Hybrid finite difference/finite element immersed boundary method.

Science.gov (United States)

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1998-12-31

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)

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

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)

New formulations on the finite element method for boundary value problems with internal/external boundary layers

International Nuclear Information System (INIS)

Pereira, Luis Carlos Martins

1998-06-01

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)

The boundary element method : errors and gridding for problems with hot spots

NARCIS (Netherlands)

Kakuba, G.

2011-01-01

Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear

A Novel Mesh Quality Improvement Method for Boundary Elements

Directory of Open Access Journals (Sweden)

Hou-lin Liu

2012-01-01

Full Text Available In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.

Temperature and stress distribution in pressure vessel by the boundary element method

International Nuclear Information System (INIS)

Alujevic, A.; Apostolovic, D.

1990-01-01

The aim of this paper is to demonstrate the applicability of boundary element method for the solution of temperatures and thermal stresses in the body of reactor pressure vessel of the NPP Krsko . In addition to the theory of boundary elements for thermo-elastic continua (2D, 3D) results are given of a numerically evaluated meridional cross-section. (author)

Application of the dual reciprocity boundary element method for numerical modelling of solidification process

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.

Boundary element methods applied to two-dimensional neutron diffusion problems

International Nuclear Information System (INIS)

Itagaki, Masafumi

1985-01-01

The Boundary element method (BEM) has been applied to two-dimensional neutron diffusion problems. The boundary integral equation and its discretized form have been derived. Some numerical techniques have been developed, which can be applied to critical and fixed-source problems including multi-region ones. Two types of test programs have been developed according to whether the 'zero-determinant search' or the 'source iteration' technique is adopted for criticality search. Both programs require only the fluxes and currents on boundaries as the unknown variables. The former allows a reduction in computing time and memory in comparison with the finite element method (FEM). The latter is not always efficient in terms of computing time due to the domain integral related to the inhomogeneous source term; however, this domain integral can be replaced by the equivalent boundary integral for a region with a non-multiplying medium or with a uniform source, resulting in a significant reduction in computing time. The BEM, as well as the FEM, is well suited for solving irregular geometrical problems for which the finite difference method (FDM) is unsuited. The BEM also solves problems with infinite domains, which cannot be solved by the ordinary FEM and FDM. Some simple test calculations are made to compare the BEM with the FEM and FDM, and discussions are made concerning the relative merits of the BEM and problems requiring future solution. (author)

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

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.

Acoustic boundary element method formulation with treatment of nearly singular integrands by element subdivision

DEFF Research Database (Denmark)

Cutanda Henríquez, Vicente; Juhl, Peter Møller

2008-01-01

It is well known that the Boundary Element Method (BEM) in its standard version cannot readily handle situations where the calculation point is very close to a surface. These problems are found: i) when two boundary surfaces are very close together, such as in narrow gaps and thin bodies, and ii)...

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity.

Science.gov (United States)

Atroshchenko, Elena; Bordas, Stéphane P A

2015-07-08

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.

Three-dimensional wake field analysis by boundary element method

International Nuclear Information System (INIS)

Miyata, K.

1987-01-01

A computer code HERTPIA was developed for the calculation of electromagnetic wake fields excited by charged particles travelling through arbitrarily shaped accelerating cavities. This code solves transient wave problems for a Hertz vector. The numerical analysis is based on the boundary element method. This program is validated by comparing its results with analytical solutions in a pill-box cavity

An introductory study of the convergence of the direct boundary element method

DEFF Research Database (Denmark)

Juhl, Peter Møller

1997-01-01

of an axisymmetric boundary element formulation is studied using linear, quadratic or superparametric elements. It is demonstrated that the rate of convergence of these formulations is reduced for calculations involving bodies with edges (geometric singularities). Two methods for improving the rate of convergence...

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

Science.gov (United States)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Near shore seismic movements induced by seaquakes using the boundary element method

Institute of Scientific and Technical Information of China (English)

Manuel Carbajal-Romero; Norberto Flores-Guzmán; J.Efraín Rodríguez-Sánchez; Andriy Kryvko

2017-01-01

This study quantifies seismic amplifications in near-shore arising from seaquakes.Within the Boundary Element Method,boundary elements are used to irradiate waves and force densities obtained for each element.Huygens Principle is implemented since the diffracted waves are constructed at the boundary from which they are radiated,which is equivalent to Somigliana's theorem.Application of boundary conditions leads to a system of integral equations of the Fredholm type of second kind and zero order.Several numerical configurations are analyzed:The first is used to verify the present formulation with ideal sea floor configurations to estimate seismic amplifications.With the formulation verified,simple slope configurations are studied to estimate spectra of seismic motions.It is found that P-waves can produce seismic amplifications from 1.2 to 3.9 times the amplitude of the incident wave.SV-waves can generate seismic amplifications up to 4.5 times the incident wave.Another relevant finding is that the highest amplifications are at the shore compared to the ones at the sea floor.

Element stacking method for topology optimization with material-dependent boundary and loading conditions

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...... independent degrees of freedom. Some test problems are considered to check the effectiveness of the proposed stacking method....

A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

Science.gov (United States)

Brovont, Aaron D.

The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

Use of the iterative solution method for coupled finite element and boundary element modeling

International Nuclear Information System (INIS)

Koteras, J.R.

1993-07-01

Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver

Micromechanical Study of Interface Stress in a Fiber-Reinforced Composite under Transverse Loading Using Boundary Element Method

National Research Council Canada - National Science Library

Eren, Hakan

2000-01-01

.... The objective of this study is, by using Boundary Element Method, to examine different shapes of reinforcement elements under unit traction and unit displacement boundary conditions in transversal...

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...

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...

A boundary integral equation for boundary element applications in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Ozgener, B.

1998-01-01

A boundary integral equation (BIE) is developed for the application of the boundary element method to the multigroup neutron diffusion equations. The developed BIE contains no explicit scattering term; the scattering effects are taken into account by redefining the unknowns. Boundary elements of the linear and constant variety are utilised for validation of the developed boundary integral formulation

Seismic response of three-dimensional rockfill dams using the Indirect Boundary Element Method

International Nuclear Information System (INIS)

Sanchez-Sesma, Francisco J; Arellano-Guzman, Mauricio; Perez-Gavilan, Juan J; Suarez, Martha; Marengo-Mogollon, Humberto; Chaillat, Stephanie; Jaramillo, Juan Diego; Gomez, Juan; Iturraran-Viveros, Ursula; Rodriguez-Castellanos, Alejandro

2010-01-01

The Indirect Boundary Element Method (IBEM) is used to compute the seismic response of a three-dimensional rockfill dam model. The IBEM is based on a single layer integral representation of elastic fields in terms of the full-space Green function, or fundamental solution of the equations of dynamic elasticity, and the associated force densities along the boundaries. The method has been applied to simulate the ground motion in several configurations of surface geology. Moreover, the IBEM has been used as benchmark to test other procedures. We compute the seismic response of a three-dimensional rockfill dam model placed within a canyon that constitutes an irregularity on the surface of an elastic half-space. The rockfill is also assumed elastic with hysteretic damping to account for energy dissipation. Various types of incident waves are considered to analyze the physical characteristics of the response: symmetries, amplifications, impulse response and the like. Computations are performed in the frequency domain and lead to time response using Fourier analysis. In the present implementation a symmetrical model is used to test symmetries. The boundaries of each region are discretized into boundary elements whose size depends on the shortest wavelength, typically, six boundary segments per wavelength. Usually, the seismic response of rockfill dams is simulated using either finite elements (FEM) or finite differences (FDM). In most applications, commercial tools that combine features of these methods are used to assess the seismic response of the system for a given motion at the base of model. However, in order to consider realistic excitation of seismic waves with different incidence angles and azimuth we explore the IBEM.

Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

Directory of Open Access Journals (Sweden)

Samira Hosseini

Full Text Available Abstract One of the main drawbacks of Element Free Galerkin (EFG method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.

International Symposium on Boundary Element Methods : Advances in Solid and Fluid Mechanics

CERN Document Server

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 ...

Prediction of radiation ratio and sound transmission of complex extruded panel using wavenumber domain Unite element and boundary element methods

International Nuclear Information System (INIS)

Kim, H; Ryue, J; Thompson, D J; Müller, A D

2016-01-01

Recently, complex shaped aluminium panels have been adopted in many structures to make them lighter and stronger. The vibro-acoustic behaviour of these complex panels has been of interest for many years but conventional finite element and boundary element methods are not efficient to predict their performance at higher frequencies. Where the cross-sectional properties of the panels are constant in one direction, wavenumber domain numerical analysis can be applied and this becomes more suitable for panels with complex cross-sectional geometries. In this paper, a coupled wavenumber domain finite element and boundary element method is applied to predict the sound radiation from and sound transmission through a double-layered aluminium extruded panel, having a typical shape used in railway carriages. The predicted results are compared with measured ones carried out on a finite length panel and good agreement is found. (paper)

New implementation method for essential boundary condition to extended element-free Galerkin method. Application to nonlinear problem

International Nuclear Information System (INIS)

Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

2011-01-01

A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)

Boundary element and speckle photography method for solving elasto-plastic problems

International Nuclear Information System (INIS)

Hadjikov, L.; Kavardjikov, V.; Valeva, V.

1985-01-01

The stress-strain state of metal specimens in the vicinity of a stress concentrator (circular hole) is investigated in case of a quasistatic loading. The displacements are evaluated numerically by the Boundary Element Method (BEM) and they are estimated experimentally by speckle photography. The experimentally and theoretically obtained results are compared and considered. A unified method for a simultaneous employment of both techniques is suggested. The experimental and theoretical techniques complement each other which results in an enhanced capability of the method proposed. (orig.)

