English)
陈颂英; 王乐勤; 焦磊
2003-01-01
This paper discusses the application of the boundary contour method for resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirchhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points, even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corner point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.
A Geometrical Approach to the Boundary Element Method
Auchmann, B; Rjasanow, S
2008-01-01
We introduce a geometric formulation of the boundary element method (BEM), using concepts of the discrete electromagnetic theory. Geometric BEM is closely related to Galerkin-BEM and to the generalized collocation scheme. It is easy to implement, accurate, and computationally efficient. We validate our approach with 2-D examples and give an outlook to 3-D results.
The use of discrete orthogonal projections in boundary element methods
Brandts, J.
2001-01-01
In recent papers by Sloan and Wendland Grigorie and Sloan and Grigorie Sloan and Brandts a formalismwas developed that serves many important and interesting applications in boundary element methods the commutator property for splines Based on superapproximation results this property is for exam
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
Finite element method for solving geodetic boundary value problems
Fašková, Zuzana; Čunderlík, Róbert; Mikula, Karol
2010-02-01
The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions.
Advanced boundary element methods in aeroacoustics and elastodynamics
Lee, Li
In the first part of this dissertation, advanced boundary element methods (BEM) are developed for acoustic radiation in the presence of subsonic flows. A direct boundary integral formulation is first introduced for acoustic radiation in a uniform flow. This new formulation uses the Green's function derived from the adjoint operator of the governing differential equation. Therefore, it requires no coordinate transformation. This direct BEM formulation is then extended to acoustic radiation in a nonuniform-flow field. All the terms due to the nonuniform-flow effect are taken to the right-hand side and treated as source terms. The source terms result in a domain integral in the standard boundary integral formulation. The dual reciprocity method is then used to convert the domain integral into a number of boundary integrals. The second part of this dissertation is devoted to the development of advanced BEM algorithms to overcome the multi-frequency and nonuniqueness difficulties in steady-state elastodynamics. For the multi-frequency difficulty, two different interpolation schemes, borrowed from recent developments in acoustics, are first extended to elastodynamics to accelerate the process of matrix re-formation. Then, a hybrid scheme that retains only the merits of the two different interpolation schemes is suggested. To overcome the nonuniqueness difficulty, an enhanced CHIEF (Combined Helmholtz Integral Equation Formulation) method using a linear combination of the displacement and the traction boundary integral equations on the surface of a small interior volume is proposed. Numerical examples are given to demonstrate all the advanced BEM formulations.
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.
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.
A Boundary Element Method for Simulation of Deformable Objects
Institute of Scientific and Technical Information of China (English)
徐美和; 唐泽圣
1996-01-01
In this paper,a boundary element method is first applied to real-tim animation of deformable objects and to simplify data preparation.Next,the visibleexternal surface of the object in deforming process is represented by B-spline surface,whose control points are embedded in dynamic equations of BEM.Fi-nally,the above method is applied to anatomical simulation.A pituitary model in human brain,which is reconstructed from a set of anatomical sections, is selected to be the deformable object under action of virtual tool such as scapel or probe.It produces fair graphic realism and high speed performance.The results show that BEM not only has less computational expense than FEM,but also is convenient to combine with the 3D reconstruction and surface modeling as it enables the reduction of the dimensionality of the problem by one.
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.
Novel TMS coils designed using an inverse boundary element method
Cobos Sánchez, Clemente; María Guerrero Rodriguez, Jose; Quirós Olozábal, Ángel; Blanco-Navarro, David
2017-01-01
In this work, a new method to design TMS coils is presented. It is based on the inclusion of the concept of stream function of a quasi-static electric current into a boundary element method. The proposed TMS coil design approach is a powerful technique to produce stimulators of arbitrary shape, and remarkably versatile as it permits the prototyping of many different performance requirements and constraints. To illustrate the power of this approach, it has been used for the design of TMS coils wound on rectangular flat, spherical and hemispherical surfaces, subjected to different constraints, such as minimum stored magnetic energy or power dissipation. The performances of such coils have been additionally described; and the torque experienced by each stimulator in the presence of a main magnetic static field have theoretically found in order to study the prospect of using them to perform TMS and fMRI concurrently. The obtained results show that described method is an efficient tool for the design of TMS stimulators, which can be applied to a wide range of coil geometries and performance requirements.
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.
Lubrication approximation in completed double layer boundary element method
Nasseri, S.; Phan-Thien, N.; Fan, X.-J.
This paper reports on the results of the numerical simulation of the motion of solid spherical particles in shear Stokes flows. Using the completed double layer boundary element method (CDLBEM) via distributed computing under Parallel Virtual Machine (PVM), the effective viscosity of suspension has been calculated for a finite number of spheres in a cubic array, or in a random configuration. In the simulation presented here, the short range interactions via lubrication forces are also taken into account, via the range completer in the formulation, whenever the gap between two neighbouring particles is closer than a critical gap. The results for particles in a simple cubic array agree with the results of Nunan and Keller (1984) and Stoksian Dynamics of Brady etal. (1988). To evaluate the lubrication forces between particles in a random configuration, a critical gap of 0.2 of particle's radius is suggested and the results are tested against the experimental data of Thomas (1965) and empirical equation of Krieger-Dougherty (Krieger, 1972). Finally, the quasi-steady trajectories are obtained for time-varying configuration of 125 particles.
Geodynamic simulations using the fast multipole boundary element method
Drombosky, Tyler W.
Interaction between viscous fluids models two important phenomena in geophysics: (i) the evolution of partially molten rocks, and (ii) the dynamics of Ultralow-Velocity Zones. Previous attempts to numerically model these behaviors have been plagued either by poor resolution at the fluid interfaces or high computational costs. We employ the Fast Multipole Boundary Element Method, which tracks the evolution of the fluid interfaces explicitly and is scalable to large problems, to model these systems. The microstructure of partially molten rocks strongly influences the macroscopic physical properties. The fractional area of intergranular contact, contiguity, is a key parameter that controls the elastic strength of the grain network in the partially molten aggregate. We study the influence of matrix deformation on the contiguity of an aggregate by carrying out pure shear and simple shear deformations of an aggregate. We observe that the differential shortening, the normalized difference between the major and minor axes of grains is inversely related to the ratio between the principal components of the contiguity tensor. From the numerical results, we calculate the seismic anisotropy resulting from melt redistribution during pure and simple shear deformation. During deformation, the melt is expelled from tubules along three grain corners to films along grain edges. The initially isotropic fractional area of intergranular contact, contiguity, becomes anisotropic due to deformation. Consequently, the component of contiguity evaluated on the plane parallel to the axis of maximum compressive stress decreases. We demonstrate that the observed global shear wave anisotropy and shear wave speed reduction of the Lithosphere-Asthenosphere Boundary are best explained by 0.1 vol% partial melt distributed in horizontal films created by deformation. We use our microsimulation in conjunction with a large scale mantle deep Earth simulation to gain insight into the formation of
Johnson, Anthony N; Hromadka, T V
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
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.
Directory of Open Access Journals (Sweden)
E. Majchrzak
2008-12-01
Full Text Available The dual reciprocity boundary element method is applied for numerical modelling of solidification process. This variant of the BEM is connected with the transformation of the domain integral to the boundary integrals. In the paper the details of the dual reciprocity boundary element method are presented and the usefulness of this approach to solidification process modelling is demonstrated. In the final part of the paper the examples of computations are shown.
Solving forward and inverse seismic problems by boundary-element method in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Xianxi, J.
1988-01-01
Solving the boundary value problem of wave equation by boundary element method in frequency domain involves these steps: 1. ID Fourier transform of time variable is made to convert the wave equation into Helmholtz equation; 2. this equation is then solved using boundary-element method in frequency domain; 3. the result is returned to time domain by making inverse Fourier transform. Compared with other formulas, the formula in this paper brings higher accuracy but less computation.
An Investigation of the Indirect Boundary Element Method in One- and Two-Dimensional Elastostatics.
1983-05-01
Editors. Development in boundary element methods - 1. London, England, Applied Sciences Publishers Ltd., 1979. 6. G. Arfken . Mathematical methods for...FD-R133 142 AN INVESTIGATION OF THE INDIRECT BOUNDARY ELEMENT 112 METHOD IN ONE- AND TWO-..(U) NAVAL CIVIL ENGINEERING LAB PORT HUENEME CA T A SHUGAR...BOUNDARY ELEMENT METHOD IN ONE- AND TWO-DIMENSIONAL ELASTOSTATICS LDTIW AUTHOR: T.A. Shugar and J. V. Cox S E CTE !& S3 0 1983M DATE: May 1983 B SPONSOR
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
NEW BOUNDARY ELEMENT METHOD FOR TORSION PROBLEMS OF CYLINDER WITH CURVILINEAR CRACKS
Institute of Scientific and Technical Information of China (English)
WANG Yin-bang; LU Zi-zi
2005-01-01
The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight,kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas,which demonstrates the validity and applicability of the present boundary element method.
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.
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...... element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have...
SOLVING CONTACT PROBLEM WITH FRICTION BY A NEW FAST BOUNDARY ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
1998-01-01
The formulation of boundary element method for handling contact problems with friction and the technique for high-speed contact analysis are presented. This formulation is based on the idea of modifying the length of contact elements without altering the total number of elements. The high precision of solution and high-speed analysis are verified according to the results of conventional method and analysis method.
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..
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.
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
Institute of Scientific and Technical Information of China (English)
YIN Hong-jun; HE Ying-fu; FU Chun-quan
2005-01-01
The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the solution of model is expanded into a series in powers of perturbation parameter. By using the Boundary Element Method (BEM) and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barriers. Finally, the results obtained by perturbation boundary element method is compared with the analytical solution and is available for the transient pressure analysis of arbitrary shaped reservoirs.
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.
Institute of Scientific and Technical Information of China (English)
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
On the modeling of narrow gaps using the standard boundary element method
DEFF Research Database (Denmark)
Cutanda Henríquez, Vicente; Juhl, Peter Møller; Jacobsen, Finn
2001-01-01
. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both...
Petrov-Galerkin Spectral Element Method for Mixed Inhomogeneous Boundary Value Problems on Polygons
Institute of Scientific and Technical Information of China (English)
Hongli JIA; Benyu GUO
2010-01-01
The authors investigate Petrov-Galerkin spectral element method.Some results on Legendre irrational quasi-orthogonal approximations are established,which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons.As examples of applications,spectral element methods for two model problems,with the spectral accuracy in certain Jacobi weighted Sobolev spaces,are proposed.The techniques developed in this paper are also applicable to other higher order methods.
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.
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.
The Boundary Element Method Applied to the Two Dimensional Stefan Moving Boundary Problem
1991-03-15
iterate 12 times to reach :34 BOUNDARY TIME EVOLUION Figure 3.4. Fixed Boundary Time Evolution ’onvergence in the successive approximation. The squares...memory requirements of the code, especially if more intricate geometries are to be considered. If fast conmput.- ing resources are not available, the
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.
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...
Finite Element - Artificial Transmitting Boundary Method for Acoustical Field on Tapered Waveguide
Institute of Scientific and Technical Information of China (English)
J.; S.; Yang; G; F.; Fan; J.; P.; Zhu; C.K.; Sun; Y.; H.; Zhu
2003-01-01
In earlier approach, the 2-D acoustical field profiles on the substrate region are often calculated with BPM. In this paper, we present a new approach based on the finite element -artificial transmitting boundary method and calculate acoustical field on the substrate region.
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.
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 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...
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.
Institute of Scientific and Technical Information of China (English)
LIU FuPing; WANG AnLing; WANG AnXuan; CAO YueZu; CHEN Qiang; YANG ChangChun
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 significance for computing the field and the potential generated by OMNE in bio-tissue, which is a fast, effective and accurate computing method.
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...... 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....
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.
DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT
Institute of Scientific and Technical Information of China (English)
GAO Suo-wen; WANG Yue-sheng; ZHANG Zi-mao; MA Xing-rui
2005-01-01
The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given.The results obtained demonstrate good agreement with other reported results and show high accuracy.
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 ...
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.
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).
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...
Simmons, Daniel; Cools, Kristof; Sewell, Phillip
2016-11-01
Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications.
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.
Analysis of radiation noise from cylinder block by boundary element method
Energy Technology Data Exchange (ETDEWEB)
Miura, Akinori; Sakurai, Yoichi
1987-08-01
As an approach toward low noise in the cylinder blocks of engines for large vehicles, the analysis of emitted noise was attempted. The method of forecasting the sound pressure level emitted from a cylinder block using boundary element method, from the calculated values or the measured values of vibration modes by partial structure synthesis method, was developed. The method of forecasting emitted noise using the result of holography measurement was developed, and by utilizing this method, the experimental optimizing technique for reducing noise was worked up. By applying the combination of the partial structure synthesis method and boundary element method to the cylinder blocks of large and medium sized diesel engines, the investigation of low noise cylinder blocks has become feasible at the stage of desk work. By these methods, from the result of holography, the part which is most effective when its noise level is reduced is determined, and the effect of reduction can be forecast. Besides, low noise structures can be studied on a desk, and the products manufactured for trial can be decreased, and the efficient development can be made. (9 figs, 2 tabs, 15 refs)
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.
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........ In order to verify the reconstruction process, part of the measurement data is used together with Near-Field Acoustical Holography (NAH). Estimated distributions of sound pressure and particle velocity over a plane surface obtained from the two methods are compared....
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)
Interpretation of horizontal well performance in complicated systems by the boundary element method
Energy Technology Data Exchange (ETDEWEB)
Jongkittinarukorn, K.; Tiab, D. [Oklahoma Univ., School of Petroleum and Geological Engineering (United States); Escobar, F. H. [Surcolombiana Univ., Dept. of Petroleum Engineering (Colombia)
1998-12-31
A solution obtained by using the boundary element method to simulate pressure behaviour of horizontal wells in complicated reservoir-wellbore configurations is presented. Three different types of well bore and reservoir models were studied, i.e. a snake-shaped horizontal wellbore intersecting a two-layer reservoir with cross flow, a horizontal well in a three-layer reservoir with cross flow, and a vertical well intersecting a two-layer reservoir without cross flow. In each case, special attention was paid to the influence of wellbore inclination angle, the distance from the wellbore to the different boundaries and the permeability ratio. Performance of each of these types of wells are discussed. 9 refs., 18 figs.
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.
OpenBEM - An open source Boundary Element Method software in Acoustics
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2010-01-01
-symmetric and half-space problems. It also contains a number of improvements such a dealing with thin objects and close surfaces, meshing for 2D and axisymmetrical problems, analytical solutions for verification, and a number of additional functions. This paper gives an overview of the capabilities of the program......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...
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...
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.
Institute of Scientific and Technical Information of China (English)
韩厚德; 郑春雄
2002-01-01
The mixed finite element method is used to solve the exterior Poisson equations with higher-order local artificial boundary conditions in 3-D space. New unknowns are introduced to reduce the order of the derivatives of the unknown to two. The result is an equivalent mixed variational problem which was solved using bilinear finite elements. The primary advantage is that special finite elements are not needed on the adjacent layer of the artificial boundary for the higher-order derivatives. Error estimates are obtained for some local artificial boundary conditions with prescibed orders. A numerical example demonstrates the effectiveness of this method.
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.
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...