Application of Boundary Element Method in Galvanic Corrosion Analysis for Metallic Materials used in Nuclear Power Plant

International Nuclear Information System (INIS)

Zaifol Samsu; Muhamad Daud; Siti Radiah Mohd Kamarudin

2011-01-01

Boundary element method (BEM) is a numerical technique that used for modeling infinite domain as is the case for galvanic corrosion analysis. This paper presents the application of boundary element method for galvanic corrosion analysis between two different metallic materials. Aluminium (Al), and zinc (Zn) alloys were used separately coupled with the Carbon Steel (CS) in natural seawater. The measured conductivity of sea water is 30,800 μS/ cm at ambient temperature. Computer software system based on boundary element likes BEASY and ABAQUS can be used to accurately model and simulate the galvanic corrosion. However, the BEM based BEASY program will be used reasonably for predicting the galvanic current density distribution of coupled Al-CS and Zn-CS in this study. (author)

Second-order wave diffraction by a circular cylinder using scaled boundary finite element method

International Nuclear Information System (INIS)

Song, H; Tao, L

2010-01-01

The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

OpenBEM - An open source Boundary Element Method software in Acoustics

DEFF Research Database (Denmark)

Cutanda Henriquez, Vicente; Juhl, Peter Møller

2010-01-01

OpenBEM is a collection of open source programs for solving the Helmholtz Equation using the Boundary Element Method. The collection is written in Matlab by the authors and contains codes for dealing with exterior and interior problems in two or three dimensions as well as implementation of axi...... with examples of its use. Previous research results where OpenBEM was employed will be mentioned....

ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF TWO-DIMENSIONAL STRUCTURAL ANALYSIS WITH THE USE OF COMBINED APPLICATION OF FINITE ELEMENT METHOD AND DISCRETE-CONTINUAL FINITE ELEMENT METHOD PART 2: SPECIAL ASPECTS OF FINITE ELEMENT APPROXIMATION

Directory of Open Access Journals (Sweden)

Pavel A. Akimov

2017-12-01

Full Text Available As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM, and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM. In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic variants are available are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.

Boundary element numerical method for the electric field generated by oblique multi-needle electrodes

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.

Dynamic-stiffness matrix of embedded and pile foundations by indirect boundary-element method

International Nuclear Information System (INIS)

Wolf, J.P.; Darbre, G.R.

1984-01-01

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. (orig.)

Seismic response of three-dimensional topographies using a time-domain boundary element method

Science.gov (United States)

Janod, François; Coutant, Olivier

2000-08-01

We present a time-domain implementation for a boundary element method (BEM) to compute the diffraction of seismic waves by 3-D topographies overlying a homogeneous half-space. This implementation is chosen to overcome the memory limitations arising when solving the boundary conditions with a frequency-domain approach. This formulation is flexible because it allows one to make an adaptive use of the Green's function time translation properties: the boundary conditions solving scheme can be chosen as a trade-off between memory and cpu requirements. We explore here an explicit method of solution that requires little memory but a high cpu cost in order to run on a workstation computer. We obtain good results with four points per minimum wavelength discretization for various topographies and plane wave excitations. This implementation can be used for two different aims: the time-domain approach allows an easier implementation of the BEM in hybrid methods (e.g. coupling with finite differences), and it also allows one to run simple BEM models with reasonable computer requirements. In order to keep reasonable computation times, we do not introduce any interface and we only consider homogeneous models. Results are shown for different configurations: an explosion near a flat free surface, a plane wave vertically incident on a Gaussian hill and on a hemispherical cavity, and an explosion point below the surface of a Gaussian hill. Comparison is made with other numerical methods, such as finite difference methods (FDMs) and spectral elements.

Free surface simulation of a two-layer fluid by boundary element method

Directory of Open Access Journals (Sweden)

Weoncheol Koo

2010-09-01

Full Text Available A two-layer fluid with free surface is simulated in the time domain by a two-dimensional potential-based Numerical Wave Tank (NWT. The developed NWT is based on the boundary element method and a leap-frog time integration scheme. A whole domain scheme including interaction terms between two layers is applied to solve the boundary integral equation. The time histories of surface elevations on both fluid layers in the respective wave modes are verified with analytic results. The amplitude ratios of upper to lower elevation for various density ratios and water depths are also compared.

An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration

NARCIS (Netherlands)

Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.

1997-01-01

Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be

Three-dimensional multiple reciprocity boundary element method for one-group neutron diffusion eigenvalue computations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1996-01-01

The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)

Investigation of the stability of blocks around underground openings by using the boundary element method

Directory of Open Access Journals (Sweden)

Murat Ünal

2002-03-01

Full Text Available In this study, a two-dimensional software was developed by using the boundary element method, in order to model and solve the rock mechanics problems encountered in surface and underground excavations. Stability of rock wedges formed at the roof of underground excavations were investigated in detail by using this software. The behaviour of the symmetric wedge on different joint stiffnesses was studied using a modified boundary element software. Then the results obtained were discussed and compared with the analytical solution, considering the surface tractions, shear stresses (developed along the discontinuity, wedge displacements and strains (along the wedge height.

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...

Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods

CERN Document Server

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...

A multi-region boundary element method for multigroup neutron diffusion calculations

International Nuclear Information System (INIS)

Ozgener, H.A.; Ozgener, B.

2001-01-01

For the analysis of a two-dimensional nuclear system consisting of a number of homogeneous regions (termed cells), first the cell matrices which depend solely on the material composition and geometrical dimension of the cell (hence on the cell type) are constructed using a boundary element formulation based on the multigroup boundary integral equation. For a particular nuclear system, the cell matrices are utilized in the assembly of the global system matrix in block-banded form using the newly introduced concept of virtual side. For criticality calculations, the classical fission source iteration is employed and linear system solutions are by the block Gaussian-elimination algorithm. The numerical applications show the validity of the proposed formulation both through comparison with analytical solutions and assessment of benchmark problem results against alternative methods

Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1997-01-01

The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

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 simple finite element method for boundary value problems with a Riemann–Liouville derivative

KAUST Repository

Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

2016-01-01

© 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.

A simple finite element method for boundary value problems with a Riemann–Liouville derivative

KAUST Repository

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.

On some examples of pollutant transport problems solved numerically using the boundary element method

Science.gov (United States)

Azis, Moh. Ivan; Kasbawati; Haddade, Amiruddin; Astuti Thamrin, Sri

2018-03-01

A boundary element method (BEM) is obtained for solving a boundary value problem of homogeneous anisotropic media governed by diffusion-convection equation. The application of the BEM is shown for two particular pollutant transport problems of Tello river and Unhas lake in Makassar Indonesia. For the two particular problems a variety of the coefficients of diffusion and the velocity components are taken. The results show that the solutions vary as the parameters change. And this suggests that one has to be careful in measuring or determining the values of the parameters.

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

Energy Technology Data Exchange (ETDEWEB)

Simmons, Daniel, E-mail: daniel.simmons@nottingham.ac.uk; 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. - Graphical abstract:.

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.

Improved design of special boundary elements for T-shaped reinforced concrete walls

Science.gov (United States)

Ji, Xiaodong; Liu, Dan; Qian, Jiaru

2017-01-01

This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements of T-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

Science.gov (United States)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Analysis of heat transfer on extended surfaces of fuel elements in cooling channels by boundary elements method; Analiza prenosa toplote na orebrenjih gorivnih elementov hladilnih kanalov z metodo robnih elementov

Energy Technology Data Exchange (ETDEWEB)

Namestnik, B; Skerget, L; Beadar, D [tehniska fakulteta, Maribor (Yugoslavia)

1989-07-01

The paper presents numerical method for evaluating heat transfer on two-dimensional ribbed surfaces. Governing elliptic partial differential equation is transformed to boundary integral equation, and solved by the boundary element method. Efficiency of fins is calculated from boundary heat flux balance. Several test cases have shown usefulness of the presented method. (author)

Development of the hierarchical domain decomposition boundary element method for solving the three-dimensional multiregion neutron diffusion equations

International Nuclear Information System (INIS)

Chiba, Gou; Tsuji, Masashi; Shimazu, Yoichiro

2001-01-01

A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the 'lower level' calculations. At the 'higher level' calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time. (author)

Novel TMS coils designed using an inverse boundary element method

Science.gov (United States)

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.

Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains

International Nuclear Information System (INIS)

Ferraro, N.M.; Jardin, S.C.; Luo, X.

2010-01-01

The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.

A study on the bonding residual thermal stress analysis of dissimilar materials using boundary element method

International Nuclear Information System (INIS)

Yi, Won; Yu, Yeong Chul; Jeong, Eui Seob; Lee, Chang Ho

1995-01-01

It is very important to evaluate the bonding residual thermal stress in dissimilar materials such as LSI package. In this study, the bonding residual thermal stress was calculated using the boundary element method, varing with the sub-element, geometry of specimen and adhesive thickness. The present results reveal a stress singularity at the edge of the interface, therefore the bonding strength of metal/resin interface can be estimated by taking into account it.

Strength Reduction Method for Stability Analysis of Local Discontinuous Rock Mass with Iterative Method of Partitioned Finite Element and Interface Boundary Element

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.

Natural convection in a composite fluid-porous cavity by the boundary element method

International Nuclear Information System (INIS)

Jecl, R.; Skerget, L.

2005-01-01

The main purpose of this work is to present the use of the boundary element method (BEM) for analyzing the convective fluid flow and heat transfer in composite fluid-porous media domain when the fluid is compressible. In our case the flow is modeled by utilizing the Brinkman extended Darcy momentum equation (Brinkman model) which is commonly used when it is important to satisfy the no-slip boundary condition and when one wishes to compare flows in porous medium with those in pure fluids. The Brinkman equation reduce to the classical Navier Stokes equation for clear fluid when the permeability tends to infinity (porosity is equal to unity), i.e. when the solid matrix in the porous medium disappears and, when the permeability is finite the equation is valid for porous medium. Therefore it is possible to handle porous medium free fluid interface problems by changing the properties of the medium in the computational domain appropriately. Our goal is to widen the applicability of the computational model based on the boundary domain integral method (BDIM) which is an extension of the classical BEM. The governing equations are transformed by using the velocity-vorticity variables formulation and therefore the computation scheme is partitioned into kinematic and kinetic part. (authors)

Indirect boundary element method for three dimensional problems. Analytical solution for contribution to wave field by triangular element; Sanjigen kansetsu kyokai yosoho. Sankakukei yoso no kiyo no kaisekikai

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.

The use of Fourier eigen transform to the boundary element method for transient elastodynamic problems

International Nuclear Information System (INIS)

Ji, X.; Chen, Y.M.

1989-01-01

The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes

Inverse boundary element calculations based on structural modes

DEFF Research Database (Denmark)

Juhl, Peter Møller

2007-01-01

The inverse problem of calculating the flexural velocity of a radiating structure of a general shape from measurements in the field is often solved by combining a Boundary Element Method with the Singular Value Decomposition and a regularization technique. In their standard form these methods sol...

Formulation of electromagnetic-wave analysis by boundary element method and its application to the analysis of RF cavities

International Nuclear Information System (INIS)

Washizu, Masao; Tanabe, Yoshio.

1986-01-01

In a system handling the electromagnetic waves of large power such as the cavity resonator for a high energy accelerator and the high frequency heater for a nuclear fusion apparatus, the margin in the thermal and mechanical design of a wave guide system cannot be taken large, accordingly, the detailed analysis of electromagnetic waves is required. When the analysis in a general form is carried out, boundary element method may be a useful method of solution. This time, the authors carried out the formulation of steady electromagnetic wave problems by boundary element method, and it was shown that the formulation was able to be carried out under the physically clear boundary condition also in this case, and especially in the case of a perfect conductor system, a very simple form was obtained. In this paper, first, the techniques of formulation in a general case, and next, as a special case, the formulation for a perfect conductor system are described. Taking the analysis of the cavity resonators of cylindrical and rectangular parallelepiped forms as examples, the comparison with the analytical solution was carried out. (Kako, I.)

Stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions.

Science.gov (United States)

Jang, Hae-Won; Ih, Jeong-Guon

2012-04-01

The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.

A boundary integral method for numerical computation of radar cross section of 3D targets using hybrid BEM/FEM with edge elements

Science.gov (United States)

Dodig, H.

2017-11-01

This contribution presents the boundary integral formulation for numerical computation of time-harmonic radar cross section for 3D targets. Method relies on hybrid edge element BEM/FEM to compute near field edge element coefficients that are associated with near electric and magnetic fields at the boundary of the computational domain. Special boundary integral formulation is presented that computes radar cross section directly from these edge element coefficients. Consequently, there is no need for near-to-far field transformation (NTFFT) which is common step in RCS computations. By the end of the paper it is demonstrated that the formulation yields accurate results for canonical models such as spheres, cubes, cones and pyramids. Method has demonstrated accuracy even in the case of dielectrically coated PEC sphere at interior resonance frequency which is common problem for computational electromagnetic codes.

Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method

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.

Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

International Nuclear Information System (INIS)

Koteras, J.R.

1996-01-01

The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

Sound Radiation from a Loudspeaker Cabinet using the Boundary Element Method

DEFF Research Database (Denmark)

Fernandez Grande, Efren

had been reported, based on subjective testing. This study aims to detect the reported problem. The radiation from the cabinet is calculated using the Boundary Element Method. The analysis examines both the frequency domain and the time domain characteristics (in other words, the steady state response......, in some cases becoming clearly audible. The aim of this study is to provide a tool that can evaluate the contribution from the cabinet to the overall sound radiated by a loudspeaker. The specific case of a B&O Beolab 9 early prototype has been investigated. An influence by the cabinet of this prototype...... and the impulse response) of the loudspeaker and the cabinet. A significant influence of the cabinet has been detected, which becomes especially apparent in the time domain, during the sound decay process....

A geometric buckling expression for regular polygons: II. Analyses based on the multiple reciprocity boundary element method

International Nuclear Information System (INIS)

Itagaki, Masafumi; Miyoshi, Yoshinori; Hirose, Hideyuki

1993-01-01

A procedure is presented for the determination of geometric buckling for regular polygons. A new computation technique, the multiple reciprocity boundary element method (MRBEM), has been applied to solve the one-group neutron diffusion equation. The main difficulty in applying the ordinary boundary element method (BEM) to neutron diffusion problems has been the need to compute a domain integral, resulting from the fission source. The MRBEM has been developed for transforming this type of domain integral into an equivalent boundary integral. The basic idea of the MRBEM is to apply repeatedly the reciprocity theorem (Green's second formula) using a sequence of higher order fundamental solutions. The MRBEM requires discretization of the boundary only rather than of the domain. This advantage is useful for extensive survey analyses of buckling for complex geometries. The results of survey analyses have indicated that the general form of geometric buckling is B g 2 = (a n /R c ) 2 , where R c represents the radius of the circumscribed circle of the regular polygon under consideration. The geometric constant A n depends on the type of regular polygon and takes the value of π for a square and 2.405 for a circle, an extreme case that has an infinite number of sides. Values of a n for a triangle, pentagon, hexagon, and octagon have been calculated as 4.190, 2.281, 2.675, and 2.547, respectively

An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations

Science.gov (United States)

Simpson, R. N.; Liu, Z.; Vázquez, R.; Evans, J. A.

2018-06-01

We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-order approximations and crucially provides a direct link with CAD data structures that allows for efficient design workflows. After outlining the construction of div- and curl-conforming B-splines defined over 3D surfaces we describe their use with the electric and magnetic field integral equations using a Galerkin formulation. We use Bézier extraction to accelerate the computation of NURBS and B-spline terms and employ H-matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization. The method is verified using the well known Mie scattering problem posed over a perfectly electrically conducting sphere and the classic NASA almond problem. Finally, we demonstrate the ability of the approach to handle models with complex geometry directly from CAD without mesh generation.

Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

KAUST Repository

Liu, Shaolin

2017-09-28

The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

PARALLEL ALGORITHM FOR THREE-DIMENSIONAL STOKES FLOW SIMULATION USING BOUNDARY ELEMENT METHOD

Directory of Open Access Journals (Sweden)

D. G. Pribytok

2016-01-01

Full Text Available Parallel computing technique for modeling three-dimensional viscous flow (Stokes flow using direct boundary element method is presented. The problem is solved in three phases: sampling and construction of system of linear algebraic equations (SLAE, its decision and finding the velocity of liquid at predetermined points. For construction of the system and finding the velocity, the parallel algorithms using graphics CUDA cards programming technology have been developed and implemented. To solve the system of linear algebraic equations the implemented software libraries are used. A comparison of time consumption for three main algorithms on the example of calculation of viscous fluid motion in three-dimensional cavity is performed.

About solution of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method and discrete-continual finite element method. part 1: formulation of the problem and general principles of approximation

Directory of Open Access Journals (Sweden)

Lyakhovich Leonid

2017-01-01

Full Text Available This paper is devoted to formulation and general principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method (FEM discrete-continual finite element method (DCFEM. The field of application of DCFEM comprises structures with regular physical and geometrical parameters in some dimension (“basic” dimension. DCFEM presupposes finite element approximation for non-basic dimension while in the basic dimension problem remains continual. DCFEM is based on analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients.

The boundary element method for the solution of the multidimensional inverse heat conduction problem

International Nuclear Information System (INIS)

Lagier, Guy-Laurent

1999-01-01

This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author) [fr

An inverse model for locating skin tumours in 3D using the genetic algorithm with the Dual Reciprocity Boundary Element Method

Directory of Open Access Journals (Sweden)

Fabrício Ribeiro Bueno

Full Text Available Here, the Dual Reciprocity Boundary Element Method is used to solve the 3D Pennes Bioheat Equation, which together with a Genetic Algorithm, produces an inverse model capable of obtaining the location and the size of a tumour, having as data input the temperature distribution measured on the skin surface. Given that the objective function, which is solved inversely, involves the DRBEM (Dual Reciprocity Boundary Element Method the Genetic Algorithm in its usual form becomes slower, in such a way that it was necessary to develop functions based the solution history in order that the process becomes quicker and more accurate. Results for 8 examples are presented including cases with convection and radiation boundary conditions. Cases involving noise in the readings of the equipment are also considered. This technique is intended to assist health workers in the diagnosis of tumours.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

Science.gov (United States)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons

New formulations on the finite element method for boundary value problems with internal/external boundary layers; Novas formulacoes de elementos finitos para problemas de valor de contorno com camadas limite interna/externa

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)

Resistive wall impedance of the LHC beam screen without slots calculated by boundary element method

CERN Document Server

Tsutsui, H

2002-01-01

In order to calculate the resistive wall impedance of the LHC beam screen without slots, the Boundary Element Method (BEM) is used. The result at 1 GHz is Re(ZL/L) = 6.689×10−3 Ω/m, Re(Zx/L) = 1.251 Ω/m2, Re(Zy/L) = 1.776 Ω/m2, andRe(2Z0,2 cos/kL) = −0.525 Ω/m2, assuming σ = 5.8 × 109 /Ωm.

A finite element method for neutron transport

International Nuclear Information System (INIS)

Ackroyd, R.T.

1983-01-01

A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)

KIN SP: A boundary element method based code for single pile kinematic bending in layered soil

Directory of Open Access Journals (Sweden)

Stefano Stacul

2018-02-01

Full Text Available In high seismicity areas, it is important to consider kinematic effects to properly design pile foundations. Kinematic effects are due to the interaction between pile and soil deformations induced by seismic waves. One of the effect is the arise of significant strains in weak soils that induce bending moments on piles. These moments can be significant in presence of a high stiffness contrast in a soil deposit. The single pile kinematic interaction problem is generally solved with beam on dynamic Winkler foundation approaches (BDWF or using continuous models. In this work, a new boundary element method (BEM based computer code (KIN SP is presented where the kinematic analysis is preceded by a free-field response analysis. The analysis results of this method, in terms of bending moments at the pile-head and at the interface of a two-layered soil, are influenced by many factors including the soil–pile interface discretization. A parametric study is presented with the aim to suggest the minimum number of boundary elements to guarantee the accuracy of a BEM solution, for typical pile–soil relative stiffness values as a function of the pile diameter, the location of the interface of a two-layered soil and of the stiffness contrast. KIN SP results have been compared with simplified solutions in literature and with those obtained using a quasi-three-dimensional (3D finite element code.