General Boundary Element Method：an Application of Homotopy Analysis Method
Institute of Scientific and Technical Information of China (English)
ShijunLIAO
1998-01-01
In this paper,based on a new kind of analytic method,namely the homotopy analysis method(HAM),we greatly generalize the traditional boundary element method(BEM) and propose a so-called general BEM approach,The general BEM can overcome the limitations and restrictions of the traditional BEM.It is valid even for strongly nonlinear problems whose governing equations don't contain any linear terms.Moreover,by the proposed general BEM,one can solve a nonlinear problem even by means of no iterations! This shakes the governing place of the iterative methodology of the BEM for nonlinear problems.Besides,the proposed general BEM contains the traditional BEM in logic.The general BEM approach greatly increases the application area of the BEM as a numerical tool.
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.
Acoustic scattering for 3D multi-directional periodic structures using the boundary element method.
Karimi, Mahmoud; Croaker, Paul; Kessissoglou, Nicole
2017-01-01
An efficient boundary element formulation is proposed to solve three-dimensional exterior acoustic scattering problems with multi-directional periodicity. The multi-directional periodic acoustic problem is represented as a multilevel block Toeplitz matrix. By exploiting the Toeplitz structure, the computational time and storage requirements to construct and to solve the linear system of equations arising from the boundary element formulation are significantly reduced. The generalized minimal residual method is implemented to solve the linear system of equations. To efficiently calculate the matrix-vector product in the iterative algorithm, the original matrix is embedded into a multilevel block circulant matrix. A multi-dimensional discrete Fourier transform is then employed to accelerate the matrix-vector product. The proposed approach is applicable to a periodic acoustic problem for any arbitrary shape of the structure in both full space and half space. Two case studies involving sonic crystal barriers are presented. In the first case study, a sonic crystal barrier comprising rigid cylindrical scatterers is modeled. To demonstrate the effectiveness of the proposed technique, periodicity in one, two, or three directions is examined. In the second case study, the acoustic performance of a sonic crystal barrier with locally resonant C-shaped scatterers is studied.
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.
Tang, Fa-Kuan; Wang, Qian; Hua, Ning; Tang, Xue-Zheng; Lu, Hong; Ma, Ping
2010-12-01
This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials. A torso-heart model established by boundary element method (BEM) is used for studying the distributions of cardiac magnetic fields and electric potentials. Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions, their properties and influences are compared. Then based on constructed torso-heart model and supposed current source functional model—current dipole array, the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time. Through figure and reconstructing parameter comparison, though the magnetic current dipole array imaging possesses better reconstructing effect, however node-to-node BEM and triangle-to-triangle BEM make little difference to magnetic and electric imaging.
Cheng, J Y; Chahine, G L
2001-12-01
The slender body theory, lifting surface theories, and more recently panel methods and Navier-Stokes solvers have been used to study the hydrodynamics of fish swimming. This paper presents progress on swimming hydrodynamics using a boundary integral equation method (or boundary element method) based on potential flow model. The unsteady three-dimensional BEM code 3DynaFS that we developed and used is able to model realistic body geometries, arbitrary movements, and resulting wake evolution. Pressure distribution over the body surface, vorticity in the wake, and the velocity field around the body can be computed. The structure and dynamic behavior of the vortex wakes generated by the swimming body are responsible for the underlying fluid dynamic mechanisms to realize the high-efficiency propulsion and high-agility maneuvering. Three-dimensional vortex wake structures are not well known, although two-dimensional structures termed 'reverse Karman Vortex Street' have been observed and studied. In this paper, simulations about a swimming saithe (Pollachius virens) using our BEM code have demonstrated that undulatory swimming reduces three-dimensional effects due to substantially weakened tail tip vortex, resulting in a reverse Karman Vortex Street as the major flow pattern in the three-dimensional wake of an undulating swimming fish.
Directory of Open Access Journals (Sweden)
Esteban Flores-Mendez
2012-01-01
Full Text Available This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.
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.
Precision enhancement in boundary element methods with application to electron optics.
Loyd, Jody S; Gregory, Don A
2016-08-01
A hybrid approach is presented for obtaining electric potentials for use in electron optics modeling. An initial solution from the boundary element method (BEM) is used to derive the bounding potential of a cylindrical subdomain subsequently used in a Fourier series solution. The approach combines the inherent precision of this analytic solution with the flexibility of BEM to describe practical, non-idealized systems of electrodes. The resulting lens field in the Fourier series subdomain is of higher precision, thereby allowing smaller errors in subsequent calculations of electron ray paths. The effects of aberrations are thus easier to observe in tracing non-paraxial rays. Example ray-traces through a simple, known einzel lens are given as validation of this approach.
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.
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
Computation of Aerodynamic Noise Radiated from Ducted Tail Rotor Using Boundary Element Method
Directory of Open Access Journals (Sweden)
Yunpeng Ma
2017-01-01
Full Text Available A detailed aerodynamic performance of a ducted tail rotor in hover has been numerically studied using CFD technique. The general governing equations of turbulent flow around ducted tail rotor are given and directly solved by using finite volume discretization and Runge-Kutta time integration. The calculations of the lift characteristics of the ducted tail rotor can be obtained. In order to predict the aerodynamic noise, a hybrid method combining computational aeroacoustic with boundary element method (BEM has been proposed. The computational steps include the following: firstly, the unsteady flow around rotor is calculated using the CFD method to get the noise source information; secondly, the radiate sound pressure is calculated using the acoustic analogy Curle equation in the frequency domain; lastly, the scattering effect of the duct wall on the propagation of the sound wave is presented using an acoustic thin-body BEM. The aerodynamic results and the calculated sound pressure levels are compared with the known technique for validation. The sound pressure directivity and scattering effect are shown to demonstrate the validity and applicability of the method.
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.
The boundary element method applied to viscous and vortex shedding flows around cylinders
Farrant, Tim
Studies are presented to further extend the use of the boundary element method (BEM) for the solution of viscous flows around bluff bodies, governed by the incompressible Navier-Stokes equations. Two distinct formulations are applied to various flows around cylindrical geometries for Reynolds numbers Tan (1994) and known herein as the global BEM, was coded to execute in parallel on multi-processor computers. Reductions in execution time were achieved and the method was employed to solve an oscillating cylinder problem. In this study, the displacement undergone by the body was very large but the Reynolds number was always Tan et al (1998). A validation for isolated and double circular cylinders in a uniform stream was performed against experimental evidence to demonstrate the method's stability and accuracy for laminar vortex shedding with geometries involving multiply connected domains. Finally, computational results for flows around four equispaced circular cylinders of equal diameter and two cylinders, one circular the other elliptical, are reported. Many of the concepts established for the flow around two cylinders of equal diameter were found to be useful in interpretation of these more complicated arrangements.
Goldberg, Robert K.; Hopkins, Dale A.
1994-01-01
The boundary element method is utilized in this study to conduct thermal analysis of functionally graded composites, materials in which the internal microstructure or properties are explicitly tailored in order to obtain an optimal response, on the micromechanical (constituent) scale. A unique feature of the boundary element formulations used here is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one dimensional integrations. Using the computer code BEST-CMS, the through the thickness temperature profiles are computed for a representative material with varying numbers of fibers and fiber spacing in the thickness direction. The computed temperature profiles are compared to those obtained using an alternate analytical theory which explicitly couples the heterogeneous microstructure to the global analysis. The boundary element results compared favorably to the analytical calculations, with discrepancies that are explainable based on the boundary element formulation. The results serve both to demonstrate the ability of the boundary element method to analyze these types of materials, and to verify the accuracy of the analytical theory.
Institute of Scientific and Technical Information of China (English)
Xianmin Xu; Zhiping Li
2009-01-01
An a posteriori error estimator is obtained for a nonconforming finite element approx-imation of a linear elliptic problem, which is derived from a corresponding unbounded domain problem by applying a nonlocal approximate artificial boundary condition. Our method can be easily extended to obtain a class of a posteriori error estimators for various conforming and nonconforming finite element approximations of problems with different artificial boundary conditions. The reliability and efficiency of our a posteriori error esti-mator are rigorously proved and axe verified by numerical examples.
Institute of Scientific and Technical Information of China (English)
方蜀州; 王泽毅
2002-01-01
The high frequency resistance and inductance of the 3-D complex interconnect structures can be calculated by solving an eddy current electromagnetic problem. In this paper, a model for charactering such a 3-D eddy current problem is proposed, in which the electromagnetic fields in both the conducting and non-conducting regions are described in terms of the magnetic vector potential, and a set of the indirect boundary integral equations (IBIE) is obtained. The IBIEs can be solved by boundary element method, so this method avoids discretizing the domain of the conductors. As an indirect boundary element method, it is of minimum order. It does not restrict the direction of the current in conductors, and hence it can consider the mutual impedance between two perpendicular conductors. The numerical results can well meet the analytical solution of a 2-D problem. The mutual impedance of two perpendicular conductors is also shown under the different gaps between conductors and different frequencies.
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.
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...
Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.
2017-02-01
A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.
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.
Xie, Wenhao; Deng, Yong; Lian, Lichao; Yan, Dongmei; Yang, Xiaoquan; Luo, Qingming
2016-01-01
The functional information, the absorption and diffusion coefficients, as well as the structural information of biological tissues can be provided by the DOT(Diffuse Optical Tomograph)/MicroCT. In this paper, we use boundary element method to calculate the forward problem of DOT based on the structure prior given by the MicroCT, and then we reconstruct the absorption and diffusion coefficients of different biological tissues by the Levenberg-Marquardt algorithm. The method only needs surface meshing, reducing the complexity of calculation; in addition, it reconstructs a single value within an organ, which reduces the ill-posedness of the inverse problem to make reconstruction results have good noise stability. This indicates that the boundary element method-based reconstruction can serve as an new scheme for getting absorption and diffusion coefficients in DOT/MicroCT multimodality imaging.
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.
DEFF Research Database (Denmark)
Cutanda Henríquez, Vicente; Juhl, Peter Møller
2008-01-01
of the integrand or the whole method. On the other hand, it is also possible to refine or improve the numerical integration, and maintain the standard BEM formulation. In this paper a numerical technique based on element subdivision, previously proposed by the authors, is made more general to cover most cases...
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.
Wright, Louise; Robinson, Stephen P; Humphrey, Victor F
2009-03-01
This paper presents a computational technique using the boundary element method for prediction of radiated acoustic waves from axisymmetric surfaces with nonaxisymmetric boundary conditions. The aim is to predict the far-field behavior of underwater acoustic transducers based on their measured behavior in the near-field. The technique is valid for all wavenumbers and uses a volume integral method to calculate the singular integrals required by the boundary element formulation. The technique has been implemented on a distributed computing system to take advantage of its parallel nature, which has led to significant reductions in the time required to generate results. Measurement data generated by a pair of free-flooding underwater acoustic transducers encapsulated in a polyurethane polymer have been used to validate the technique against experiment. The dimensions of the outer surface of the transducers (including the polymer coating) were an outer diameter of 98 mm with an 18 mm wall thickness and a length of 92 mm. The transducers were mounted coaxially, giving an overall length of 185 mm. The cylinders had resonance frequencies at 13.9 and 27.5 kHz, and the data were gathered at these frequencies.
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.
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
satisfy the radiation conditions exactly. In this paper a model based on the BEM is formulated for the solution of the mentioned problem. A numerical solution is obtained for the 2D plane strain case, and comparison is made with the results obtained from a corresponding FEM solution with an impedance...... absorbing boundary condition....
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller; Barrera Figueroa, Salvador
2009-01-01
Secondary calibration of microphones in free field is performed by placing the microphone under calibration in an anechoic chamber with a sound source, and exposing it to a controlled sound field. A calibrated microphone is also measured as a reference. While the two measurements are usually made...... consecutively, a variation of this procedure, where the microphones are measured simultaneously, is considered more advantageous from the metrological point of view. However, it must be guaranteed that the two microphones receive the same excitation from the source, although their positions are some distance...... apart to avoid acoustic interaction. As a part of the project Euromet-792, aiming to investigate and improve methods for secondary free-field calibration of microphones, a sound source suitable for simultaneous secondary free-field calibration has been designed using the Boundary Element Method...
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.
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'.
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.
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)
Mohd Zamri Jusoh
2013-06-01
Full Text Available The Direct Piercing Carved Wood Panel (DPCWP installed in Masjid Abidin, Kuala Terengganu, is one example that carries much aesthetic and artistic value. The use of DPCWP in earlier mosques was envisaged to improve the intelligibility of indoor speech because the perforated panels allow some of the sound energy to pass through. In this paper, the normal incidence sound absorption coefficient of DPCWP with Daun Sireh motif, which is a form of floral pattern, is discussed. The Daun Sireh motif was chosen and investigated for 30%, 35%, 40%, and 45% perforation ratios. The simulations were conducted using BEASY Acoustic Software based on the boundary element method. The simulation results were compared with measurements obtained by using the sound intensity technique. An accompanying discussion on both the numerical and the measurement tendencies of the sound absorption characteristics of the DPCWP is provided. The results show that the DPCWP with Daun Sireh motif can act as a good sound absorber.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Juhl, Peter Møller
2008-01-01
The project Euromet-792 aims to investigate and improve methods for secondary free-field calibration of microphones. In this framework, the comparison method is being studied at DFM in relation to the more usual substitution method of microphone calibration. The design of the sound source is of p...
Energy Technology Data Exchange (ETDEWEB)
Alleon, G. [EADS-CCR, 31 - Blagnac (France); Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E. [Cerfacs, 31 - Toulouse (France)
2003-07-01
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)
Implementation of a boundary element method to solve for the near field effects of an array of WECs
Oskamp, J. A.; Ozkan-Haller, H. T.
2010-12-01
When Wave Energy Converters (WECs) are installed, they affect the shoreline wave climate by removing some of the wave energy which would have reached the shore. Before large WEC projects are launched, it is important to understand the potential coastal impacts of these installations. The high cost associated with ocean scale testing invites the use of hydrodynamic models to play a major role in estimating these effects. In this study, a wave structure interaction program (WAMIT) is used to model an array of WECs. The program predicts the wave field throughout the array using a boundary element method to solve the potential flow fluid problem, taking into account the incident waves, the power dissipated, and the way each WEC moves and interacts with the others. This model is appropriate for a small domain near the WEC array in order to resolve the details in the interactions, but not extending to the coastline (where the far-field effects must be assessed). To propagate these effects to the coastline, the waves leaving this small domain will be used as boundary conditions for a larger model domain which will assess the shoreline effects caused by the array. The immediate work is concerned with setting up the WAMIT model for a small array of point absorbers. A 1:33 scale lab test is planned and will provide data to validate the WAMIT model on this small domain before it is nested with the larger domain to estimate shoreline effects.
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.
Prediction of Cavitating Waterjet Propulsor Performance Using a Boundary Element Method
2007-10-01
Cavitation, September 11-15, 2006, Wageningen , The Netherlands. Kinnas, S.A., Choi, J.-K., Lee, H., Young, Y.L., Gu, H., Kakar, K. and Natarajan, S...inviscid component Propulsors and their Interaction interactive method", in CA V2006: Sixth International 13 Symposium on Cavitation, Wageningen , The
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.