The Perfectly Matched Layer absorbing boundary for fluid-structure interactions using the Immersed Finite Element Method.

Science.gov (United States)

Yang, Jubiao; Yu, Feimi; Krane, Michael; Zhang, Lucy T

2018-01-01

In this work, a non-reflective boundary condition, the Perfectly Matched Layer (PML) technique, is adapted and implemented in a fluid-structure interaction numerical framework to demonstrate that proper boundary conditions are not only necessary to capture correct wave propagations in a flow field, but also its interacted solid behavior and responses. While most research on the topics of the non-reflective boundary conditions are focused on fluids, little effort has been done in a fluid-structure interaction setting. In this study, the effectiveness of the PML is closely examined in both pure fluid and fluid-structure interaction settings upon incorporating the PML algorithm in a fully-coupled fluid-structure interaction framework, the Immersed Finite Element Method. The performance of the PML boundary condition is evaluated and compared to reference solutions with a variety of benchmark test cases including known and expected solutions of aeroacoustic wave propagation as well as vortex shedding and advection. The application of the PML in numerical simulations of fluid-structure interaction is then investigated to demonstrate the efficacy and necessity of such boundary treatment in order to capture the correct solid deformation and flow field without the requirement of a significantly large computational domain.

Boundary element analysis of earthquake induced hydrodynamic pressures in a water reservoir

International Nuclear Information System (INIS)

Jablonski, A.M.

1988-11-01

The seismic analysis of concrete gravity and arch dams is affected by the hydrodynamic pressures in the water reservoir. Boundary element method (BEM) formulations are derived for the hydrodynamic pressures arising in a gravity dam-reservoir-foundation system, treating both 2- and 3-dimensional cases. The formulations are based on the respective mathematical models which are governed by two- and three-dimensional Helmholtz equations with appropriate boundary conditions. For infinite reservoirs, loss of energy due to pressure waves moving away toward infinity strongly influence response. Since it is not possible to discretize an infinite extent, the radiation damping due to outgoing waves is accounted for by incorporating special boundary conditions at the far end, and in a similar manner the loss of energy due to absorption of waves by a flexible bottom of reservoir and banks can be accounted for by a special condition along the boundaries. Numerical results are obtained and compared with available classical solutions and convergence of numerical results with the size and number of boundary elements is studied. It is concluded that the direct boundary element method is an effective tool for the evaluation of the hydrodynamic pressures in finite and infinite dam-reservoir-foundation systems subjected to harmonic-type motion, and can easily be extended to any type of random motion with fast Fourier transform techniques. 82 refs., 65 figs., 25 tabs

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...

Heat conduction in a plate-type fuel element with time-dependent boundary conditions

International Nuclear Information System (INIS)

Faya, A.J.G.; Maiorino, J.R.

1981-01-01

A method for the solution of boundary-value problems with variable boundary conditions is applied to solve a heat conduction problem in a plate-type fuel element with time dependent film coefficient. The numerical results show the feasibility of the method in the solution of this class of problems. (Author) [pt

International Conference on Computer Modelling of Seas and Coastal Regions and Boundary Elements and Fluid Dynamics

CERN Document Server

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...

Boundary element simulation of petroleum reservoirs with hydraulically fractured wells

Science.gov (United States)

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

An assessment of the DORT method on simple scatterers using boundary element modelling.

Science.gov (United States)

Gélat, P; Ter Haar, G; Saffari, N

2015-05-07

The ability to focus through ribs overcomes an important limitation of a high-intensity focused ultrasound (HIFU) system for the treatment of liver tumours. Whilst it is important to generate high enough acoustic pressures at the treatment location for tissue lesioning, it is also paramount to ensure that the resulting ultrasonic dose on the ribs remains below a specified threshold, since ribs both strongly absorb and reflect ultrasound. The DORT (décomposition de l'opérateur de retournement temporel) method has the ability to focus on and through scatterers immersed in an acoustic medium selectively without requiring prior knowledge of their location or geometry. The method requires a multi-element transducer and is implemented via a singular value decomposition of the measured matrix of inter-element transfer functions. The efficacy of a method of focusing through scatterers is often assessed by comparing the specific absorption rate (SAR) at the surface of the scatterer, and at the focal region. The SAR can be obtained from a knowledge of the acoustic pressure magnitude and the acoustic properties of the medium and scatterer. It is well known that measuring acoustic pressures with a calibrated hydrophone at or near a hard surface presents experimental challenges, potentially resulting in increased measurement uncertainties. Hence, the DORT method is usually assessed experimentally by measuring the SAR at locations on the surface of the scatterer after the latter has been removed from the acoustic medium. This is also likely to generate uncertainties in the acoustic pressure measurement. There is therefore a strong case for assessing the efficacy of the DORT method through a validated theoretical model. The boundary element method (BEM) applied to exterior acoustic scattering problems is well-suited for such an assessment. In this study, BEM was used to implement the DORT method theoretically on locally reacting spherical scatterers, and to assess its focusing

An Atomistic Modeling Study of Alloying Element Impurity Element, and Transmutation Products on the cohesion of A Nickel E5 {001} Twist Grain Boundary

International Nuclear Information System (INIS)

Young, G.A. Jr.; Najafabadi, R.; Strohmayer, W.; Baldrey, D.G.; Hamm, B.; Harris, J.; Sticht, J.; Wimmer, E.

2003-01-01

Atomistic modeling methods were employed to investigate the effects of impurity elements on the metallurgy, irradiation embrittlement, and environmentally assisted cracking of nickel-base alloys exposed to nuclear environments. Calculations were performed via ab initio atomistic modeling methods to ensure the accuracy and reliability of the results. A Griffith-type fracture criterion was used to quantitatively assess the effect of elements or element pairs on the grain boundary cohesive strength. In order of most embrittling to most strengthening, the elements are ranked as: He, Li, S, H, C, Zr, P, Fe, Mn, Nb, Cr, and B. Helium is strongly embrittling (-2.04 eV/atom lowering of the Griffith energy), phosphorus has little effect on the grain boundary (0.1 eV/atom), and boron offers appreciable strengthening (1.03 eV/atom increase in the Griffith energy). Calculations for pairs of elements (H-Li, H-B, H-C, H-P, and H-S) show little interaction on the grain boundary cohesive energy, so that for the conditions studied, linear superposition of elemental effects is a good approximation. These calculations help explain metallurgical effects (e.g. why boron can strengthen grain boundaries), irradiation embrittlement (e.g. how boron transmutation results in grain boundary embrittlement), as well as how grain boundary impurity elements can affect environmentally assisted cracking (i.e. low temperature crack propagation and stress corrosion cracking) of nickel-base alloys

Frequency domain finite-element and spectral-element acoustic wave modeling using absorbing boundaries and perfectly matched layer

Science.gov (United States)

Rahimi Dalkhani, Amin; Javaherian, Abdolrahim; Mahdavi Basir, Hadi

2018-04-01

Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.

Quantification of elemental segregation to lath and grain boundaries in low-alloy steel by STEM X-ray mapping combined with the zeta-factor method

CERN Document Server

Watanabe, M

2003-01-01

Elemental segregation to two types of boundaries in a low-alloy steel were studied by X-ray mapping using scanning transmission electron microscopy (STEM). To quantify the acquired X-ray maps, the zeta-factor method was applied, and then the compositional maps and the thickness map were obtained. Based on these quantified maps, further information about the analytical sensitivity of solute-element detection and the spatial resolution of segregation analysis were extracted. Furthermore, maps of the number of excess atoms on the boundary were also calculated from the compositional and thickness maps. It was concluded that Cr, Ni and Mo are co-segregated on the prior-austenite grain boundary and only Ni was segregated on the lath boundary. (orig.)

Lubricated immersed boundary method in two dimensions

Science.gov (United States)

Fai, Thomas G.; Rycroft, Chris H.

2018-03-01

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids.

A finite element conjugate gradient FFT method for scattering

Science.gov (United States)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

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.

Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

KAUST Repository

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.

Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary

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.

Rayleigh-wave scattering by shallow cracks using the indirect boundary element method

International Nuclear Information System (INIS)

Ávila-Carrera, R; Rodríguez-Castellanos, A; Ortiz-Alemán, C; Sánchez-Sesma, F J

2009-01-01

The scattering and diffraction of Rayleigh waves by shallow cracks using the indirect boundary element method (IBEM) are investigated. The detection of cracks is of interest because their presence may compromise structural elements, put technological devices at risk or represent economical potential in reservoir engineering. Shallow cracks may give rise to scattered body and surface waves. These waves are sensitive to the crack's geometry, size and orientation. Under certain conditions, amplitude spectra clearly show conspicuous resonances that are associated with trapped waves. Several applications based on the scattering of surface waves (e.g. Rayleigh and Stoneley waves), such as non-destructive testing or oil well exploration, have shown that the scattered fields may provide useful information to detect cracks and other heterogeneities. The subject is not new and several analytical and numerical techniques have been applied for the last 50 years to understand the basis of multiple scattering phenomena. In this work, we use the IBEM to calculate the scattered fields produced by single or multiple cracks near a free surface. This method is based upon an integral representation of the scattered displacement fields, which is derived from Somigliana's identity. Results are given in both frequency and time domains. The analyses of the displacement field using synthetic seismograms and snapshots reveal some important effects from various configurations of cracks. The study of these simple cases may provide an archetype to geoscientists and engineers to understand the fundamental aspects of multiple scattering and diffraction by cracks

Boundary Element Solution of Geometrical Inverse Heat Conduction Problems for Development of IR CAT Scan

International Nuclear Information System (INIS)

Choi, C. Y.; Park, C. T.; Kim, T. H.; Han, K. N.; Choe, S. H.

1995-01-01

A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis

Stability estimates for hp spectral element methods for general ...

Indian Academy of Sciences (India)

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 ...

Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

KAUST Repository

Sirenko, Kostyantyn; Liu, Meilin; Bagci, Hakan

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

Periodic Boundary Conditions in the ALEGRA Finite Element Code

International Nuclear Information System (INIS)

Aidun, John B.; Robinson, Allen C.; Weatherby, Joe R.