Sun, Qiang; Wu, Guo Xiong
2013-03-01
A mathematical model and a numerical solution procedure are developed to simulate flow field through a 3D permeable vessel with multibranches embedded in a solid tumour. The model is based on Poisseuille's law for the description of the flow through the vessels, Darcy's law for the fluid field inside the tumour interstitium, and Starling's law for the flux transmitted across the vascular walls. The solution procedure is based on a coupled method, in which the finite difference method is used for the flow in the vessels and the boundary element method is used for the flow in the tumour. When vessels meet each other at a junction, the pressure continuity and mass conservation are imposed at the junction. Three typical representative structures within the tumour vasculature, symmetrical dichotomous branching, asymmetrical bifurcation with uneven radius of daughter vessels and trifurcation, are investigated in detail as case studies. These results have demonstrated the features of tumour flow environment by the pressure distributions and flow velocity field.
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.
Fast multipole boundary element method for Helmholtz equation problems%Helmholtz方程问题的快速多极边界元求解方法
Institute of Scientific and Technical Information of China (English)
于海源; 陈一鸣; 于春肖
2012-01-01
In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale Helmholtz equation problems, a fast multipole boundary element method for the problems of Helmholtz equation is presented. Two theorems are obtained based on the multipole expansion and the local expansion of the boundary element method fundamental solutions'Kernel function. What's more, the basic formulas and the main steps of the fast multipole boundary element method are described for 2D and 3D Helmholtz equation problems.%为了改善传统边界元在求解大规模Helmholtz方程的实际问题时计算效率低、存储量大的缺点,针对快速多极边界元法求解Helmholtz方程进行了理论分析.通过对二维和三维Helmholtz方程的基本解的核函数进行多极展开和局部展开,得到了相应的展开定理,并基于展开定理分别推导了二维和三维问题Helmholtz方程的快速多极边界元计算公式,给出了快速多极边界元法求解Helmholtz方程的主要计算步骤.
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.
Directory of Open Access Journals (Sweden)
L. Jones Tarcius Doss
2012-01-01
Full Text Available A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.
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
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...... 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...
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)
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.
Institute of Scientific and Technical Information of China (English)
彭兵
2000-01-01
A modified boundary element method(BEM) is presented for computation of the fourth non-mixed boundary-value problems，of electrostatic field.The BEM equation is de-rived,and the equation of constraint is presented.By theoretical analyzing and calculating engineering examples,it is proven that the BEM is a more effective approach to computation of the fourth non-mixed boundary-value problems of electrostatic field,it may obtain better calculating results and is applicable to calculating electrostatic field engineering problems of the fourth non-mixed boundary-value problems.%本文提出用边界元法计算介质分区均匀情况下的静电场第四类非混合边值问题，推导出用边界元法计算第四类非混合边值问题的边界元方程组。理论分析和实例计算结果表明：边界元法是计算第四类非混合边值问题的一种有效方法，不仅具有较高的算精度，而且可以很方便地应用于静电场工程问题的设计与计算。
Park, Jong M.; Eversman, W.
1992-01-01
2D sound propagation over an arbitrarily-shaped barrier situated on a locally reacting infinite plane in a homogeneous medium is treated utilizing the BEM. The BIE is formulated so that the integral along an infinite homogeneous plane disappears if the half space Green's function is selected to satisfy the boundary condition of this plane. Comparison of the BEM results with test results by Habault and by Kearns shows good agreement of the sound field utilizing the BEM.
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...
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...
Gumerov, Nail A; O'Donovan, Adam E; Duraiswami, Ramani; Zotkin, Dmitry N
2010-01-01
The head-related transfer function (HRTF) is computed using the fast multipole accelerated boundary element method. For efficiency, the HRTF is computed using the reciprocity principle by placing a source at the ear and computing its field. Analysis is presented to modify the boundary value problem accordingly. To compute the HRTF corresponding to different ranges via a single computation, a compact and accurate representation of the HRTF, termed the spherical spectrum, is developed. Computations are reduced to a two stage process, the computation of the spherical spectrum and a subsequent evaluation of the HRTF. This representation allows easy interpolation and range extrapolation of HRTFs. HRTF computations are performed for the range of audible frequencies up to 20 kHz for several models including a sphere, human head models [the Neumann KU-100 ("Fritz") and the Knowles KEMAR ("Kemar") manikins], and head-and-torso model (the Kemar manikin). Comparisons between the different cases are provided. Comparisons with the computational data of other authors and available experimental data are conducted and show satisfactory agreement for the frequencies for which reliable experimental data are available. Results show that, given a good mesh, it is feasible to compute the HRTF over the full audible range on a regular personal computer.
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.
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.
Sound source reconstruction using inverse boundary element calculations
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo
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...
Boundary element simulation of petroleum reservoirs with hydraulically fractured wells
Pecher, Radek
The boundary element method is applied to solve the linear pressure-diffusion equation of fluid-flow in porous media. The governing parabolic partial differential equation is transformed into the Laplace space to obtain the elliptic modified-Helmholtz equation including the homogeneous initial condition. The free- space Green's functions, satisfying this equation for anisotropic media in two and three dimensions, are combined with the generalized form of the Green's second identity. The resulting boundary integral equation is solved by following the collocation technique and applying the given time-dependent boundary conditions of the Dirichlet or Neumann type. The boundary integrals are approximated by the Gaussian quadrature along each element of the discretized domain boundary. Heterogeneous regions are represented by the sectionally-homogeneous zones of different rock and fluid properties. The final values of the interior pressure and velocity fields and of their time-derivatives are found by numerically inverting the solutions from the Laplace space by using the Stehfest's algorithm. The main extension of the mostly standard BEM-procedure is achieved in the modelling of the production and injection wells represented by internal sources and sinks. They are treated as part of the boundary by means of special single-node and both-sided elements, corresponding to the line and plane sources respectively. The wellbore skin and storage effects are considered for the line and cylindrical sources. Hydraulically fractured wells of infinite conductivity are handled directly according to the specified constraint type, out of the four alternatives. Fractures of finite conductivity are simulated by coupling the finite element model of their 1D-interior with the boundary element model of their 2D- exterior. Variable fracture width, fractures crossing zone boundaries, ``networking'' of fractures, fracture-tip singularity handling, or the 3D-description are additional advanced
Huijssen, Jacobus; Fiala, Péter; Hallez, Raphael; Donders, Stijn; Desmet, Wim
2012-04-01
The Fast Multipole Boundary Element Method (FMBEM) is adopted for the numerical evaluation of source-receiver transfer functions for predicting ISO-362 pass-by noise levels of automotive vehicles. The pass-by noise configuration is discussed, as well as the FMBEM approach to evaluate the transfer functions in the frequency domain. An amplitude/phase frequency interpolation scheme with a geometrically based phase unwrapping scheme is presented that enables the long time frame reconstruction of the impulse responses from coarsely sampled frequency response functions. The performance of the interpolation scheme is compared to other schemes for 12 frequency response functions obtained from measurements on a passenger vehicle in a semi-anechoic room, and a sampling and interpolation scheme is proposed that yields a mean error of 0.5 dB in the third octave band SPLs. Several parameters related to the simulation method, the most important of which is the density of the BEM surface mesh, are investigated for their influence on the trade-off between accuracy and evaluation time. Guidelines for selecting these parameters are presented which can be used to predict sound pressure levels and third octave band levels up to the 2 kHz third octave band. Compared to more accurate simulations, these guidelines result in an average approximation error in the transfer functions of 1.3 dB in the third octave band SPLs while considerably reducing the evaluation time. Comparison of the simulated and the measured transfer functions show an average error of 4 dB in the third octave band SPLs.
Institute of Scientific and Technical Information of China (English)
彭丽
2002-01-01
The finite element solution of two points boundary value problem for nonlinear ordinary differential equation is studied by using the collocation-Galerkin method.The Jacobi points are introduced to establish high orders of accuracy for the approximate solution.Numerical results are presented for a sample problem.
Finite element analysis of three dimensional crack growth by the use of a boundary element sub model
DEFF Research Database (Denmark)
Lucht, Tore
2009-01-01
A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...
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.
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.
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)
方源; 章桐; 于蓬; 郭荣
2014-01-01
Evaluation of the NVH (noise, vibration and harshness) performance of automotive powertrain has been an integral part of the vehicle development process. Although electric vehicles are generally considerably quieter than their counterparts powered by internal combustion engines, some problems about NVH still exist, which are becoming more challenging in terms of the future of vehicle. Firstly, the sound only from dominant engine but not from tire, wind or auxiliaries disappears, which consequently becomes increasingly audible due to the removal of the masking sound of broadband engine. Moreover, the interior noise is characterized by high-frequency noise components which can be subjectively perceived as annoying and unpleasant. Thirdly, as the electric vehicle develops toward the direction of high speed and large torque, electric vehicle vibration and noise problems highlight gradually. The subject of this paper is the numerical and experimental evaluation of the acoustic behavior of an electric powertrain, which is helpful for the electric vehicle in the design stage. For this purpose, a co-simulation method based on finite element modeling (FEM) and boundary element method (BEM) for the acoustic radiation analysis of an electric powertrain under multi-excitations is presented. The vibration and noise characteristics of electric vehicle are quite different from that of internal combustion engine due to different exciting forces. The calculation of the internal excitations of motor-reducer integrated drive system is the foundation of dynamic analysis. The internal dynamic excitations of a certain electric powertrain in rated revolution are calculated by theoretical analysis and numerical simulation method on the basis of gear dynamics and electromagnetism, including the electromagnetic radial force, electromagnetic tangential force and external circuit in the motor, and the time-varying gear meshing stiffness, meshing error and meshing impact in the gear system
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.
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
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 solve...... for the unknown normal velocities of the structure at the relatively large number of nodes in the numerical model. Efficiently the regularization technique smoothes the solution spatially, since a fast spatial variation is associated with high index singular values, which is filtered out or damped...... in the regularization. Hence, the effective number of degrees of freedom in the model is often much lower than the number of nodes in the model. The present paper deals with an alternative formulation possible for the subset of radiation problems in which a (structural) modal expansion is known for the structure...
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.
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...
Cutanda-Henríquez, Vicente; Juhl, Peter Møller
2013-11-01
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 assume (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.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses ar...
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.
Boundary control of parabolic systems - Finite-element approximation
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
Institute of Scientific and Technical Information of China (English)
杜宁
2001-01-01
Mixed finite element method is used to treat a kind of second-order nonlinear hyperbolic equations with absorbing boundary conditions. explicit-intime procedures are formulated and analyzed. Optimal L2-in-space error estimates are derived.
Anisotropic Boundary Layer Adaptivity of Multi-Element Wings
Chitale, Kedar C; Sahni, Onkar; Shephard, Mark S; Jansen, Kenneth E
2014-01-01
Multi-element wings are popular in the aerospace community due to their high lift performance. Turbulent flow simulations of these configurations require very fine mesh spacings especially near the walls, thereby making use of a boundary layer mesh necessary. However, it is difficult to accurately determine the required mesh resolution a priori to the simulations. In this paper we use an anisotropic adaptive meshing approach including adaptive control of elements in the boundary layers and study its effectiveness for two multi-element wing configurations. The results are compared with experimental data as well as nested refinements to show the efficiency of adaptivity driven by error indicators, where superior resolution in wakes and near the tip region through adaptivity are highlighted.
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)
卢文强; 范庆梅; 郭文
2001-01-01
论文发展了一个能求解带相变运动界面非定常传热和非线性热物理特性问题的双倒易边界元方法。数值模拟了半透明单晶生长中热过程的一个例子。由于方法是纯边界积分方法，计算量与计算内存都大大减少。获得了单晶生长过程瞬态温度场分布和固液相界面形状时间推进的一些结果。%The dual reciprocity boundary element method (DRBEM) has been developed tosolve unsteady heat transfer problems with phase change moving interface andnon-linear thermophysical properties. An example of numerical simulation ofthe thermal process in semi-transparent crystal growth has been made. Sincethe method is pure boundary integral method, this provides a considerablereduction in the storage and the computational requirements while improvingaccuracy. Some results of transient temperature fields and time marchingsolid-liquid phase-change moving interface in the crystal growth are presentedin this paper.
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.
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 conditions for viscous vortex methods
Energy Technology Data Exchange (ETDEWEB)
Koumoutsakos, P.; Leonard, A.; Pepin, F. (California Institute of Technology, Pasadena, CA (United States))
1994-07-01
This paper presents a Neumann-type vorticity boundary condition for the vorticity formulation of the Navier-Stokes equations. The vorticity creation process at the boundary, due to the no-slip condition, is expressed in terms of a vorticity flux. The scheme is incorporated then into a Lagrangian vortex blob method that uses a particle strength exchange algorithm for viscous diffusion. The no-slip condition is not enforced by the generation of new vortices at the boundary but instead by modifying the strength of the vortices in the vicinity of the boundary. 19 refs., 5 figs.
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.
Kriging-Based Finite Element Method: Element-By-Element Kriging Interpolation
Directory of Open Access Journals (Sweden)
W. Kanok-Nukulchai
2009-01-01
Full Text Available An enhancement of the finite element method with Kriging shape functions (K-FEM was recently proposed. In this method, the field variables of a boundary value problem are approximated using ‘element-by-element’ piecewise Kriging interpolation (el-KI. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.
Exterior optical cloaking and illusions by using active sources: A boundary element perspective
Zheng, H. H.; Xiao, J. J.; Lai, Y.; Chan, C. T.
2010-05-01
Recently, it was demonstrated that active sources can be used to cloak any objects that lie outside the cloaking devices [F. Guevara Vasquez, G. W. Milton, and D. Onofrei, Phys. Rev. Lett. 103, 073901 (2009)]. Here, we propose that active sources can create illusion effects so that an object outside the cloaking device can be made to look like another object. Invisibility is a special case in which the concealed object is transformed to a volume of air. From a boundary element perspective, we show that active sources can create a nearly “silent” domain which can conceal any objects inside and at the same time make the whole system look like an illusion of our choice outside a virtual boundary. The boundary element method gives the fields and field gradients, which can be related to monopoles and dipoles, on continuous curves which define the boundary of the active devices. Both the cloaking and illusion effects are confirmed by numerical simulations.
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...
RESEARCH METHODS OF LOCATIVE ELEMENT
Directory of Open Access Journals (Sweden)
SULAYMANOVA N.J.
2012-01-01
Full Text Available The article is devoted to the methods of investigation of locative elements. Sentence analysis with locative elements is taken according to the results of component analysis in the system of contradicting – opposition. More over the article is full of examples related to the description of various syntactic units.
Gwinner, Joachim
2016-12-01
This contribution deals with unilateral contact problems with Tresca friction (given friction model) in hemitropic mi-cropolar elasticity. Based on a boundary integral approach such problems can be reduced to boundary variational inequalities. This suggests the use of boundary element methods for their numerical treatment. With higher order approximation this leads to a nonconforming approximation what can numerically be realized by means of Gauss-Lobatto quadrature. The contribution is based on the recent papers [7, 8] of the author and on joint work [3] with A. Gachechiladze, R. Gachechi-ladze, and D. Natroshvili.
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.
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
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...
Experimental validation of a boundary element solver for exterior acoustic radiation problems
Visser, Rene; Nilsson, A.; Boden, H.