1999-01-01

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

Dual reciprocity boundary element analysis for the laminar forced heat convection problem in concentric annulus

International Nuclear Information System (INIS)

Choi, Chang Yong

1999-01-01

This paper presents a study of the Dual Reciprocity Boundary Element Method (DRBEM) for the laminar heat convection problem in a concentric annulus with constant heat flux boundary condition. DRBEM is one of the most successful technique used to transform the domain integrals arising from the nonhomogeneous term of the poisson equation into equivalent boundary only integrals. This recently developed and highly efficient numerical method is tested for the solution accuracy of the fluid flow and heat transfer study in a concentric annulus. Since their exact solutions are available, DRBEM solutions are verified with different number of boundary element discretization and internal points. The results obtained in this study are discussed with the relative error percentage of velocity and temperature solutions, and potential applicability of the method for the more complicated heat convection problems with arbitrary duct geometries

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...

An enriched finite element model with q-refinement for radiative boundary layers in glass cooling

Energy Technology Data Exchange (ETDEWEB)

Mohamed, M. Shadi [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Seaid, Mohammed; Trevelyan, Jon [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Laghrouche, Omar [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

2014-02-01

Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.

Programming the finite element method

CERN Document Server

Smith, I M; Margetts, L

2013-01-01

Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c

Improvements on the directional characteristics of a calibration sound source using the Boundary Element Method

DEFF Research Database (Denmark)

Henriquez, Vicente Cutanda; Barrera Figueroa, Salvador; Juhl, Peter Møller

2008-01-01

is of particular importance to achieve a sound field that reaches both microphones with the same level and that is sufficiently uniform at the microphone positions, in order to reduce the effect of misalignment. An existing sound source has been modeled using the Boundary Element Method, and the simulations have......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...... been used to modify the source and make it suitable for this kind of calibration. It has been found that a central plug, already present in the device, can be re-shaped in such a way that makes the sound field on the microphone positions more uniform, even at rather high frequencies. Measurements have...

Fast and accurate algorithm for repeated optical trapping simulations on arbitrarily shaped particles based on boundary element method

International Nuclear Information System (INIS)

Xu, Kai-Jiang; Pan, Xiao-Min; Li, Ren-Xian; Sheng, Xin-Qing

2017-01-01

In optical trapping applications, the optical force should be investigated within a wide range of parameter space in terms of beam configuration to reach the desirable performance. A simple but reliable way of conducting the related investigation is to evaluate optical forces corresponding to all possible beam configurations. Although the optical force exerted on arbitrarily shaped particles can be well predicted by boundary element method (BEM), such investigation is time costing because it involves many repetitions of expensive computation, where the forces are calculated from the equivalent surface currents. An algorithm is proposed to alleviate the difficulty by exploiting our previously developed skeletonization framework. The proposed algorithm succeeds in reducing the number of repetitions. Since the number of skeleton beams is always much less than that of beams in question, the computation can be very efficient. The proposed algorithm is accurate because the skeletonization is accuracy controllable. - Highlights: • A fast and accurate algorithm is proposed in terms of boundary element method to reduce the number of repetitions of computing the optical forces from the equivalent currents. • The algorithm is accuracy controllable because the accuracy of the associated rank-revealing process is well-controlled. • The accelerate rate can reach over one thousand because the number of skeleton beams can be very small. • The algorithm can be applied to other methods, e.g., FE-BI.

Analysis of Piezoelectric Solids using Finite Element Method

Science.gov (United States)

Aslam, Mohammed; Nagarajan, Praveen; Remanan, Mini

2018-03-01

Piezoelectric materials are extensively used in smart structures as sensors and actuators. In this paper, static analysis of three piezoelectric solids is done using general-purpose finite element software, Abaqus. The simulation results from Abaqus are compared with the results obtained using numerical methods like Boundary Element Method (BEM) and meshless point collocation method (PCM). The BEM and PCM are cumbersome for complex shape and complicated boundary conditions. This paper shows that the software Abaqus can be used to solve the governing equations of piezoelectric solids in a much simpler and faster way than the BEM and PCM.

Local defect correction for boundary integral equation methods

NARCIS (Netherlands)

Kakuba, G.; Anthonissen, M.J.H.

2014-01-01

The aim in this paper is to develop a new local defect correction approach to gridding for problems with localised regions of high activity in the boundary element method. The technique of local defect correction has been studied for other methods as finite difference methods and finite volume

Local defect correction for boundary integral equation methods

NARCIS (Netherlands)

Kakuba, G.; Anthonissen, M.J.H.

2013-01-01

This paper presents a new approach to gridding for problems with localised regions of high activity. The technique of local defect correction has been studied for other methods as ¿nite difference methods and ¿nite volume methods. In this paper we develop the technique for the boundary element

Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method

Directory of Open Access Journals (Sweden)

Mehdi Panji

2016-08-01

Full Text Available In this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method (BEM. The existing full-plane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.

Boundary element inverse analysis for rebar corrosion detection: Study on the 2004 tsunami-affected structure in Aceh

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S. Fonna

2018-06-01

Full Text Available Evaluation of rebar/reinforcing-steel corrosion for the 2004 tsunami-affected reinforced concrete (RC buildings in Aceh was conducted using half-cell potential mapping technique. However, the results only show qualitative meaning as corrosion risk rather than the corrosion itself, such as the size and location of corrosion. In this study, boundary element inverse analysis was proposed to be performed to detect rebar corrosion of the 2004 tsunami-affected structure in Aceh, using several electrical potential measurement data on the concrete surface. One RC structure in Peukan Bada, an area heavily damaged by the tsunami, was selected for the study. In 2004 the structure was submerged more than 5 m by the tsunami. Boundary element inverse analysis was developed by combining the boundary element method (BEM and particle swarm optimization (PSO. The corrosion was detected by evaluating measured and calculated electrical potential data. The measured and calculated electrical potential on the concrete surface was obtained by using a half-cell potential meter and by performing BEM, respectively. The solution candidates were evaluated by employing PSO. Simulation results show that boundary element inverse analysis successfully detected the size and location of corrosion for the case study. Compared with the actual corrosion, the error of simulation result was less than 5%. Hence, it shows that boundary element inverse analysis is very promising for further development to detect rebar corrosion. Keywords: Inverse analysis, Boundary element method, PSO, Corrosion, Reinforced concrete

The Indirect Boundary Element Method (IBEM) for Seismic Response of Topographical Irregularities in Layered Media

Science.gov (United States)

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

A Hamiltonian-based derivation of Scaled Boundary Finite Element Method for elasticity problems

International Nuclear Information System (INIS)

Hu Zhiqiang; Lin Gao; Wang Yi; Liu Jun

2010-01-01

The Scaled Boundary Finite Method (SBFEM) is a semi-analytical solution approach for solving partial differential equation. For problem in elasticity, the governing equations can be obtained by mechanically based formulation, Scaled-boundary-transformation-based formulation and principle of virtual work. The governing equations are described in the frame of Lagrange system and the unknowns are displacements. But in the solution procedure, the auxiliary variables are introduced and the equations are solved in the state space. Based on the observation that the duality system to solve elastic problem proposed by W.X. Zhong is similar to the above solution approach, the discretization of the SBFEM and the duality system are combined to derive the governing equations in the Hamilton system by introducing the dual variables in this paper. The Precise Integration Method (PIM) used in Duality system is also an efficient method for the solution of the governing equations of SBFEM in displacement and boundary stiffness matrix especially for the case which results some numerical difficulties in the usually uses the eigenvalue method. Numerical examples are used to demonstrate the validity and effectiveness of the PIM for solution of boundary static stiffness.

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.

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

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Marco Gonzalez

Full Text Available Abstract The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs. The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.

The finite element method in electromagnetics

CERN Document Server

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

Coupled Boundary and Finite Element Analysis of Vibration from Railway Tunnels

DEFF Research Database (Denmark)

Andersen, Lars; Jones, C.J.C.

2006-01-01

The analysis of vibration from railway tunnels is of growing interest as new and higher-speed railways are built under the ground to address the transport problems of growing modern urban areas around cities. Such analysis can be carried out using numerical methods but models and therefore comput...... body vibration (about 4 to 80 Hz). A coupled finite element and boundary element scheme is applied in both two and three dimensions. Two tunnel designs are considered: a cut-and-cover tunnel for a double track and a single-track tunnel dug with the New Austrian Tunnelling Method (NATM)....

An analytical boundary element integral approach to track the boundary of a moving cavity using electrical impedance tomography

International Nuclear Information System (INIS)

Khambampati, Anil Kumar; Kim, Sin; Lee, Bo An; Kim, Kyung Youn

2012-01-01

This paper is about locating the boundary of a moving cavity within a homogeneous background from the voltage measurements recorded on the outer boundary. An inverse boundary problem of a moving cavity is formulated by considering a two-phase vapor–liquid flow in a pipe. The conductivity of the flow components (vapor and liquid) is assumed to be constant and known a priori while the location and shape of the inclusion (vapor) are the unknowns to be estimated. The forward problem is solved using the boundary element method (BEM) with the integral equations solved analytically. A special situation is considered such that the cavity changes its location and shape during the time taken to acquire a full set of independent measurement data. The boundary of a cavity is assumed to be elliptic and is parameterized with Fourier series. The inverse problem is treated as a state estimation problem with the Fourier coefficients that represent the center and radii of the cavity as the unknowns to be estimated. An extended Kalman filter (EKF) is used as an inverse algorithm to estimate the time varying Fourier coefficients. Numerical experiments are shown to evaluate the performance of the proposed method. Through the results, it can be noticed that the proposed BEM with EKF method is successful in estimating the boundary of a moving cavity. (paper)

Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

Science.gov (United States)

Li, Qiang; Popov, Valentin L.

2018-03-01

Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation.

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...... from tyre noise measurements will be presented at the conference....

Finite element time domain modeling of controlled-Source electromagnetic data with a hybrid boundary condition

DEFF Research Database (Denmark)

Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin

2017-01-01

method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping...... method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary...... condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies....