2003-01-01
The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for b
Webb, Christopher J; Zakian, Virginia A
2015-09-08
The stem terminus element (STE), which was discovered 13 y ago in human telomerase RNA, is required for telomerase activity, yet its mode of action is unknown. We report that the Schizosaccharomyces pombe telomerase RNA, TER1 (telomerase RNA 1), also contains a STE, which is essential for telomere maintenance. Cells expressing a partial loss-of-function TER1 STE allele maintained short stable telomeres by a recombination-independent mechanism. Remarkably, the mutant telomere sequence was different from that of wild-type cells. Generation of the altered sequence is explained by reverse transcription into the template boundary element, demonstrating that the STE helps maintain template boundary element function. The altered telomeres bound less Pot1 (protection of telomeres 1) and Taz1 (telomere-associated in Schizosaccharomyces pombe 1) in vivo. Thus, the S. pombe STE, although distant from the template, ensures proper telomere sequence, which in turn promotes proper assembly of the shelterin complex.
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.
Institute of Scientific and Technical Information of China (English)
马杭
2002-01-01
With the aid of the properties of the hypersingular kernels,a geometric conversion approach was presented in this paper.The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary integrals encountered in a variety of applications with boundary element method.Based on the conversion,the hypersingularity in the boundary integrals could be lowered by one order,resulting in the simplification of the computer code.Moreover,an integral transformation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar coordinate system for the nearly hypersingular case.The approach is simple to use,which can be inserted readily to computer code,thus getting rid of the dull routine deduction of formulae before the numerical implementatins,as the expressions of these kernels are in general complicated.The numerical examples were gien in three-dimensional elasticity,verifying the effectiveness of the proposed approach,which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernels across the boundary.
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.
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 ...
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...
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-01
A Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel continuous boundary force (CBF) method is proposed for solving the Navier-Stokes equations subject to the Robin boundary condition. In the CBF method, the Robin boundary condition is replaced by the homogeneous Neumann boundary condition and a volumetric force term added to the momentum conservation equation. Smoothed particle hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two- and three-dimensional flows subject to various forms of the Robin boundary condition in domains bounded by flat and curved boundaries. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite-element method. Considering the no-slip boundary condition as a special case of the slip boundary condition, we demonstrate that the SPH-CBF method accurately describes both the no-slip and slip conditions.
Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements
Talebi, Hossein; Saputra, Albert; Song, Chongmin
2016-10-01
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.
On accurate boundary conditions for a shape sensitivity equation method
Duvigneau, R.; Pelletier, D.
2006-01-01
This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier-Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least-squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite-element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015).
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.
Institute of Scientific and Technical Information of China (English)
LI Ning; XIE Li-li; ZHAI Chang-hai
2007-01-01
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed.Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in corner and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.
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.
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.
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.
Experimental validation of a boundary element solver for exterior acoustic radiation problems
Visser, Rene; Nilsson, A; Boden, H.
2003-01-01
The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for both sound radiation and nearfield acoustic source localization purposes. After validation of the solver with analytic solutions of simple test problems, a well-defined experimental setup has been d...
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....
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
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
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.
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...
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.
Numerical methods for hypersonic boundary layer stability
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Topological structures of boundary value problems in block elements
Babeshko, V. A.; Evdokimova, O. V.; Babeshko, O. M.
2016-10-01
Block structures are considered; a boundary value problem for a system of inhomogeneous partial differential equations with constant coefficients is formulated in each block of a structure. The problem of matching solutions to boundary value problems in blocks with each other by topological study of the properties of solutions in the block structure is examined in the conditions of correct solvability of boundary value problems in blocks of the block structure. Some new properties of solutions to boundary value problems in block structures are found that are important for applications.
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.
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.
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.
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
Least-squares finite-element lattice Boltzmann method.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2004-06-01
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.
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.
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.
Seismic wave propagation in non-homogeneous elastic media by boundary elements
Manolis, George D; Rangelov, Tsviatko V; Wuttke, Frank
2017-01-01
This book focuses on the mathematical potential and computational efficiency of the Boundary Element Method (BEM) for modeling seismic wave propagation in either continuous or discrete inhomogeneous elastic/viscoelastic, isotropic/anisotropic media containing multiple cavities, cracks, inclusions and surface topography. BEM models may take into account the entire seismic wave path from the seismic source through the geological deposits all the way up to the local site under consideration. The general presentation of the theoretical basis of elastodynamics for inhomogeneous and heterogeneous continua in the first part is followed by the analytical derivation of fundamental solutions and Green's functions for the governing field equations by the usage of Fourier and Radon transforms. The numerical implementation of the BEM is for antiplane in the second part as well as for plane strain boundary value problems in the third part. Verification studies and parametric analysis appear throughout the book, as do both ...
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.
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.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The effect of alloying element (Ni, Co, Mn) on P doped Fe 5.3° low angle grain boundary (GB) embrittlement was investigated by the Recursion method. The model of dislocations was used to construct the atomic structure for the P doped GB. The result indicated that the role of impurity and alloying element segregation to GB can be studied with BOI and the difference between their segregation energies at GB and at free surface (FS) (ΔE=Egbseg-Efsseg). The BOI results showed that P leads the “loosening” of the 5.3° low angle GB and decreases the cohesion strength of P doped GB when the alloying element (Ni, Co, or Mn) is added into the P doped 5.3° low angle GB. The ΔE value reveals that the alloying element Ni, Co and Mn have higher energy at P doped 5.3° low angle GB, indicating it serves as a GB embrittler. The BOI results and ΔE calculation were comparable with each other, and they are also consistent with the experimental results, which confirm the embrittling effect of alloying element (Ni, Co, Mn) on P-induced GB embrittlement.
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.
Viscous incompressible flow simulation using penalty finite element method
Directory of Open Access Journals (Sweden)
Sharma R.L.
2012-04-01
Full Text Available Numerical analysis of Navier–Stokes equations in velocity– pressure variables with traction boundary conditions for isothermal incompressible flow is presented. Specific to this study is formulation of boundary conditions on synthetic boundary characterized by traction due to friction and surface tension. The traction and open boundary conditions have been investigated in detail. Navier-Stokes equations are discretized in time using Crank-Nicolson scheme and in space using Galerkin finite element method. Pressure being unknown and is decoupled from the computations. It is determined as post processing of the velocity field. The justification to simulate this class of flow problems is presented through benchmark tests - classical lid-driven cavity flowwidely used by numerous authors due to its simple geometry and complicated flow behavior and squeezed flow between two parallel plates amenable to analytical solution. Results are presented for very low to high Reynolds numbers and compared with the benchmark results.
Boundary integral methods for unsaturated flow
Energy Technology Data Exchange (ETDEWEB)
Martinez, M.J.; McTigue, D.F.
1990-12-31
Many large simulations may be required to assess the performance of Yucca Mountain as a possible site for the nations first high level nuclear waste repository. A boundary integral equation method (BIEM) is described for numerical analysis of quasilinear steady unsaturated flow in homogeneous material. The applicability of the exponential model for the dependence of hydraulic conductivity on pressure head is discussed briefly. This constitutive assumption is at the heart of the quasilinear transformation. Materials which display a wide distribution in pore-size are described reasonably well by the exponential. For materials with a narrow range in pore-size, the exponential is suitable over more limited ranges in pressure head. The numerical implementation of the BIEM is used to investigate the infiltration from a strip source to a water table. The net infiltration of moisture into a finite-depth layer is well-described by results for a semi-infinite layer if {alpha}D > 4, where {alpha} is the sorptive number and D is the depth to the water table. the distribution of moisture exhibits a similar dependence on {alpha}D. 11 refs., 4 figs.,
The finite element method for the global gravity field modelling
Kollár, Michal; Macák, Marek; Mikula, Karol; Minarechová, Zuzana
2014-05-01
We present a finite element approach for solving the fixed gravimetric boundary-value problem on a global level. To that goal, we have defined the computational domain bounded by the real topography and a chosen satellite level. The boundary-value problem consists of the Laplace equation for the disturbing potential and the Neumann boundary condition given by the gravity disturbances applied on the bottom boundary, and the Dirichlet boundary condition given by the disturbing potential applied on the upper boundary. Afterwards, the computational domain is meshed with several different meshes chosen to avoid the problem of simple spherical meshes that contain a singularity at poles. Our aim has been to show how the right mesh can improve results as well as significantly reduce the computational time. The practical implementation has been done in the FEM software ANSYS using 3D linear elements SOLID70 and for solving the linear system of equations, the preconditioned conjugate gradients method has been chosen. The obtained disturbing potential has been applied to calculate the geopotential value W0.
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.
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.
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 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...
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.
Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method
Bogner, Simon; Rüde, Ulrich
2014-01-01
In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\\"orner et al. (2005) is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.
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.
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.
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
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.
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.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...... developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce...
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
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 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)
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.
Complex variable element-free Galerkin method for viscoelasticity problems
Institute of Scientific and Technical Information of China (English)
Cheng Yu-Min; Li Rong-Xin; Peng Miao-Juan
2012-01-01
Based on the complex variable moving least-square (CVMLS) approximation,the complex variable element-free Galerkin (CVEFG) method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper.The Galerkin weak form is employed to obtain the equation system,and the penalty method is used to apply the essential boundary conditions,then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin (EFG) method,with the same node distribution,the CVEFG method has higher precision,and to obtain the similar precision,the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.
FRACTURE CALCULATION OF BENDING PLATES BY BOUNDARY COLLOCATION METHOD
Institute of Scientific and Technical Information of China (English)
王元汉; 伍佑伦; 余飞
2003-01-01
Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it ts only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time This is an effective semi-analytical and semi-numerical method.
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...... accepted scientific methods yet. The objective of this research is to present a comprehensive discussion of system boundaries in LCA and to develop an appropriate boundary delimitation method.A product system is partitioned into the primary system and interrelated subsystems. The hierarchical relationship......, technical, geographical and temporal dimensions are presented to limit the boundaries of LCA. An algorithm is developed to identify an appropriate boundary by searching the process tree and evaluating the environmental impact contribution of each process while it is added into the studied system...
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.
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.
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).
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.
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
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.
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).
Stenroos, Matti
2016-11-01
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 the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
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.
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.
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.
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.
Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation
Directory of Open Access Journals (Sweden)
V. Radhika
2016-01-01
Full Text Available Let R denote the family of functions f(z=z+∑n=2∞anzn of bounded boundary rotation so that Ref′(z>0 in the open unit disk U={z:z<1}. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions f∈R.
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...
Finite element formulation of unilateral boundary conditions for unsaturated flow in porous continua
Abati, A.; Callari, C.
2014-06-01
This paper presents the numerical resolution of unilateral boundary conditions able to effectively model several problems of unsaturated flow, as those involving rainfall infiltration and seepage faces. Besides the penalty technique, we also consider the novel regularization of these conditions by means of the more effective augmented Lagrangian method. The performance of the so-obtained finite element method is carefully investigated in terms of accuracy and ill-conditioning effects, including comparisons with analytical solutions and a complete identification of the analogies with the problem of frictionless contact. In this way, we provide a priori estimates of optimal and admissible ranges for the penalty coefficient as functions of permeability and spatial discretization. The proposed method and the estimated coefficient ranges are validated in further numerical examples, involving the propagation of a wetting front due to rainfall and the partial saturation of an aged concrete dam. These applications show that the proposed regularizations do not induce any detrimental effect on solution accuracy and on convergence rate of the employed Newton-Raphson method. Hence, the present approach should be preferred to the commonly used iterative switching between the imposed-flow and the imposed-pressure conditions, which often leads to spurious oscillations and convergence failures.
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.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Improved non-singular local boundary integral equation method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM), singularities in the local boundary integrals need to be treated specially. In the current paper, local integral equations are adopted for the nodes inside the domain and moving least square approximation (MLSA)for the nodes on the global boundary, thus singularities will not occur in the new algorithm. At the same time, approximation errors of boundary integrals are reduced significantly. As applications and numerical tests, Laplace equation and Helmholtz equation problems are considered and excellent numerical results are obtained. Furthermore,when solving the Helmholtz problems, the modified basis functions with wave solutions areadapted to replace the usually-used monomial basis functions. Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.
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.
The application of finite element method to forward and inverse seismic problems in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shaoyou, J.; Xiangheng, J.; Shizhe, X.
1987-04-01
Unstable result is obtained when the boundary problem of wave equation is solved using finite element method in time domain. However, when the boundary problem of wave equation is solved by finite element method in frequency domain, not only the unstablity can be avoided but also computation is speeded up because of using FFT. The procedure for solving the boundary problem using finite element method in frequency domain is as follows: 1. the wave equation is transformed into Helmholtz equation by making one-dimensional Fourier transform with respect to time; 2. Helmholtz equation is solved using finite element method in frequency domain; 3. the obtained result is returned to time domain by making inverse Fourier transform. Both forward and inverse seismic problems can be solved by this method.
Vdovichenko, I. I.; Yakovlev, M. Ya; Vershinin, A. V.; Levin, V. A.
2016-11-01
One of the key problems of mechanics of composite materials is an estimation of effective properties of composite materials. This article describes the algorithms for numerical evaluation of the effective thermal conductivity and thermal expansion of composites. An algorithm of effective thermal conductivity evaluation is based on sequential solution of boundary problems of thermal conductivity with different boundary conditions (in the form of the temperature on the boundary) on representative volume element (RVE) of composite with subsequent averaging of the resulting vector field of heat flux. An algorithm of effective thermal expansion evaluation is based on the solution of the boundary problem of elasticity (considering the thermal expansion) on a RVE of composite material with subsequent averaging of a resulting strain tensor field. Numerical calculations were performed with the help of Fidesys Composite software module of CAE Fidesys using the finite element method. The article presents the results of numerical calculations of the effective coefficients of thermal conductivity and thermoelasticity for two types of composites (single-layer fiber and particulate materials) in comparison with the analytical estimates. The comparison leads to the conclusion about the correctness of algorithms and program developed.
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).
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.
Pindza, Edson; Maré, Eben
2017-03-01
A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions. The obtained results from discrete singular convolution methods based on single and double exponential transformations are compared with each other, and with the existing methods too. Numerical results confirm that these methods are considerably efficient and accurate in solving singular and regular problems. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.
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.
Vlahopoulos, Nickolas; Lyle, Karen H.; Burley, Casey L.
1998-01-01
An algorithm for generating appropriate velocity boundary conditions for an acoustic boundary element analysis from the kinematics of an operating propeller is presented. It constitutes the initial phase of Integrating sophisticated rotorcraft models into a conventional boundary element analysis. Currently, the pressure field is computed by a linear approximation. An initial validation of the developed process was performed by comparing numerical results to test data for the external acoustic pressure on the surface of a tilt-rotor aircraft for one flight condition.
Efficient ghost cell reconstruction for embedded boundary methods
Rapaka, Narsimha; Al-Marouf, Mohamad; Samtaney, Ravi
2016-11-01
A non-iterative linear reconstruction procedure for Cartesian grid embedded boundary methods is introduced. The method exploits the inherent geometrical advantage of the Cartesian grid and employs batch sorting of the ghost cells to eliminate the need for an iterative solution procedure. This reduces the computational cost of the reconstruction procedure significantly, especially for large scale problems in a parallel environment that have significant communication overhead, e.g., patch based adaptive mesh refinement (AMR) methods. In this approach, prior computation and storage of the weightage coefficients for the neighbour cells is not required which is particularly attractive for moving boundary problems and memory intensive stationary boundary problems. The method utilizes a compact and unique interpolation stencil but also provides second order spatial accuracy. It provides a single step/direct reconstruction for the ghost cells that enforces the boundary conditions on the embedded boundary. The method is extendable to higher order interpolations as well. Examples that demonstrate the advantages of the present approach are presented. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1394-01.
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.