Numerical design and testing of a sound source for secondary calibration of microphones using the Boundary Element Method

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...... 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...... of the Danish Fundamental Metrology Institute (DFM). The design and verification of the source are presented in this communication....

Finite cover method with mortar elements for elastoplasticity problems

Science.gov (United States)

Kurumatani, M.; Terada, K.

2005-06-01

Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Science.gov (United States)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Experimental validation of a boundary element solver for exterior acoustic radiation problems

NARCIS (Netherlands)

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

Nonlinear soil-structure interaction analysis based on the boundary-element method in time domain with application to embedded foundation

International Nuclear Information System (INIS)

Wolf, J.P.; Darbre, G.R.

1985-01-01

The computational procedure of the so-called truncated indirect boundary-element method is derived. The latter, which is non-local in space and time, represents a rigorous generally applicable procedure for taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basement and separation of the side wall is investigated. (orig.)

HEFF---A user's manual and guide for the HEFF code for thermal-mechanical analysis using the boundary-element method

International Nuclear Information System (INIS)

St John, C.M.; Sanjeevan, K.

1991-12-01

The HEFF Code combines a simple boundary-element method of stress analysis with the closed form solutions for constant or exponentially decaying heat sources in an infinite elastic body to obtain an approximate method for analysis of underground excavations in a rock mass with heat generation. This manual describes the theoretical basis for the code, the code structure, model preparation, and step taken to assure that the code correctly performs its intended functions. The material contained within the report addresses the Software Quality Assurance Requirements for the Yucca Mountain Site Characterization Project. 13 refs., 26 figs., 14 tabs

A multilevel correction adaptive finite element method for Kohn-Sham equation

Science.gov (United States)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Advances in boundary elements. Vol. 1-3

International Nuclear Information System (INIS)

Brebbia, C.A.; Connor, J.J.

1989-01-01

This book contains some of the edited papers presented at the 11th Boundary Element Conference, held in Cambridge, Massachusetts, during August 1989. The papers are arranged in three different books comprising the following topics: Vol. 1: Computations and Fundamentals - comprises sections on fundamentals, adaptive techniques, error and convergence, numerical methods and computational aspects. (283 p.). Vol. 2: Field and fluid flow solutions - includes the following topics: potential problems, thermal studies, electrical and electromagnetic problems, wave propagation, acoustics and fluid flow. (484 p.). Vol. 3: Stress analysis - deals with advances in linear problems, nonlinear problems, fracture mechanics, contact mechanics, optimization, geomechanics, plates and shells, vibrations and industrial applications. (450 p). (orig./HP)

A Hybrid Finite Element-Fourier Spectral Method for Vibration Analysis of Structures with Elastic Boundary Conditions

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.

Modelling of pressurized water reactor fuel, rod time dependent radial heat flow with boundary element method; Modeliranje spremenljivega radijalnega toplotnega toka tlacnovodne gorivne palice z metodo robnih elementov

Energy Technology Data Exchange (ETDEWEB)

Sarler, B [Institut Jozef Stefan, Ljubljana (Yugoslavia)

1987-07-01

The basic principles of the boundary element method numerical treatment of the radial flow heat diffusion equation are presented. The algorithm copes the time dependent Dirichlet and Neumann boundary conditions, temperature dependent material properties and regions from different materials in thermal contact. It is verified on the several analytically obtained test cases. The developed method is used for the modelling of unsteady radial heat flow in pressurized water reactor fuel rod. (author)

An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging

International Nuclear Information System (INIS)

Akalin-Acar, Zeynep; Gencer, Nevzat G

2004-01-01

The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obtain the potential and magnetic field patterns using realistic head models. The formulations incorporate the use of the isolated problem approach for increased accuracy in solutions. If a personal computer is used for computations, each transfer matrix is calculated in 2.2 h. After this pre-computation period, solutions for arbitrary source configurations can be obtained in milliseconds for a realistic head model. A hybrid algorithm that uses snakes, morphological operations, region growing and thresholding is used for segmentation. The scalp, skull, grey matter, white matter and eyes are segmented from the multimodal magnetic resonance images and meshes for the corresponding surfaces are created. A mesh generation algorithm is developed for modelling the intersecting tissue compartments, such as eyes. To obtain more accurate results quadratic elements are used in the realistic meshes. The resultant BEM implementation provides more accurate forward problem solutions and more efficient calculations. Thus it can be the firm basis of the future inverse problem solutions

Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements.

Science.gov (United States)

Korolkov, Victor P; Nasyrov, Ruslan K; Shimansky, Ruslan V

2006-01-01

Enhancing the diffraction efficiency of continuous-relief diffractive optical elements fabricated by direct laser writing is discussed. A new method of zone-boundary optimization is proposed to correct exposure data only in narrow areas along the boundaries of diffractive zones. The optimization decreases the loss of diffraction efficiency related to convolution of a desired phase profile with a writing-beam intensity distribution. A simplified stepped transition function that describes optimized exposure data near zone boundaries can be made universal for a wide range of zone periods. The approach permits a similar increase in the diffraction efficiency as an individual-pixel optimization but with fewer computation efforts. Computer simulations demonstrated that the zone-boundary optimization for a 6 microm period grating increases the efficiency by 7% and 14.5% for 0.6 microm and 1.65 microm writing-spot diameters, respectively. The diffraction efficiency of as much as 65%-90% for 4-10 microm zone periods was obtained experimentally with this method.

INVESTIGATION OF HYDROELASTIC BEHAVIOR OF A PONTOON-TYPE VLFS DURING UNSTEADY EXTERNAL LOADS IN WAVE CONDITION USING A HYBRID FINITE ELEMENT-BOUNDARY ELEMENT (FE-ME METHOD

Directory of Open Access Journals (Sweden)

Yong Cheng

2017-01-01

Full Text Available The hydroelastic behaviour of a pontoon-type VLFS subjected to unsteady external loads in wave condition is investigated in the context of the time-domain modal expansion theory, in which the boundary element method (BEM based on time domain Kelvin sources is used for hydrodynamic forces and the finite element method (FEM is adopted for solving the deflections of the VLFS. In this analysis, the interpolation-tabulation scheme is applied to assess rapidly and accurately the free-surface Green function in finite water depth, and the boundary integral equation of a quarter VLFS model is further established taking advantage of symmetry of flow field and structure. The VLFS is modelled as an equivalent solid plate based on the Mindlin plate theory. The coupled plate-water model is performed to determine the wave-induced responses and transient behaviour under external loads such as a huge mass impact onto the structure and moving loads of an airplane, respectively. These results are verified with existing numerical results and experimental test. Then, the developed numerical tools are used in the study of the combined action taking into account of the mass drop/airplane landing as well as forward or reverse incident wave action. The deflections of the runway, the time history of vertical positions and the trajectory of the airplane are also presented through a systematic time-domain simulation, which illustrates the usefulness of the presently developed numerical solutions.

9th International Conference on Boundary Elements

CERN Document Server

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...

Green's function and boundary elements of multifield materials

CERN Document Server

Qin, Qing-Hua

2007-01-01

Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically important challenges. You will benefit from the authors' thorough coverage of general principles for each topic, followed by detailed mathematical derivation and worked examples as well as tables and figures where appropriate. In-depth explanations of the concept of Green's function Coupled thermo-magneto-electro-elastic analysis Detailed mathematical derivation for Green's functions.

Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method.

Science.gov (United States)

Hamanaka, Ryo; Yamaoka, Satoshi; Anh, Tuan Nguyen; Tominaga, Jun-Ya; Koga, Yoshiyuki; Yoshida, Noriaki

2017-11-01

Although many attempts have been made to simulate orthodontic tooth movement using the finite element method, most were limited to analyses of the initial displacement in the periodontal ligament and were insufficient to evaluate the effect of orthodontic appliances on long-term tooth movement. Numeric simulation of long-term tooth movement was performed in some studies; however, neither the play between the brackets and archwire nor the interproximal contact forces were considered. The objectives of this study were to simulate long-term orthodontic tooth movement with the edgewise appliance by incorporating those contact conditions into the finite element model and to determine the force system when the space is closed with sliding mechanics. We constructed a 3-dimensional model of maxillary dentition with 0.022-in brackets and 0.019 × 0.025-in archwire. Forces of 100 cN simulating sliding mechanics were applied. The simulation was accomplished on the assumption that bone remodeling correlates with the initial tooth displacement. This method could successfully represent the changes in the moment-to-force ratio: the tooth movement pattern during space closure. We developed a novel method that could simulate the long-term orthodontic tooth movement and accurately determine the force system in the course of time by incorporating contact boundary conditions into finite element analysis. It was also suggested that friction is progressively increased during space closure in sliding mechanics. Copyright © 2017. Published by Elsevier Inc.

Stress intensity evaluation for surface crack with use of boundary element method and influence function method and the surface crack extension analysis

International Nuclear Information System (INIS)

Yuuki, R.; Ejima, K.

1991-01-01

In this study, three-dimensional boundary element elastostatic analysis is carried out on various surface crack problems. The present BEM uses a Mindlin's solution as well as a Kelvin's solution as a fundamental solution. So we can obtain accurate solutions for a surface crack just before or after a penetration. The obtained solutions for various shapes of surface cracks are stored as the data base, based on the influence function method. We develop the surface crack extension analysis system using the stress intensity factor data base and also the fatigue crack growth law. Our system seems to be useful especially for the analysis of the surface crack just before or after the penetration and also under the residual stresses

Complex variable boundary elements for fluid flow; Robni elementi kompleksne spremenljivke za pretok fluidov

Energy Technology Data Exchange (ETDEWEB)

Bizjak, D; Alujevic, A [Institut ' Jozef Stefan' , Ljubljana (Yugoslavia)

1988-07-01

The Complex Variable Boundary Element Method is a numerical method for solving two-dimensional problems of Laplace or Poisson type. It is based on the theory of analytic functions. This paper resumes the basic facts about the method. Application of the method to the stationary incompressible irrotational flow is carried out after that. At the end, a sample problem of flow through an abrupt area change channel is shown. (author)

A numerical study of the second-order wave excitation of ship springing by a higher-order boundary element method

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.