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...
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.
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.
FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS
Institute of Scientific and Technical Information of China (English)
Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon
2002-01-01
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
Institute of Scientific and Technical Information of China (English)
赵慧明; 杨敏; 倪海敏; 臧彤
2011-01-01
Using five different staining methods (I. E. ,H. E. Staining method,Azan (Mallory-Heidenhain-A-zan) staining method, PbH (plumbum hematoxylin) staining method, PAS-OG (periodic acid Schiff's orange G) staining method and Jafri combined staining method for fish pituitary), the histological structure of adenohypophysis during reproduction period in mullet and crucian was observed in depth. Stereology method was applied to measure and calculate the percentage,volume density,average volume and numerical density of the endocrine cells in these two kinds of fish. The results indicated that:l) The pituitary was of front-back style in mullet and dorsoventral style in crucian. 2) Different kinds of endocrine cells could be distinguished in adenohypophysis, with different and special pituitary staining methods. 3) No distinct difference was found between the endocrine cells in adenohypophysis in percentage,volume density,average volume and numerical density using different pituitary staining method in one kind of fish (P>0. 05). 4) It existed distinct difference in percentage, volume density,average volume and numerical density of the endocrine cells in adenohypophysis between the two kinds of fish using the same pituitary staining method (P> 0.05).%为充分利用无网格方法和自然边界元的优点,用无网格和自然边界元耦合的方法来解决带方孔的无界平面弹性问题,通过引入人工边界,用自然边界元方法来描述无界问题,编制无网格和自然边界元耦合方法的相应计算程序.与有限元方法计算结果的比较,表明了耦合方法的有效性.
A new method for constructing analytic elements for groundwater flow.
Strack, O. D.
2007-12-01
The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.
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.
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.
Trace-element anomalies at the Mississippian/Pennsylvanian boundary in Oklahoma and Texas
Orth, Charles J.; Quintana, Leonard R.; Gilmore, James S.; Grayson, Robert C., Jr.; Westergaard, Edwin H.
1986-12-01
Trace-element abundance anomalies have been found at the Mississippian/Pennsylvania boundary at sites in Oklahoma and Texas where the boundary has been precisely located on the basis of an abrupt change in conodont diversity and species composition. Enriched elements include osmium, indium, platinum, chromium, most chalcophiles, rare earths, and uranium. The anomalies are more intense (e.g., Os = 4 ppb, Ir = 0.38 ppb, Pt = 6 ppb, Cr = 12000 ppm, U = 380 ppm) and peisist through a thicker interval at the south-central Texas locality than in Oklahoma, and in bolh locations the anomalies are associated with an increase in phosphate content of the rocks. There is no tangible evidence of an asteroid or comet impact source for the excess Pt-group elements and fauna! crisis. The cause of the elemental enrichments and the biological disturbance may possibly be related to a change in the ocean chemistry of the Paleozoic seaway, such as increased upwelling, stagnation, or nearby submarine volcanism.
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.
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...
Iterative methods for mixed finite element equations
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
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.
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. .
Numerical solution of fuzzy boundary value problems using Galerkin method
Indian Academy of Sciences (India)
SMITA TAPASWINI; S CHAKRAVERTY; JUAN J NIETO
2017-01-01
This paper proposes a new technique based on Galerkin method for solving nth order fuzzy boundary value problem. The proposed method has been illustrated by considering three different cases depending upon the sign of coefficients with benchmark example problems. To show the applicability of the proposed method, an application problem related to heat conduction has also been studied. The results obtained by the proposed methods are compared with the exact solution and other existing methods for demonstrating the validity and efficiency of the present method.
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.
A spectral boundary integral equation method for the 2-D Helmholtz equation
Hu, Fang Q.
1994-01-01
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 nonsmoothness 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 nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.
Discontinuous finite element method for vector radiative transfer
Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping
2017-03-01
The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.
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
ABAQUS动力无限元人工边界研究%Study of ABAQUS dynamic infinite element artificial boundary
Institute of Scientific and Technical Information of China (English)
戚玉亮; 大塚久哲
2014-01-01
Some valuable studies have been done in the aspects of numerical simulation of natural infinite foundation and seismic wave input. The thesis comments the advantages and disadvantages of infinite element, and expatiates on the theory system of ABAQUS infinite element which is improved. The artificial boundary of ABAQUS dynamic infinite element considering the impact of outland fluctuations is proposed. Based on the equivalent boundary force superposition principle, the incident and scattered waves are dealt with separately, and assumed that they are independently to each other. The input ground motion is converted to equivalent stress acting on the interface between the finite element and infinite element to solve the problem of exogenous incident wave. Case study results show that:for the calculation results obtained from inside vibration source and the fixed boundary, the distortion and disturbances appear;the results calculated by the method mentioned above are compared with the results of viscoelastic boundary, which make it certain that the filter function of outgoing scattered wave with the method mentioned above is better than viscoelastic boundary. Therefore, the improved ABAQUS dynamic infinite element boundary method is effective and has certain stability.%针对动力场天然无限地基的数值模拟与地震波输入问题进行了一些有意义的研究，评述了现有动力计算常用无限元的优缺点，详细阐述了ABAQUS无限元理论体系框架，并加以改进，提出一种考虑外域地震动影响的ABAQUS动力无限元人工边界。采用等效边界力的叠加原理，对入射波和散射波分开处理，视入射波和散射波在边界上互不影响，将输入地震动转化为作用于有限元无限元交界面上的等效应力的方法来解决外源波的入射问题。算例验证结果表明：内源振动和固定边界会出现失真和扰动现象，同时该计算结果与黏弹性边界的计算结果对
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.
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.
OPUS-Dom: applying the folding-based method VECFOLD to determine protein domain boundaries.
Wu, Yinghao; Dousis, Athanasios D; Chen, Mingzhi; Li, Jialin; Ma, Jianpeng
2009-01-30
In this article, we present a de novo method for predicting protein domain boundaries, called OPUS-Dom. The core of the method is a novel coarse-grained folding method, VECFOLD, which constructs low-resolution structural models from a target sequence by folding a chain of vectors representing the predicted secondary-structure elements. OPUS-Dom generates a large ensemble of folded structure decoys by VECFOLD and labels the domain boundaries of each decoy by a domain parsing algorithm. Consensus domain boundaries are then derived from the statistical distribution of the putative boundaries and three empirical sequence-based domain profiles. OPUS-Dom generally outperformed several state-of-the-art domain prediction algorithms over various benchmark protein sets. Even though each VECFOLD-generated structure contains large errors, collectively these structures provide a more robust delineation of domain boundaries. The success of OPUS-Dom suggests that the arrangement of protein domains is more a consequence of limited coordination patterns per domain arising from tertiary packing of secondary-structure segments, rather than sequence-specific constraints.
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
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 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.
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]).
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.
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.
Least-squares spectral element method applied to the Euler equations
Gerritsma, M.I.; Bas, R. van der; De Maerschalck, B.; Koren, B.; Deconinck, H.
2008-01-01
This paper describes the application of the least-squares spectral element method to compressible flow problems. Special attention is paid to the imposition of the weak boundary conditions along curved walls and the influence of the time step on the position and resolution of shocks. The method is d
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.
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.
New method for solving the bending problem of rectangular plates with mixed boundary conditions
Directory of Open Access Journals (Sweden)
Liu Xin Min
2016-01-01
Full Text Available A new method is used to solve the rectangular plate bending problem with mixed boundary conditions. The method overcomes the complicated derivation of the classical solution by Fourth-order differential problem into integrating question. Under uniform loading rectangular plate bending problem with one side fixed the opposite side half simply supported half fixed the other two sides free rectangular plate, one side simply supported the opposite side half simply supported half fixed the other two sides free rectangular plate is systematically solved. According to the actual boundary conditions of the rectangular plate, the corresponding characteristic equation can easily be set up. It is presented deflection curve equation and the numerical calculation. By compared the results of the equation to the finite element program, we are able to demonstrate the correctness of the method. So the method not only has certain theoretical value, but also can be directly applied to engineering practice.
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.
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.
Numerical Methods and the Solution of Boundary Value Problems.
1979-12-01
York: The Macmillan Company, 1967. 6. Arfken G. Mathematical Methods for Physicists. New York: Academic Press, 1966. 7. Crandall, S.H. -Engineering...one and two-dimensions. 118 Bibliography 1. Hildebrand, F.B. Methods of Applied Mathematics . New York: Prentice-Hall, Inc., 1952. 2. Hajdin, J. and D...ANUO 1 MERICAL METHODS AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS. (Li weC 79 6 N NELSON UMCLmsZPI I FlTI#WIpwfl-? ii. II.1Ilh Ŗ" MEN Iiii/ I~v I
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.
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.
Directory of Open Access Journals (Sweden)
T. Islam
2012-01-01
Full Text Available This paper presents an efficient model for estimation of soil electric resistivity with depth and layer thickness in a multilayer earth structure. This model is the improvement of conventional two-layer earth model including Wenner resistivity formulations with boundary conditions. Two-layer soil model shows the limitations in specific soil characterizations of different layers with the interrelationships between soil apparent electrical resistivity (ρ and several soil physical or chemical properties. In the multilayer soil model, the soil resistivity and electric potential at any points in multilayer anisotropic soil medium are expressed according to the variation of electric field intensity for geotechnical investigations. For most soils with varying layers, multilayer soil resistivity profile is therefore more suitable to get soil type, bulk density of compacted soil and to detect anomalous materials in soil. A boundary element formulation is implemented to show the multilayer soil model with boundary conditions in soil resistivity estimations. Numerical results of soil resistivity ratio and potential differences for different layers are presented to illustrate the application, accuracy, and efficiency of the proposed model. The nobility of the research is obtaining multilayer soil characterizations through soil electric properties in near surface soil profile.
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.
A Finite Element Method for Simulation of Compressible Cavitating Flows
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
Quantifying trace element and isotope fluxes at the ocean-sediment boundary: a review
Homoky, William B.; Weber, Thomas; Berelson, William M.; Conway, Tim M.; Henderson, Gideon M.; van Hulten, Marco; Jeandel, Catherine; Severmann, Silke; Tagliabue, Alessandro
2016-11-01
Quantifying fluxes of trace elements and their isotopes (TEIs) at the ocean's sediment-water boundary is a pre-eminent challenge to understand their role in the present, past and future ocean. There are multiple processes that drive the uptake and release of TEIs, and properties that determine their rates are unevenly distributed (e.g. sediment composition, redox conditions and (bio)physical dynamics). These factors complicate our efforts to find, measure and extrapolate TEI fluxes across ocean basins. GEOTRACES observations are unveiling the oceanic distributions of many TEIs for the first time. These data evidence the influence of the sediment-water boundary on many TEI cycles, and underline the fact that our knowledge of the source-sink fluxes that sustain oceanic distributions is largely missing. Present flux measurements provide low spatial coverage and only part of the empirical basis needed to predict TEI flux variations. Many of the advances and present challenges facing TEI flux measurements are linked to process studies that collect sediment cores, pore waters, sinking material or seawater in close contact with sediments. However, such sampling has not routinely been viable on GEOTRACES expeditions. In this article, we recommend approaches to address these issues: firstly, with an interrogation of emergent data using isotopic mass-balance and inverse modelling techniques; and secondly, by innovating pursuits of direct TEI flux measurements. We exemplify the value of GEOTRACES data with a new inverse model estimate of benthic Al flux in the North Atlantic Ocean. Furthermore, we review viable flux measurement techniques tailored to the sediment-water boundary. We propose that such activities are aimed at regions that intersect the GEOTRACES Science Plan on the basis of seven criteria that may influence TEI fluxes: sediment provenance, composition, organic carbon supply, redox conditions, sedimentation rate, bathymetry and the benthic nepheloid inventory
Quantifying trace element and isotope fluxes at the ocean–sediment boundary: a review
Berelson, William M.; Severmann, Silke
2016-01-01
Quantifying fluxes of trace elements and their isotopes (TEIs) at the ocean's sediment–water boundary is a pre-eminent challenge to understand their role in the present, past and future ocean. There are multiple processes that drive the uptake and release of TEIs, and properties that determine their rates are unevenly distributed (e.g. sediment composition, redox conditions and (bio)physical dynamics). These factors complicate our efforts to find, measure and extrapolate TEI fluxes across ocean basins. GEOTRACES observations are unveiling the oceanic distributions of many TEIs for the first time. These data evidence the influence of the sediment–water boundary on many TEI cycles, and underline the fact that our knowledge of the source–sink fluxes that sustain oceanic distributions is largely missing. Present flux measurements provide low spatial coverage and only part of the empirical basis needed to predict TEI flux variations. Many of the advances and present challenges facing TEI flux measurements are linked to process studies that collect sediment cores, pore waters, sinking material or seawater in close contact with sediments. However, such sampling has not routinely been viable on GEOTRACES expeditions. In this article, we recommend approaches to address these issues: firstly, with an interrogation of emergent data using isotopic mass-balance and inverse modelling techniques; and secondly, by innovating pursuits of direct TEI flux measurements. We exemplify the value of GEOTRACES data with a new inverse model estimate of benthic Al flux in the North Atlantic Ocean. Furthermore, we review viable flux measurement techniques tailored to the sediment–water boundary. We propose that such activities are aimed at regions that intersect the GEOTRACES Science Plan on the basis of seven criteria that may influence TEI fluxes: sediment provenance, composition, organic carbon supply, redox conditions, sedimentation rate, bathymetry and the benthic nepheloid
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...
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
Well test imaging - a new method for determination of boundaries from well test data
Energy Technology Data Exchange (ETDEWEB)
Slevinsky, B.A.
1997-08-01
A new method has been developed for analysis of well test data, which allows the direct calculation of the location of arbitrary reservoir boundaries which are detected during a well test. The method is based on elements of ray tracing and information theory, and is centered on the calculation of an instantaneous {open_quote}angle of view{close_quote} of the reservoir boundaries. In the absence of other information, the relative reservoir shape and boundary distances are retrievable in the form of a Diagnostic Image. If other reservoir information, such as 3-D seismic, is available; the full shape and orientation of arbitrary (non-straight line or circular arc) boundaries can be determined in the form of a Reservoir Image. The well test imaging method can be used to greatly enhance the information available from well tests and other geological data, and provides a method to integrate data from multiple disciplines to improve reservoir characterization. This paper covers the derivation of the analytical technique of well test imaging and shows examples of application of the technique to a number of reservoirs.
ERROR ANALYSIS FOR A FAST NUMERICAL METHOD TO A BOUNDARY INTEGRAL EQUATION OF THE FIRST KIND
Institute of Scientific and Technical Information of China (English)
Jingtang Ma; Tao Tang
2008-01-01
For two-dimensional boundary integral equations of the first kind with logarithmic kernels,the use of the conventional boundary element methods gives linear systems with dense matrix.In a recent work [J.Comput.Math.,22 (2004),pp.287-298],it is demonstrated that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules.The numerical experiments also indicate that the proposed numerical methods require less computational time than the conventional ones while the formal rate of convergence can be preserved.The purpose of this work is to establish a stability and convergence theory for this fast numerical method.The stability analysis depends on a decomposition of the coefficient matrix for the collocation equation.The formal orders of convergence observed in the numerical experiments are proved rigorously.
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.