3-dimensional earthquake response analysis of embedded reactor building using hybrid model of boundary elements and finite elements

International Nuclear Information System (INIS)

Muto, K.; Motosaka, M.; Kamata, M.; Masuda, K.; Urao, K.; Mameda, T.

1985-01-01

In order to investigate the 3-dimensional earthquake response characteristics of an embedded structure with consideration for soil-structure interaction, the authors have developed an analytical method using 3-dimensional hybrid model of boundary elements (BEM) and finite elements (FEM) and have conducted a dynamic analysis of an actual nuclear reactor building. This paper describes a comparative study between two different embedment depths in soil as elastic half-space. As the results, it was found that the earthquake response intensity decreases with the increase of the embedment depth and that this method was confirmed to be effective for investigating the 3-D response characteristics of embedded structures such as deflection pattern of each floor level, floor response spectra in high frequency range. (orig.)

High-speed parallel solution of the neutron diffusion equation with the hierarchical domain decomposition boundary element method incorporating parallel communications

International Nuclear Information System (INIS)

Tsuji, Masashi; Chiba, Gou

2000-01-01

A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been fully parallelized, both for numerical computations and for data communications, to accomplish a high parallel efficiency on distributed memory message passing parallel computers. Data exchanges between node processors that are repeated during iteration processes of HDD-BEM are implemented, without any intervention of the host processor that was used to supervise parallel processing in the conventional parallelized HDD-BEM (P-HDD-BEM). Thus, the parallel processing can be executed with only cooperative operations of node processors. The communication overhead was even the dominant time consuming part in the conventional P-HDD-BEM, and the parallelization efficiency decreased steeply with the increase of the number of processors. With the parallel data communication, the efficiency is affected only by the number of boundary elements assigned to decomposed subregions, and the communication overhead can be drastically reduced. This feature can be particularly advantageous in the analysis of three-dimensional problems where a large number of processors are required. The proposed P-HDD-BEM offers a promising solution to the deterioration problem of parallel efficiency and opens a new path to parallel computations of NDEs on distributed memory message passing parallel computers. (author)

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

Science.gov (United States)

Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

2009-01-01

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry

Coupled finite difference and boundary element methods for fluid flow through a vessel with multibranches in tumours.

Science.gov (United States)

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. Copyright © 2012 John Wiley & Sons, Ltd.

Development of new finite element by source method. 2nd Report. Plate bending element; Source wo mochiita atarashii yugen yoso no kaihatsu. 2. Itamage yoso

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.

Development of new finite element by source method. 2nd Report. Plate bending element; Source wo mochiita atarashii yugen yoso no kaihatsu. 2. Itamage yoso

Energy Technology Data Exchange (ETDEWEB)

Neki, I; Tada, T [Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo (Japan)

1997-12-31

This paper reports a method to develop a new finite element by source (FES) for a two-dimensional plane problem and a three-dimensional solid problem as a method to analyze ship body structures. The paper describes development of a plate bending element by using a similar method, and the fundamental principle thereof. The present method can prepare a finite element of an arbitrary shape by simply providing a contact point only on a boundary. It can also derive good calculation accuracy with less number of contact points and elements. These facts are shown by examples of analyses on a square plate, a triangle plate and a semi-circular plate. Particularly, since a plate bending problem has a large order of differential calculus in a governing equation, this method being a semi-analytical method derives a result with very good accuracy even with less number of contact points. A hypothetical boundary method or a hypothetical electric charge method presents not a very high accuracy even if a large number of contact points are provided. This is because the method hypothesizes only a bending moment vertical to the boundary, but does not consider a source of the moment relative to the boundary. In contrast, the present method hypothesizes both of bending and twisting as the sources, hence its accuracy is better than with the above two methods. 5 refs., 11 figs., 7 tabs.

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

International Nuclear Information System (INIS)

Zhang Chen; Lu Hong; Hua Ning; Tang Xue-Zheng; Tang Fa-Kuan; Shou Guo-Fa; Xia Ling; Ma Ping

2013-01-01

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 HT c ·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. (general)

Boundary elements; Proceedings of the Fifth International Conference, Hiroshima, Japan, November 8-11, 1983

Science.gov (United States)

Brebbia, C. A.; Futagami, T.; Tanaka, M.

The boundary-element method (BEM) in computational fluid and solid mechanics is examined in reviews and reports of theoretical studies and practical applications. Topics presented include the fundamental mathematical principles of BEMs, potential problems, EM-field problems, heat transfer, potential-wave problems, fluid flow, elasticity problems, fracture mechanics, plates and shells, inelastic problems, geomechanics, dynamics, industrial applications of BEMs, optimization methods based on the BEM, numerical techniques, and coupling.

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.

Multisymplectic Structure－Preserving in Simple Finite Element Method in High Dimensional Case

Institute of Scientific and Technical Information of China (English)

BAIYong-Qiang; LIUZhen; PEIMing; ZHENGZhu-Jun

2003-01-01

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.

The Boundary Function Method. Fundamentals

Science.gov (United States)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

A non-reflecting boundary for use in a finite element beam model of a railway track

Science.gov (United States)

Yang, Jiannan; Thompson, David J.

2015-02-01

Some beam-like structures such as a railway track are effectively infinite in nature. Analytical solutions exist for simple structures but numerical methods like the finite element (FE) method are often employed to study more complicated problems. However, when the FE method is used for structures of infinite extent it is essential to introduce artificial boundaries to limit the area of computation. Here, a non-reflecting boundary is developed using a damped tapered tip for application in a finite element model representing an infinite supported beam. The FE model of the tapered tip is validated against an analytical model based on Bessel functions. The reflection characteristics of the FE tapered tip are quantified using a wave/FE superposition method. It is shown that the damped tapered tip is much more effective than its constant counterpart and achieves reduction of the model size. The damped tapered tip is applied to a simple FE railway track model and good agreement is found when its point mobility is compared with an analytical infinite track model.

Effect of a Roughness Element on the Receptivity of a Hypersonic Boundary Layer over a Blunt Cone Due to Pulse Entropy Disturbance with a Single Frequency

Directory of Open Access Journals (Sweden)

Zhenqing Wang

2018-05-01

Full Text Available A high-order finite difference method was used to simulate the hypersonic flow field over a blunt cone with different height roughness elements. The unsteady flow field induced by pulse disturbances was analyzed and compared with that under continuous disturbances. The temporal and spatial evolution characteristics of disturbances in the boundary layer were investigated and the propagation of different disturbance modes in the boundary layer was researched through the fast Fourier transform (FFT method. The effect of the roughness element on the receptivity characteristic of the hypersonic boundary layer under pulse entropy disturbances was explored. The results showed that the different mode disturbances near roughness in the boundary layer were enlarged in the upstream half of the roughness element and suppressed in the downstream half. However, the effect of roughness weakened gradually as the disturbance frequency increased in the boundary layer. A phenomenon of mode competition in the downstream region of the roughness element exited. As the disturbances propagated downstream, the fundamental mode gradually became the dominant mode. A certain promotion effect on the mode competition was induced by the roughness element and the effect was enhanced with the increase in the roughness element height.

Wake Instabilities Behind Discrete Roughness Elements in High Speed Boundary Layers

Science.gov (United States)

Choudhari, Meelan; Li, Fei; Chang, Chau-Lyan; Norris, Andrew; Edwards, Jack

2013-01-01

Computations are performed to study the flow past an isolated, spanwise symmetric roughness element in zero pressure gradient boundary layers at Mach 3.5 and 5.9, with an emphasis on roughness heights of less than 55 percent of the local boundary layer thickness. The Mach 5.9 cases include flow conditions that are relevant to both ground facility experiments and high altitude flight ("cold wall" case). Regardless of the Mach number, the mean flow distortion due to the roughness element is characterized by long-lived streamwise streaks in the roughness wake, which can support instability modes that did not exist in the absence of the roughness element. The higher Mach number cases reveal a variety of instability mode shapes with velocity fluctuations concentrated in different localized regions of high base flow shear. The high shear regions vary from the top of a mushroom shaped structure characterizing the centerline streak to regions that are concentrated on the sides of the mushroom. Unlike the Mach 3.5 case with nearly same values of scaled roughness height k/delta and roughness height Reynolds number Re(sub kk), the odd wake modes in both Mach 5.9 cases are significantly more unstable than the even modes of instability. Additional computations for a Mach 3.5 boundary layer indicate that the presence of a roughness element can also enhance the amplification of first mode instabilities incident from upstream. Interactions between multiple roughness elements aligned along the flow direction are also explored.

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.

2013-01-01

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.

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

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.

A general mixed boundary model reduction method for component mode synthesis

International Nuclear Information System (INIS)

Voormeeren, S N; Van der Valk, P L C; Rixen, D J

2010-01-01

A classic issue in component mode synthesis (CMS) methods is the choice for fixed or free boundary conditions at the interface degrees of freedom (DoF) and the associated vibration modes in the components reduction base. In this paper, a novel mixed boundary CMS method called the 'Mixed Craig-Bampton' method is proposed. The method is derived by dividing the substructure DoF into a set of internal DoF, free interface DoF and fixed interface DoF. To this end a simple but effective scheme is introduced that, for every pair of interface DoF, selects a free or fixed boundary condition for each DoF individually. Based on this selection a reduction basis is computed consisting of vibration modes, static constraint modes and static residual flexibility modes. In order to assemble the reduced substructures a novel mixed assembly procedure is developed. It is shown that this approach leads to relatively sparse reduced matrices, whereas other mixed boundary methods often lead to full matrices. As such, the Mixed Craig-Bampton method forms a natural generalization of the classic Craig-Bampton and more recent Dual Craig-Bampton methods. Finally, the method is applied to a finite element test model. Analysis reveals that the proposed method has comparable or better accuracy and superior versatility with respect to the existing methods.