Test Simulation using Finite Element Method
Energy Technology Data Exchange (ETDEWEB)
Ali, M B; Abdullah, S; Nuawi, M Z; Ariffin, A K, E-mail: abgbas@yahoo.com [Department of Mechanical and Materials Engineering, Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia 43600 Bangi, Selangor (Malaysia)
2011-02-15
The dynamic responses of the standard Charpy impact machine are experimentally studied using the relevant data acquisition system, for the purpose of obtaining the impact response. For this reason, the numerical analysis by means of the finite element method has been used for experiment findings. Modelling of the charpy test was performed in order to obtain strain in the striker during the test. Two types of standard charpy specimens fabricated from different materials, i.e. aluminium 6061 and low carbon steel 1050, were used for the impact simulation testing. The related parameters on between different materials, energy absorbed, strain signal, power spectrum density (PSD) and the relationship between those parameters was finally correlated and discussed.
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.
Chen, Li-Chieh; Huang, Mei-Jiau
2017-02-01
A 2D simulation method for a rigid body moving in an incompressible viscous fluid is proposed. It combines one of the immersed-boundary methods, the DFFD (direct forcing fictitious domain) method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid-structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. A pseudo body force is imposed within the solid domain to enforce the rigid body motion and a Lagrangian mesh composed of triangular elements is employed for tracing the rigid body. In particular, a so called sub-cell scheme is proposed to smooth the discontinuity at the fluid-solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures.
Stenroos, Matti; Haueisen, Jens
2008-09-01
In electrocardiographic imaging, epicardial potentials are reconstructed computationally from electrocardiographic measurements. The reconstruction is typically done with the help of the boundary element method (BEM), using the point collocation weighting and constant or linear basis functions. In this paper, we evaluated the performance of constant and linear point collocation and Galerkin BEMs in the epicardial potential problem. The integral equations and discretizations were formulated in terms of the single- and double-layer operators. All inner element integrals were calculated analytically. The computational methods were validated against analytical solutions in a simplified geometry. On the basis of the validation, no method was optimal in all testing scenarios. In the forward computation of the epicardial potential, the linear Galerkin (LG) method produced the smallest errors. The LG method also produced the smallest discretization error on the epicardial surface. In the inverse computation of epicardial potential, the electrode-specific transfer matrix performed better than the full transfer matrix. The Tikhonov 2 regularization outperformed the Tikhonov 0. In the optimal modeling conditions, the best BEM technique depended on electrode positions and chosen error measure. When large modeling errors such as omission of the lungs were present, the choice of the basis and weighting functions was not significant.
Application of higher-order numerical methods to the boundary-layer equations
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
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.
A two-dimensional embedded-boundary method for convection problems with moving boundaries
Hassen, Y.J.; Koren, B.
2010-01-01
In this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes in the imme
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.
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.
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.
Applications of Taylor-Galerkin finite element method to compressible internal flow problems
Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.
1989-01-01
A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.
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.
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.
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)
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.
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.
Singularity Preserving Numerical Methods for Boundary Integral Equations
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Scheiber, D.; Pippan, R.; Puschnig, P.; Romaner, L.
2016-12-01
We report high throughput density functional theory (DFT) calculations to simulate segregation of s- and p-elements in Mo and W. First, the preference of solutes for interstitial or substitutional positions in the bulk is evaluated and then the segregation energies for the solutes to interstitial and different substitutional sites at a grain boundary (GB) and a free surface (FS) are computed. We show that several solutes change their site preference from substitutional to interstitial position upon segregation to the GB. With the segregation energies to GB and FS, the changes in cohesion can be calculated and GB cohesion enhancing solutes can be identified. The results show striking similarity for both W and Mo. In addition, we collected the available literature data from experimental and theoretical side, which we consequently compare to our results. From our results and the comparison to literature, we identify B, C and Be as potential alloying additions for an increased GB cohesion in Mo and W.
High-speed boundary layer transition induced by a discrete roughness element
Iyer, Prahladh; Mahesh, Krishnan
2011-11-01
The effect of a hemispherical bump on a Mach 3.37 laminar boundary layer is studied using DNS for three conditions with k / δ = 2.54, 0.25 and 0.125, where k is the roughness height. The simulation parameters are based on the experiment by Danehy et. al. (AIAA-2009-394). The flow downstream of the roughness is transitional for all the three conditions accompanied by a rise in skin friction and heat transfer. Upon interaction with the roughness element, the boundary layer separates to form a series of spanwise vortices upstream and a shear layer. These vortices wrap around the roughness to yield a system of streamwise vortices downstream. Perturbation of the shear layer due to the vortices results in the formation of hairpin-shaped vortices further downstream of the roughness. While hairpin vortices were observed in both the center plane and off-symmetry planes on either side for the smallest δ case, they were observed only in the center plane for the other cases. This work was supported by NASA under the hypersonics NRA program under grant NNX08AB33A.
Directory of Open Access Journals (Sweden)
Wen-Jeng Huang
2016-02-01
Full Text Available We develop a folding boundary element model in a medium containing a fault and elastic layers to show that anticlines growing over slipping reverse faults can be significantly amplified by mechanical layering buckling under horizontal shortening. Previous studies suggested that folds over blind reverse faults grow primarily during deformation increments associated with slips on the fault during and immediately after earthquakes. Under this assumption, the potential for earthquakes on blind faults can be determined directly from fold geometry because the amount of slip on the fault can be estimated directly from the fold geometry using the solution for a dislocation in an elastic half-space. Studies that assume folds grown solely by slip on a fault may therefore significantly overestimate fault slip. Our boundary element technique demonstrates that the fold amplitude produced in a medium containing a fault and elastic layers with free slip and subjected to layer-parallel shortening can grow to more than twice the fold amplitude produced in homogeneous media without mechanical layering under the same amount of shortening. In addition, the fold wavelengths produced by the combined fault slip and buckling mechanisms may be narrower than folds produced by fault slip in an elastic half space by a factor of two. We also show that subsurface fold geometry of the Kettleman Hills Anticline in Central California inferred from seismic reflection image is consistent with a model that incorporates layer buckling over a dipping, blind reverse fault and the coseismic uplift pattern produced during a 1985 earthquake centered over the anticline forelimb is predicted by the model.
Enhanced patch test of finite element methods
Institute of Scientific and Technical Information of China (English)
CHEN; Wanji
2006-01-01
Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.
A method for making an alkaline element
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.
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.
Three-dimensional nanoelectronic device simulation using spectral element methods
Cheng, Candong
The purpose of this thesis is to develop an efficient 3-Dimensional (3-D) nanoelectronic device simulator. Specifically, the self-consistent Schrodinger-Poisson model was implemented in this simulator to simulate band structures and quantum transport properties. Also, an efficient fast algorithm, spectral element method (SEM), was used in this simulator to achieve spectral accuracy where the error decreases exponentially with the increase of sampling densities and the basis order of the polynomial functions, thus significantly reducing the CPU time and memory usage. Moreover, within this simulator, a perfectly matched layer (PML) boundary condition method was used for the Schrodinger solver, which significantly simplifies the problem and reduces the computational time. Furthermore, the effective mass in semiconductor devices was treated as a full anisotropic mass tensor, which provides an excellent tool to study the anisotropy characteristics along arbitrary orientation of the device. Nanoelectronic devices usually involve the simulations of energy band and quantum transport properties. One of the models to perform these simulations is by solving a self-consistent Schrodinger-Poisson system. Two efficient fast algorithms, spectral grid method (SGM) and SEM, are investigated and implemented in this thesis. The spectral accuracy is achieved in both algorithms, whose errors decrease exponentially with the increase of the sampling density and basis orders. The spectral grid method is a pseudospectral method to achieve a high-accuracy result by choosing special nonuniform grid set and high-order Lagrange interpolants for a partial differential equation. Spectral element method is a high-order finite element method which uses the Gauss-Lobatto-Legendre (GLL) polynomials to represent the field variables in the Schrodinger-Poisson system and, therefore, to achieve spectral accuracy. We have implemented the SGM in the Schrodinger equation to solve the energy band structures
Directory of Open Access Journals (Sweden)
Ping Zhang
2014-01-01
Full Text Available The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.
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.
New numerical analysis method in computational mechanics: composite element method
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new type of FEM, called CEM (composite element method), is proposed to solve the static and dynamic problems of engineering structures with high accuracy and efficiency. The core of this method is to define two sets of coordinate systems for DOF's description after discretizing the structure, i.e. the nodal coordinate system UFEM(ξ) for employing the conventional FEM, and the field coordinate system UCT(ξ) for utilizing classical theory. Then, coupling these two sets of functional expressions could obtain the composite displacement field U(ξ) of CEM. The computations of the stiffness and mass matrices can follow the conventional procedure of FEM. Since the CEM inherents some good properties of the conventional FEM and classical analytical method, it has the powerful versatility to various complex geometric shapes and excellent approximation. Many examples are presented to demonstrate the ability of CEM.
New numerical analysis method in computational mechanics: composite element method
Institute of Scientific and Technical Information of China (English)
曾攀
2000-01-01
A new type of FEM, called CEM (composite element method), is proposed to solve the static and dynamic problems of engineering structures with high accuracy and efficiency. The core of this method is to define two sets of coordinate systems for DOF’ s description after discretizing the structure, i.e. the nodal coordinate system UFEM(ζ) for employing the conventional FEM, and the field coordinate system UCT(ζ) for utilizing classical theory. Then, coupling these two sets of functional expressions could obtain the composite displacement field U(ζ) of CEM. The computations of the stiffness and mass matrices can follow the conventional procedure of FEM. Since the CEM inherents some good properties of the conventional FEM and classical analytical method, it has the powerful versatility to various complex geometric shapes and excellent approximation. Many examples are presented to demonstrate the ability of CEM.
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.
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.
Xia, Yi-Ming
2015-01-01
A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a multireolution finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The rational MRA enables the implementation of the multiresolution Mindlin plate element method to be more rational and efficient than that of the conventional monoresolution or o...
A method for making a dry element
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.
A coupled BEM-FEM method for finite strain magneto-elastic boundary-value problems
Nedjar, B.
2016-12-01
The first objective of this contribution is the formulation of nonlinear problems in magneto-elasticity involving finite geometry of the surrounding free space. More specifically for the magnetic part of the problem, the surrounding free space is described by means of a boundary integral equation for which boundary elements are used that are appropriately coupled with the finite element discretization used inside the material. The second objective is to develop a numerical strategy to solve the strongly coupled magneto-mechanics problem at hand. Herein we provide a staggered scheme consisting of a magnetostatic resolution employing the above coupled BEM-FEM procedure at fixed deformation, followed by a mechanical resolution at fixed magnetic fields. This decoupled method renders the whole solution strategy very appealing since, among others, the first BEM-FEM resolution is linear for some prototype models, and the remaining mechanical resolution is analogous to nowadays classical nonlinear elastostatic problems in the finite strain range. Some nonlinear boundary-value problems are simulated to demonstrate the applicability of the proposed framework.
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.
Level set immersed boundary method for gas-liquid-solid interactions
Wang, Shizhao; Balaras, Elias
2015-11-01
We will discuss an approach to simulate the interaction between free surface flows and deformable structures. In our formulation the Navier-Stokes equations are solved on a block-structured grid with adaptive mesh refinement, and the pressure jumps across the interface between different phases, which is tracked using a level set approach, are sharply defined. Deformable structures are simulated with a solid mechanics solver utilizing a finite element method. The overall approach is tailored to problems with large displacement/deformations. The boundary conditions on a solid body are imposed using a direct forcing, immersed boundary method (Vanella & Balaras, J. Comput. Physics, 228(18), 6617-6628, 2009). The flow and structural solvers are coupled by a predictor-corrector, strong-coupling scheme. The consistency between the Eulerian field based level set method for fluid-fluid interface and Lagrangian marker based immersed boundary method for fluid-structure interface is ensured by reconstructing the flow field around the three phase intersections. A variety of 2D and 3D problems ranging from water impact of wedges, entry and exit of cylinders and flexible plates interacting with a free surfaces, are presented to demonstrate the accuracy of the proposed approach. Supported by ONR N000141110588 monitored by Dr. Thomas Fu.
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.
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.
A FINITE ELEMENT MODEL OF IN VIVO MOUSE TIBIAL COMPRESSION LOADING: INFLUENCE OF BOUNDARY CONDITIONS
Directory of Open Access Journals (Sweden)
Hajar Razi
2014-12-01
Full Text Available Though bone is known to adapt to its mechanical challenges, the relationship between the local mechanical stimuli and the adaptive tissue response seems so far unclear. A major challenge appears to be a proper characterization of the local mechanical stimuli of the bones (e.g. strains. The finite element modeling is a powerful tool to characterize these mechanical stimuli not only on the bone surface but across the tissue. However, generating a predictive finite element model of biological tissue strains (e.g., physiological-like loading encounters aspects that are inevitably unclear or vague and thus might significantly influence the predicted findings. We aimed at investigating the influence of variations in bone alignment, joint contact surfaces and displacement constraints on the predicted strains in an in vivo mouse tibial compression experiment. We found that the general strain state within the mouse tibia under compressive loading was not affected by these uncertain factors. However, strain magnitudes at various tibial regions were highly influenced by specific modeling assumptions. The displacement constraints to control the joint contact sites appeared to be the most influential factor on the predicted strains in the mouse tibia. Strains could vary up to 150% by modifying the displacement constraints. To a lesser degree, bone misalignment (from 0 to 20° also resulted in a change of strain (+300 µε = 40%. The definition of joint contact surfaces could lead to up to 6% variation. Our findings demonstrate the relevance of the specific boundary conditions in the in vivo mouse tibia loading experiment for the prediction of local mechanical strain values using finite element modeling.
Adaptive finite element-element-free Galerkin coupling method for bulk metal forming processes
Institute of Scientific and Technical Information of China (English)
Lei-chao LIU; Xiang-huai DONG; Cong-xin LI
2009-01-01
An adaptive finite element-element-free Galerkin (FE-EFG) coupling method is proposed and developed for the numerical simulation of bulk metal forming processes. This approach is able to adaptively convert distorted FE elements to EFG domain in analysis. A new scheme to implement adaptive conversion and coupling is presented. The coupling method takes both advantages of finite element method (FEM) and meshless methods. It is capable of handling large deformations with no need of remeshing procedures, while it is computationally more efficient than those full meshless methods. The effectiveness of the proposed method is demonstrated with the numerical simulations of the bulk metal forming processes including forging and extrusion.
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
A set of mixed-elements patterns for domain boundary approximation in hexahedral meshes.
Lobos, Claudio
2013-01-01
Hexahedral meshes are largely used by the Finite Element Method in a high variety of simulation problems. One of the most common problems of these type of meshes is to achieve an adequate approximation of curved domains; a feature typically found in the shape of organs. This work introduces a set of mixed-elements patterns, which are employed at the surface of target domain, and allow to conserve hexahedra elsewhere. These patterns are meant to be combined with any meshing technique producing a regular or non-regular hexahedral mesh.
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 ...
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.
A method of quaternion typification of Clifford algebra elements
Shirokov, Dmitry
2008-01-01
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method of analysis of commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebra elements.
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.
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.
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...
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.
A new multiresolution finite element method based on a multiresolution quadrilateral plate element
Xia, YiMing
2014-01-01
A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape function. The basic node shape function is constructed by extending shape function around a specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node quadrilateral plate element and method is a monoresolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is fully determined by the RL, not by th...
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.
Vibration Analysis of Plates by MLS-Element Method
Zhou, L.; Xiang, Y.
2010-05-01
This paper presents a novel numerical method, the moving least square element (MLS-element) method for the free vibration analysis of plates based on the Mindlin shear deformable plate theory. In the MLS-element method, a plate can be first divided into multiple elements which are connected through selected nodal points on the interfaces of the elements. An element can be of any shape and the size of the element varies dependent on the problem at hand. The shape functions of the element for the transverse displacement and the rotations are derived based on the MLS interpolation technique. The convergence and accuracy of the method can be controlled by either increasing the number of elements or by increasing the number of MLS interpolation points within elements. Two selected examples for vibration of a simply supported square Mindlin plate and a clamped L-shaped Mindlin plate are studied to illustrate the versatility and accuracy of the proposed method. It shows that the proposed method is highly accurate and flexible for the vibration analysis of plate problems. The method can be further developed to bridge the existing meshless method and the powerful finite element method in dealing with various engineering computational problems, such as large deformation and crack propagation in solid mechanics.
Chebyshev-Fourier Spectral Methods for Nonperiodic Boundary Value Problems
Directory of Open Access Journals (Sweden)
Bojan Orel
2014-01-01
Full Text Available A new class of spectral methods for solving two-point boundary value problems for linear ordinary differential equations is presented in the paper. Although these methods are based on trigonometric functions, they can be used for solving periodic as well as nonperiodic problems. Instead of using basis functions periodic on a given interval −1,1, we use functions periodic on a wider interval. The numerical solution of the given problem is sought in terms of the half-range Chebyshev-Fourier (HCF series, a reorganization of the classical Fourier series using half-range Chebyshev polynomials of the first and second kind which were first introduced by Huybrechs (2010 and further analyzed by Orel and Perne (2012. The numerical solution is constructed as a HCF series via differentiation and multiplication matrices. Moreover, the construction of the method, error analysis, convergence results, and some numerical examples are presented in the paper. The decay of the maximal absolute error according to the truncation number N for the new class of Chebyshev-Fourier-collocation (CFC methods is compared to the decay of the error for the standard class of Chebyshev-collocation (CC methods.
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.
Zengxi, Ge; Canyun, Wang; Ting, Lei; Xiaofei, Chen
2007-09-01
In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a two-dimensional medium with the discrete wave-number method in the vertical direction. The method is validated by comparing the results obtained by this method with those obtained by the finite-difference method. The method is used to study the effect on wave propagation in a vertical borehole of a vertical fracture. For a monopole source, the dispersion curves for Stoneley waves yield three branches. For dipole and quadrupole sources, different orientations of the source yield different results. When the dipole source is orthogonal to the fracture, the dispersion curve is similar to that of the open hole, while the curves are quite different when the source is parallel to the fracture. These characteristics enable us to determine the orientation of the vertical fracture.
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.
Parallel computation with the spectral element method
Energy Technology Data Exchange (ETDEWEB)
Ma, Hong
1995-12-01
Spectral element models for the shallow water equations and the Navier-Stokes equations have been successfully implemented on a data parallel supercomputer, the Connection Machine model CM-5. The nonstaggered grid formulations for both models are described, which are shown to be especially efficient in data parallel computing environment.
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.
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.
NON SPURIOUS SPECTRAL-LIKE ELEMENT METHODS FOR MAXWELL'S EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gary Cohen; Marc Duruflé
2007-01-01
In this paper, we give the state of the art for the so called "mixed spectral elements" for Maxwell's equations. Several families of elements, such as edge elements and discontinuous Galerkin methods (DGM) are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is a novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.
Valero, Enrique; Adán, Antonio; Cerrada, Carlos
2012-11-22
In this paper we present a method that automatically yields Boundary Representation Models (B-rep) for indoors after processing dense point clouds collected by laser scanners from key locations through an existing facility. Our objective is particularly focused on providing single models which contain the shape, location and relationship of primitive structural elements of inhabited scenarios such as walls, ceilings and floors. We propose a discretization of the space in order to accurately segment the 3D data and generate complete B-rep models of indoors in which faces, edges and vertices are coherently connected. The approach has been tested in real scenarios with data coming from laser scanners yielding promising results. We have deeply evaluated the results by analyzing how reliably these elements can be detected and how accurately they are modeled.
A parallel Processing Method in Finite Element Analysis using Domain Division
Iwano, Kenji; Cingoski, Vlatko; Kaneda, Kazufumi; Yamashita, Hideo
1994-01-01
Current parallel processing aproaches in finite element analysis can be roughly classified into two categories: In the domain method, analysis region is divided into subdomains and one CPU assigned to each subdomain. Alternatively, one may calculate in parallel the matrix and vector products which arise in the process of solving the set of simultaneous equations. In this paper, we present a hybrid of the above two methods. Iteration to bring values on the subdomain boundaries coincide is not ...
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...
High-speed laminar-turbulent boundary layer transition induced by a discrete roughness element
Iyer, Prahladh; Mahesh, Krishnan
2013-11-01
Direct numerical simulation (DNS) is used to study laminar to turbulent transition induced by a discrete hemispherical roughness element in a high-speed laminar boundary layer. The simulations are performed under conditions matching the experiments of Danehy et al. (AIAA Paper 2009-394, 2009) for free-stream Mach numbers of 3.37, 5.26 and 8.23. It is observed that the Mach 8.23 flow remains laminar downstream of the roughness, while the lower Mach numbers undergo transition. The Mach 3.37 flow undergoes transition closer to the bump when compared with Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in Cf and Ch (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in Cf until 20 D downstream. The mean van Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 show good agreement with available data. A local Reynolds number based on the wall properties is seen to correlate with the onset of transition for the cases considered. Partially supported by NASA.
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
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Mohammad Maleki
2012-01-01
Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.
Matched Interface and Boundary Method for Elasticity Interface Problems
Wang, Bao; Xia, Kelin; Wei, Guo-Wei
2015-01-01
Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms. PMID:25914439
Boundary potential of lipid bilayers: methods and interpretations
Ermakov, Yu A.; Nesterenko, A. M.
2017-01-01
The electric field distribution at the boundaries of cell membrane consists of diffuse part of the electrical double layer and the potential drop over polar area inside the membrane itself. The latter is generally attributed to the dipole effect, which depends on the lipid hydration and phase state. This report focuses on the experimental approaches developed to detect the relation between dipole effects and the bilayer structure, and to study their molecular nature. The total boundary potential (BP) of planar bilayer lipid membranes (BLM) can be controlled by Intramembranous Field Compensation (IFC) method developed in our laboratory. When combined with electrokinetic measurements in liposome suspension it allows detecting the changes of the dipole potential due to adsorption of inorganic cations and charged molecules. Multivalent inorganic cations increase the dipole potential up to 100-150 mV and make the membrane rigid. Most of these observations were simulated by Molecular Dynamics (MD) in order to visualize the relationship of electric field with the different structural factors (lipid structure, water orientation, ion adsorption etc.) responsible for its dipole component. Two principal contributors to BP – water and lipid molecules – create the opposite effects. The negative contribution with respect to the bulk is due to lipid itself and the inorganic cation penetration into the polar area of membrane. The positive contribution is caused by water orientation. Particularly, in the case of lysine adsorption, the contribution of water includes the rearrangement of H-bonds with the lipid phosphate group. This fact explains well the unusual kinetic phenomena registered by IFC in the case of polylysine adsorption at the BLM surface.
Convergence of adaptive finite element methods for eigenvalue problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2008-01-01
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
Finite element method for thermal analysis of concentrating solar receivers
Shtrakov, Stanko; Stoilov, Anton
2006-01-01
Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great number of numerical experiments is carried out. Illustrative numerical results are given for an array...
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
A finite element method for growth in biological development.
Murea, Cornel M; Hentschel, H G E
2007-04-01
We describe finite element simulations of limb growth based on Stokes flow models with a nonzero divergence representing growth due to nutrients in the early stages of limb bud development. We introduce a "tissue pressure" whose spatial derivatives yield the growth velocity in the limb and our explicit time advancing algorithm for such tissue flows is described in de tail. The limb boundary is approached by spline functions to compute the curvature and the unit outward normal vector. At each time step, a mixed hybrid finite element problem is solved, where the condition that the velocity is strictly normal to the limb boundary is treated by a Lagrange multiplier technique. Numerical results are presented.
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.
An Element Free Galerkin method for an elastoplastic coupled to damage analysis
Directory of Open Access Journals (Sweden)
Sendi Zohra
2016-01-01
Full Text Available In this work, a Meshless approach for nonlinear solid mechanics is developed based on the Element Free Galerkin method. Furthermore, Meshless is combined with an elastoplastic model coupled to ductile damage. The efficiency of the proposed methodology is evaluated through various numerical examples. Besides these, two-dimensional tensile tests under several boundary conditions were studied and solved by a Dynamic-Explicit resolution scheme. Finally, the results obtained from the numerical simulations are analyzed and critically compared with Finite Element Method results.
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.
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...
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。
Finite element methods in resistivity logging
Lovell, J. R.
1993-09-01
Resistivity measurements are used in geophysical logging to help determine hydrocarbon reserves. The derivation of formation parameters from resistivity measurements is a complicated nonlinear procedure often requiring additional geological information. This requires an excellent understanding of tool physics, both to design new tools and interpret the measurements of existing tools. The Laterolog measurements in particular are difficult to interpret because the response is very nonlinear as a function of electrical conductivity, unlike Induction measurements. Forward modeling of the Laterolog is almost invariably done with finite element codes which require the inversion of large sparse matrices. Modern techniques can be used to accelerate this inversion. Moreover, an understanding of the tool physics can help refine these numerical techniques.
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.
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method
1989-08-01
jACCESSION NO. 11. TITLE (Include Security Classification) (UNCLASSIFIED) ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS FOR THE TRANSFER MATRIX METHOD 12...SECURITY CLASSIFICATION OF THIS PAGE AFIT/CI "OVERPRINT" iii ABSTRACT Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method. (August...analysts in indus- try . ’ . ," Accesiu:, For NTIS CR,4i Fi FilC TA,: [3 0. fi A-1 B I ., ,.................. ,., ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using...
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...
A finite-volume method for convection problems with embedded moving boundaries
Hassen, Y.J.; Koren, B.
2009-01-01
An accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. Moving interior boundary conditions are embedded in the fixed-grid fluxes in the direct neighborhood of the moving boundaries. Tailor-made limiters are derived such
Efficient Finite Element Methods for Transient Analysis of Shells.
1985-04-01
Triangular Shell Element with Improved Membrane Interpolation," Communications in Applied Numerical Methods , in press 1985. Results of this work were...in Applied Numerical Methods , to appear. G.R. Cowper, G.M. Lindberg and M.D. Olson (1970), "A Shallow Shell Finite Element of Triangular Shape," Int. J
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
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.
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.
Demkowicz, L.; Oden, J. T.; Rachowicz, W.
1990-01-01
A new finite element method solving compressible Navier-Stokes equations is proposed. The method is based on a version of Strang's operator splitting and an h-p adaptive finite element approximation in space. This paper contains the formulation of the method with a detailed discussion of boundary conditions, a sample adaptive strategy and numerical examples involving compressible viscous flow over a flat plate with Reynolds number Re = 1000 and Re = 10,000.
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
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.
A high-order accurate embedded boundary method for first order hyperbolic equations
Mattsson, Ken; Almquist, Martin
2017-04-01
A stable and high-order accurate embedded boundary method for first order hyperbolic equations is derived. Where the grid-boundaries and the physical boundaries do not coincide, high order interpolation is used. The boundary stencils are based on a summation-by-parts framework, and the boundary conditions are imposed by the SAT penalty method, which guarantees linear stability for one-dimensional problems. Second-, fourth-, and sixth-order finite difference schemes are considered. The resulting schemes are fully explicit. Accuracy and numerical stability of the proposed schemes are demonstrated for both linear and nonlinear hyperbolic systems in one and two spatial dimensions.
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.
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.
Institute of Scientific and Technical Information of China (English)
J. Awrejcewicz; A.V. Krysko; J. Mrozowski; O.A. Saltykova; M.V. Zhigalov
2011-01-01
Chaotic vibrations of flexible non-linear EulerBernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ωp, q0} is reported, and scenarios of the system transition into chaos are illustrated.
Transforming Mean and Osculating Elements Using Numerical Methods
Ely, Todd A.
2010-01-01
Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order
Heyland, Mark; Trepczynski, Adam; Duda, Georg N; Zehn, Manfred; Schaser, Klaus-Dieter; Märdian, Sven
2015-12-01
Selection of boundary constraints may influence amount and distribution of loads. The purpose of this study is to analyze the potential of inertia relief and follower load to maintain the effects of musculoskeletal loads even under large deflections in patient specific finite element models of intact or fractured bone compared to empiric boundary constraints which have been shown to lead to physiological displacements and surface strains. The goal is to elucidate the use of boundary conditions in strain analyses of bones. Finite element models of the intact femur and a model of clinically relevant fracture stabilization by locking plate fixation were analyzed with normal walking loading conditions for different boundary conditions, specifically re-balanced loading, inertia relief and follower load. Peak principal cortex surface strains for different boundary conditions are consistent (maximum deviation 13.7%) except for inertia relief without force balancing (maximum deviation 108.4%). Influence of follower load on displacements increases with higher deflection in fracture model (from 3% to 7% for force balanced model). For load balanced models, follower load had only minor influence, though the effect increases strongly with higher deflection. Conventional constraints of fixed nodes in space should be carefully reconsidered because their type and position are challenging to justify and for their potential to introduce relevant non-physiological reaction forces. Inertia relief provides an alternative method which yields physiological strain results.
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.
Khayat, Roger E.; Genouvrier, Delphine
2001-05-01
An adaptive (Lagrangian) boundary element approach is proposed for the general three-dimensional simulation of confined free-surface Stokes flow. The method is stable as it includes remeshing capabilities of the deforming free surface and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free-surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several flow problems are presented to illustrate the utility of the approach, particularly as encountered in polymer processing and rheology. These problems illustrate the transient nature of the flow during the processes of extrusion and thermoforming, the elongation of a fluid sample in an extensional rheometer, and the coating of a sphere. Surface tension effects are also explored. Copyright
Immersed boundary peridynamics (IB/PD) method to simulate aortic dissection
Bhalla, Amneet Pal Singh; Griffith, Boyce
2016-11-01
Aortic dissection occurs when an intimal tear in the aortic wall propagates into the media to form a false lumen within the vessel wall. Rupture of the false lumen and collapse of the true lumen both carry a high risk of morbidity and mortality. Surgical treatment consists of either replacement of a portion of the aorta, or stent implantation to cover the affected segment. Both approaches carry significant risks: open surgical intervention is highly invasive, whereas stents can be challenging to implant and offer unclear long-term patient outcomes. It is also difficult to time optimally the intervention to ensure that the benefits of treatment outweigh its risks. In this work we develop innovative fluid-structure interaction (FSI) model combining elements from immersed boundary (IB) and peridynamics (PD) methods to simulate tears in membranes. The new approach is termed as IB/PD method. We use non-ordinary state based PD to represent material hyperelasticity. Several test problems are taken to validate peridynamics approach to model structural dynamics, with and without accounting for failure in the structures. FSI simulations using IB/PD method are compared with immersed finite element method (IB/FE) to validate the new hybrid approach. NIH Award R01HL117163 NSF Award ACI 1450327.
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.
Directory of Open Access Journals (Sweden)
Someshwar S. Pandey
2013-10-01
Full Text Available Numerical simulation using computers has increasingly become a very important approach for solving problems in engineering and science. It plays a valuable role in providing tests and examinations for theories, offering insights to complex physics, and assisting in the interpretation and even the discovery of new phenomena. Grid or mesh based numerical methods such as FDM, CFD, FEM despite of great success, suffer from difficulties in some aspects, which limit their applications in many complex problems. The major difficulties are inherited from the use of grid or mesh. A recent strong interest is focused on the next generation computational methods — meshfree methods, which are expected to be superior to conventional grid-based FDM and FEM in many applications. The Element Free Galerkin (EFG method is a meshless method because only a set of nodes and a description of model’s boundary are required to generate the discrete equations. In this paper the EFG method is applied to 2-D beam problem and results are compared with the analytical solution by using Timoshenko Beam Theory. The step by step algorithm for EFG MATLAB program is also provided inside.
The Interpolating Element-Free Galerkin Method for 2D Transient Heat Conduction Problems
Directory of Open Access Journals (Sweden)
Na Zhao
2014-01-01
Full Text Available An interpolating element-free Galerkin (IEFG method is presented for transient heat conduction problems. The shape function in the moving least-squares (MLS approximation does not satisfy the property of Kronecker delta function, so an interpolating moving least-squares (IMLS method is discussed; then combining the shape function constructed by the IMLS method and Galerkin weak form of the 2D transient heat conduction problems, the interpolating element-free Galerkin (IEFG method for transient heat conduction problems is presented, and the corresponding formulae are obtained. The main advantage of this approach over the conventional meshless method is that essential boundary conditions can be applied directly. Numerical results show that the IEFG method has high computational accuracy.
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
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.
Axisymmetric nonconforming element method and its convergence analysis
Institute of Scientific and Technical Information of China (English)
陈万吉; 高岩
1997-01-01
By virtue of the weighted Sobolev space theory, three convergence tests of the axisymmetric non-conforming element method are established. They consist of the generalized patch test, the F-E-M test and a test which could be used conveniently, called the strong patch test (SPT). In the light of SPT, a class of axisymmetric nonconforming elements is established.
A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Tian-xiao Zhou; Xiao-ping Xie
2003-01-01
In this paper, a combined hybrid method is applied to finite element discretization ofplate bending problems. It is shown that the resultant schemes are stabilized, i.e., theconvergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this, two new series of plate elements are proposed.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
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.
Thermal Analysis of Thin Plates Using the Finite Element Method
Er, G. K.; Iu, V. P.; Liu, X. L.
2010-05-01
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.
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.
An Immersed Boundary Method for Complex Flow and Heat Transfer
Paravento, F.; Pourquie, M.J.; Boersma, B.J.
2007-01-01
The need to predict flow and heat transfer problems requires a flexible and fast tool able to simulate complex geometries without increasing the complexity of the flow solver architecture. Here we use a finite volume code that uses a direct solver with pressure correction. A new immersed boundary me
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.
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
Institute of Scientific and Technical Information of China (English)
Ge Hong-Xia; Liu Yong-Qing; Cheng Rong-Jun
2012-01-01
The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin (EFG) method,which is based on the moving least-square approximation. Compared with numerical methods based on meshes,the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem.It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular.In this method,the first-order time derivative is replaced by the Caputo fractional derivative of order α (0 ＜ α ≤ 1).The Galerkin weak form is used to obtain the discrete equations,and the essential boundary conditions are enforced by the penalty method.Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.
Finite Element Model Updating Using Response Surface Method
Marwala, Tshilidzi
2007-01-01
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated parameters of the finite element model were calculated using genetic algorithm by optimizing the surface response equation. The proposed method was compared to the existing methods that use simulated annealing or genetic algorithm together with a full finite element model for finite element model updating. The proposed method was tested on an unsymmetri-cal H-shaped structure. It was observed that the proposed method gave the updated natural frequen-cies and mode shapes that were of the same order of accuracy as those given by simulated annealing and genetic algorithm. Furthermore, it was observed that the response surface method achieved these results at a computational speed that was more than 2.5 times as fast as the genetic algorithm and a full finite element model and 24 ti...
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G.; Rogers, John A.; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2009-11-24
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Research of Stamp Forming Simulation Based on Finite Element Method
Institute of Scientific and Technical Information of China (English)
SU Xaio-ping; XU Lian
2008-01-01
We point out that the finite element method offers a greta functional improvement for analyzing the stamp forming process of an automobile panel. Using the finite element theory and the simulation method of sheet stamping forming, the element model of sheet forming is built based on software HyperMesh,and the simulation of the product's sheet forming process is analyzed based on software Dynaform. A series of simulation results are obtained. It is clear that the simulation results from the theoretical basis for the product's die design and are useful for selecting process parameters.
George, Jacob
The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, k +, based on the element height (k) and the friction velocity (Utau), range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount DeltaU/U, depending on the height of the roughness element, showing that Delta U/Utau is a function
A hybrid Pseudo-spectral Immersed-Boundary Method for Applications to Aquatic Locomotion
Ren, Zheng; Hall, David; Mohseni, Kamran
2011-11-01
A hybrid pseudo-spectral immersed boundary method is developed for application in marine locomotion. Spatial derivatives are calculated using pseudo-spectral method while a 2nd-order Runge-Kutta scheme is used for time integration. The singular force applied on the immersed boundary is obtained using a direct forcing method. To avoid Gibb's phenomenon in the spectral method, we regularize the force by smoothing it over several grid cells. This method has the advantage of spectral accuracy and the flexibility to model irregular, moving boundaries on a Cartesian coordinate without complex mesh generation. The method is applied to examine locomotion of jellyfish for both jetting and paddling jellyfish.
Stelt, van der A.A.; Bor, T.C.; Geijselaers, H.J.M.; Quak, W.; Akkerman, R.; Huetink, J.; Menary, G.
2011-01-01
In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of the disc is clamped. Two numerical methods are used to sol
THE METHOD OF GRAPHIC SIMPLIFICATION OF AREA FEATURE BOUNDARY WITH RIGHT ANGLES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some rules of simplification of area feature boundary and the method of acquiring spatial knowledge,such as maintaining area and shape of area feature, are discussed.This paper focuses on the progressive method of graphic simplification of area feature boundary with right angles based on its characteristics.
The immersed boundary method for the (2D) incompressible Navier-Stokes equations
Meûlen, R.J.R. vander
2006-01-01
Immersed Boundary Methods (IBMs) are a class of methods in Computational Fluid Dynamics where the grids do not conform to the shape of the body. Instead they employ Cartesian meshes and alternative ways to incorporate the boundary conditions in the (discrete) governing equations. The simple grids an
A Boundary Element Solution to the Problem of Interacting AC Fields in Parallel Conductors
Directory of Open Access Journals (Sweden)
Einar M. Rønquist
1984-04-01
Full Text Available The ac fields in electrically insulated conductors will interact through the surrounding electromagnetic fields. The pertinent field equations reduce to the Helmholtz equation inside each conductor (interior problem, and to the Laplace equation outside the conductors (exterior problem. These equations are transformed to integral equations, with the magnetic vector potential and its normal derivative on the boundaries as unknowns. The integral equations are then approximated by sets of algebraic equations. The interior problem involves only unknowns on the boundary of each conductor, while the exterior problem couples unknowns from several conductors. The interior and the exterior problem are coupled through the field continuity conditions. The full set of equations is solved by standard Gaussian elimination. We also show how the total current and the dissipated power within each conductor can be expressed as boundary integrals. Finally, computational results for a sample problem are compared with a finite difference solution.
Garvie, Marcus R; Burkardt, John; Morgan, Jeff
2015-03-01
We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area.
Streamline upwind finite element method for conjugate heat transfer problems
Institute of Scientific and Technical Information of China (English)
Niphon Wansophark; Atipong Malatip; Pramote Dechaumphai; Yunming Chen
2005-01-01
This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components,the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.
A Jacobian Separable 2-D Finite-Element Method for Electromagnetic Waveguide Problems
Khodapanah, Ehsan
2016-01-01
We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of waveguides filled with pieces of homogeneous materials. To apply the method, we first decompose the 2-D problem domain into a set of curved polygons of a specific characteristic. Then we divide every polygon into a set of triangular elements with two straight edges. Finally, we introduce a set of hierarchical mixed-order curl-conforming vector basis functions inside every triangular element to discretize the vector wave equation. The advantages of the method are as follows. The curved boundaries of the elements are modeled exactly and hence there is no approximation in the geometrical modeling. 2-D integrals of the matrix elements are reduced to 1-D integrals. Therefore, the matrix filling can be performed very fast. Total number of elements due to the discretization of a given dom...
Kim, Sang-Wook
1988-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 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 favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.
THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS
Institute of Scientific and Technical Information of China (English)
Hongying Huang; Dehao Yu
2009-01-01
The artificial boundary method is applied to solve three-dimensional exterior problems.Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
Sirait, S. H.; Edison, R. E.; Baidillah, M. R.; Taruno, W. P.; Haryanto, F.
2016-08-01
The aim of this study is to simulate the potential distribution of 2D brain geometry based on two electrodes ECVT. ECVT (electrical capacitance tomography) is a tomography modality which produces dielectric distribution image of a subject from several capacitance electrodes measurements. This study begins by producing the geometry of 2D brain based on MRI image and then setting the boundary conditions on the boundaries of the geometry. The values of boundary conditions follow the potential values used in two electrodes brain ECVT, and for this reason the first boundary is set to 20 volt and 2.5 MHz signal and another boundary is set to ground. Poisson equation is implemented as the governing equation in the 2D brain geometry and finite element method is used to solve the equation. Simulated Hodgkin-Huxley action potential is applied as disturbance potential in the geometry. We divide this study into two which comprises simulation without disturbance potential and simulation with disturbance potential. From this study, each of time dependent potential distributions from non-disturbance and disturbance potential of the 2D brain geometry has been generated.
NUMERICAL METHOD FOR MULTI-BODY FLUID INTERACTION BASED ON IMMERSED BOUNDARY METHOD
Institute of Scientific and Technical Information of China (English)
MING Ping-jian; ZHANG Wen-ping
2011-01-01
A Cartesian grid based on Immersed Boundary Method(IBM),proposed by the present authors,is extended to unstructured grids.The advantages of IBM and Body Fitted Grid(BFG)are taken to enhance the computation efficiency of the fluid structure interaction in a complex domain.There are many methods to generate the BFG,among which the unstructured grid method is the most popular.The concept of Volume Of Solid(VOS)is used to deal with the multi rigid body and fluid interaction.Each body surface is represented by a set of points which can be traced in an anti-clockwise order with the solid area on the left side of surface.An efficient Lagrange point tracking algorithm on the fixed grid is applied to search the moving boundary grid points.This method is verified by low Reynolds number flows in the range from Re =100 to 1 000 in the cavity with a moving lid.The results are in a good agreement with experimental data in literature.Finally,the flow past two moving cylinders is simulated to test the capability of the method.
Indian Academy of Sciences (India)
S PETER; A K DE
2016-04-01
A modified version of the previously reported ghost-cell immersed boundary method is implemented in parallel environment based on distributed memory allocation. Reconstruction of the flow variables is carried out by the inverse distance weighting technique. Implementation of the normal pressure gradient on the immersed surface is demonstrated. Finite volume method with non-staggered arrangement of variables on a nonuniform cartesian grid is employed to solve the fluid flow equations. The proposed method shows reasonable agreement with the reported results for flow past a stationary sphere, rotating and transversely oscillating circular cylinder.
Benchmarking high order finite element approximations for one-dimensional boundary layer problems
Malagu, M.; Benvenuti, E.; Simone, A.
2013-01-01
In this article we investigate the application of high order approximation techniques to one-dimensional boundary layer problems. In particular, we use second order differential equations and coupled second order differential equations as case studies. The accuracy and convergence rate of numerical
Parallel computing strategy for the simulation of particulate flows with immersed boundary method
Institute of Scientific and Technical Information of China (English)
WANG ZeLi; FAN JianRen; LUO Kun
2008-01-01
A parallel computing strategy for the simulation of particulate flows with immersed boundary technique is proposed. This strategy can deal with the coupling between fluid and particle easily when particle crosses the boundaries of sub-domains which are decomposed from original computational domain. And a two-dimen-sional circular particle settling in a closed rectangular domain is simulated with the parallel technique and immersed boundary method to validate the parallel effi-ciency.
Parallel computing strategy for the simulation of particulate flows with immersed boundary method
Institute of Scientific and Technical Information of China (English)
2008-01-01
A parallel computing strategy for the simulation of particulate flows with immersed boundary technique is proposed. This strategy can deal with the coupling between fluid and particle easily when particle crosses the boundaries of sub-domains which are decomposed from original computational domain. And a two- dimen- sional circular particle settling in a closed rectangular domain is simulated with the parallel technique and immersed boundary method to validate the parallel effi- ciency.
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.
Institute of Scientific and Technical Information of China (English)
Luo Chang
2006-01-01
In this work, system of parabolic equations with discontinuous coefficients is studied. The domain decomposition method modified by a characteristic finite element procedure is applied. A function is defined to approximate the fluxes on inner boundaries by using the solution at the previous level. Thus the parallelism is achieved. Convergence analysis and error estimate are also presented.
NUMERICAL SIMULATON OF IMPROVED BOUSSINESQ EQUATIONS BY A FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
Zhao Ming; Teng Bin; Liu Shu-xue
2003-01-01
The improved Boussinesq equations for varying depth derived by Beji and Nadaoka[1]significantly improved the linear dispersive properties of wave models in intermediate water depths. In this study, a finite element method was developed to solve the improved Boussinesq equations. A spongy layer was applied at the open boundary of the computational domain to absorb the wave energy. The fourth-order predictor-corrector method was employed in the time integration. Several test cases were illustrated. The numerical results of this model were compared with laboratory data and those from other numerical models. It turns out that the present numerical model is capable of giving satisactory prediction for wave propagation.
A method for calculating turbulent boundary layers and losses in the flow channels of turbomachines
Schumann, Lawrence F.
1987-01-01
An interactive inviscid core flow-boundary layer method is presented for the calculation of turbomachine channel flows. For this method, a one-dimensional inviscid core flow is assumed. The end-wall and blade surface boundary layers are calculated using an integral entrainment method. The boundary layers are assumed to be collateral and thus are two-dimensional. The boundary layer equations are written in a streamline coordinate system. The streamwise velocity profiles are approximated by power law profiles. Compressibility is accounted for in the streamwise direction but not in the normal direction. Equations are derived for the special cases of conical and two-dimensional rectangular diffusers. For these cases, the assumptions of a one-dimensional core flow and collateral boundary layers are valid. Results using the method are compared with experiment and good quantitative agreement is obtained.
Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
Jin, Bangti
2013-01-01
We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Jin, B.
2014-05-30
© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression...... of the grains. This is true even of the resilient (or reversible) deformations. It is also interesting because the Discrete Element Method models resilient and plastic deformations as well as failure in a single process.The paper describes two types of calculations. One on a small sample of angular elements...... subjected to a pulsating (repeated) biaxial loading and another of a larger sample of circular element subjected to a plate load. Both cases are two dimensional, i.e. plane strain.The repeated biaxial loading showed a large increase in plastic strain for the first load pulse at a given load level...