Finite element and boundary element applications in quantum mechanics

International Nuclear Information System (INIS)

Ueta, Tsuyoshi

2003-01-01

Although this book is one of the Oxford Texts in Applied and Engineering Mathematics, we may think of it as a physics book. It explains how to solve the problem of quantum mechanics using the finite element method (FEM) and the boundary element method (BEM). Many examples analysing actual problems are also shown. As for the ratio of the number of pages of FEM and BEM, the former occupies about 80%. This is, however, reasonable reflecting the flexibility of FEM. Although many explanations of FEM and BEM exist, most are written using special mathematical expressions and numerical computation fields. However, this book is written in the 'language of physicists' throughout. I think that it is very readable and easy to understand for physicists. In the derivation of FEM and the argument on calculation accuracy, the action integral and a variation principle are used consistently. In the numerical computation of matrices, such as simultaneous equations and eigen value problems, a description of important points is also fully given. Moreover, the practical problems which become important in the electron device design field and the condensed matter physics field are dealt with as example computations, so that this book is very practical and applicable. It is characteristic and interesting that FEM is applied to solve the Schroedinger and Poisson equations consistently, and to the solution of the Ginzburg--Landau equation in superconductivity. BEM is applied to treat electric field enhancements due to surface plasmon excitations at metallic surfaces. A number of references are cited at the end of all the chapters, and this is very helpful. The description of quantum mechanics is also made appropriately and the actual application of quantum mechanics in condensed matter physics can also be surveyed. In the appendices, the mathematical foundation, such as numerical quadrature formulae and Green's functions, is conveniently described. I recommend this book to those who need to

Recycling inflow method for simulations of spatially evolving turbulent boundary layers over rough surfaces

Science.gov (United States)

Yang, Xiang I. A.; Meneveau, Charles

2016-01-01

The technique by Lund et al. to generate turbulent inflow for simulations of developing boundary layers over smooth flat plates is extended to the case of surfaces with roughness elements. In the Lund et al. method, turbulent velocities on a sampling plane are rescaled and recycled back to the inlet as inflow boundary condition. To rescale mean and fluctuating velocities, appropriate length scales need be identified and for smooth surfaces, the viscous scale lν = ν/uτ (where ν is the kinematic viscosity and uτ is the friction velocity) is employed for the inner layer. Different from smooth surfaces, in rough wall boundary layers the length scale of the inner layer, i.e. the roughness sub-layer scale ld, must be determined by the geometric details of the surface roughness elements and the flow around them. In the proposed approach, it is determined by diagnosing dispersive stresses that quantify the spatial inhomogeneity caused by the roughness elements in the flow. The scale ld is used for rescaling in the inner layer, and the boundary layer thickness δ is used in the outer region. Both parts are then combined for recycling using a blending function. Unlike the blending function proposed by Lund et al. which transitions from the inner layer to the outer layer at approximately 0.2δ, here the location of blending is shifted upwards to enable simulations of very rough surfaces in which the roughness length may exceed the height of 0.2δ assumed in the traditional method. The extended rescaling-recycling method is tested in large eddy simulation of flow over surfaces with various types of roughness element shapes.

Neutron activation analysis and the geochemistry of common and trace elements at extinction boundaries in the geological record

International Nuclear Information System (INIS)

Attrep, M. Jr.; Orth, C.J.; Quintana, L.R.

1994-01-01

The discovery of the iridium anomaly at the 65-Ma Cretaceous-Tertiary (K-T) extinction boundary initiated numerous investigations, including the search for the coupling of these extinctions with other astronomical events. One hypothesis is that these periodic extinctions are coupled to terrestrial impacts from cyclic swarms of comets or asteroids. The studies have focused on elucidating the conditions and causes of extinction of life at these geological boundaries using elemental abundance patterns. The authors use instrumental neutron activation methods to determine whole-rock abundances for about 40 trace and common elements in thousands of samples. The platinum group elements (iridium, gold, platinum, and osmium) and nickel are measured by radiochemical activation analysis. The authors can measure iridium at levels down to 1 picogram/gram level

A finite element modeling method for predicting long term corrosion rates

International Nuclear Information System (INIS)

Fu, J.W.; Chan, S.

1984-01-01

For the analyses of galvanic corrosion, pitting and crevice corrosion, which have been identified as possible corrosion processes for nuclear waste isolation, a finite element method has been developed for the prediction of corrosion rates. The method uses a finite element mesh to model the corrosive environment and the polarization curves of metals are assigned as the boundary conditions to calculate the corrosion cell current distribution. A subroutine is used to calculate the chemical change with time in the crevice or the pit environments. In this paper, the finite element method is described along with experimental confirmation

Magnetic field computations of the magnetic circuits with permanent magnets by infinite element method

International Nuclear Information System (INIS)

Hahn, Song Yop

1985-01-01

A method employing infinite elements is described for the magnetic field computations of the magnetic circuits with permanent magnet. The system stiffness matrix is derived by a variational approach, while the interfacial boundary conditions between the finite element regions and the infinite element regions are dealt with using collocation method. The proposed method is applied to a simple linear problems, and the numerical results are compared with those of the standard finite element method and the analytic solutions. It is observed that the proposed method gives more accurate results than those of the standard finite element method under the same computing efforts. (Author)

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.

Nonconforming h-p spectral element methods for elliptic problems

Indian Academy of Sciences (India)

In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

Directory of Open Access Journals (Sweden)

Wei Li

2012-01-01

Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.

Seismic wave propagation in non-homogeneous elastic media by boundary elements

CERN Document Server

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 ...

Simultaneous heat and moisture transfer in porous elements: transfer function method

International Nuclear Information System (INIS)

Souza, H.A. de.

1985-01-01

The presence of moisture in a porous element may strongly affect the transfer of heat through this element due to the processes which occur associated with the phase changes at the boundary surfaces and internally in the wall body. In addition, the structural properties of the element may also be meaningfully affected. The formulation of mathematical models for the simultaneous heat and mass transfer in porous elements results in a pair of nonlinear coupled equations for the temperature and moisture content distributions, in the material. It is supposed, in this work, that the actual variation of the properties of the porous medium is small in the range of variables which describe the specific problem to be analyzed. This enables us to work with linearized equations, making possible the use of linear solution methods. In this context, the present work deals with a linear procedure for the solution of simultaneous heat and moisture transfer problems in porous elements, sujected to arbitrary boundary conditions. This results in a linear relation between the heat and mass flux densities through the boundary surfaces of the elements and their associated potentials. It is shown that the model is consistent in asymptotical limiting cases; the model is then used for analyzing the drying process of a porous element, subjected to ambient actual conditions. (Author) [pt

Use of the finite element displacement method to solve solid-fluid interaction vibration problems

International Nuclear Information System (INIS)

Brown, S.J.; Hsu, K.H.

1978-01-01

It is shown through comparison to experimental, theoretical, and other finite element formulations that the finite element displacement method can solve accurately and economically a certain class of solid-fluid eigenvalue problems. The problems considered are small displacements in the absence of viscous damping and are 2-D and 3-D in nature. In this study the advantages of the finite element method (in particular the displacement formulation) is apparent in that a large structure consisting of the cylinders, support flanges, fluid, and other experimental boundaries could be modeled to yield good correlation to experimental data. The ability to handle large problems with standard structural programs is the key advantage of the displacement fluid method. The greatest obstacle is the inability of the analyst to inhibit those rotational degrees of freedom that are unnecessary to his fluid-structure vibration problem. With judicious use of element formulation, boundary conditions and modeling, the displacement finite element method can be successfully used to predict solid-fluid response to vibration and seismic loading

[Stress analysis of femoral stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer].

Science.gov (United States)

Oomori, H; Imura, S; Gesso, H

1992-04-01

To develop stem design achieving primary fixation of stems and effective load transfer to the femur, we studied stress analysis of stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer in stem-bone interface. The results of analyses of stem-bone interface stresses and von Mises stresses at the cortical bones indicated that ideal stem design features would be as follows: 1) Sufficient length, with the distal end extending beyond the isthmus region. 2) Maximum possible width, to contact the cortical bones in the isthmus region. 3) No collars but a lateral shoulder at the proximal portion. 4) A distal tip, to contact the cortical bones at the distal portion.

Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry

DEFF Research Database (Denmark)

Volakis, John L.; Sertel, Kubilay; Jørgensen, Erik

2004-01-01

n this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons of volume integral equation formulations with the finite element-boundary integral method are given in terms of accu...... of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications....

Boundary Element Analysis of the Steady-state Response of an Elastic Half-Space to a Moving Force on its Surface

DEFF Research Database (Denmark)

Andersen, Lars; Nielsen, Søren R. K.

2003-01-01

The paper deals with the boundary element method formulation of the steady-state wave propagation through elastic media due to a source moving with constant velocity. The Greens' function for the three-dimensional full-space is formulated in a local frame of reference following the source...... is approximated, but the error which is introduced in this way is insignificant. Numerical examples are given for a moving rectangular load on an elastic half-space. The result from a boundary element code based on the derived Green's function are compared with a semi-analytic solution....

Application of the boundary elements method for modeling of the fracture of cylindrical bodies by hydraulic fracturing

Science.gov (United States)

Legan, M. A.; Blinov, V. A.; Larichkin, A. Yu; Novoselov, A. N.

2017-10-01

Experimental study of hydraulic fracturing of thick-walled cylinders with a central circular hole was carried out using the machine that creates a high oil pressure. Experiments on the compression fracture of the solid cylinders by diameter and rectangular parallelepipeds perpendicular to the ends were carried out with a multipurpose test machine Zwick / Roell Z100. Samples were made of GF-177 material based on cement. Ultimate stresses in the material under study were determined for three types of stress state: under compression, with a pure shear on the surface of the hole under frecking conditions and under a compound stress state under conditions of diametral compression of a solid cylinder. The value of the critical stress intensity factor of GF-177 material was obtained. The modeling of the fracturing process taking into account the inhomogeneity of the stress state near the hole was carried out using the boundary elements method (in the variant of the fictitious load method) and the gradient fracture criterion. Calculation results of the ultimate pressure were compared with values obtained analytically on the basis of the Lame solution and with experimental data.

Application of the finite element method to neutronics problems with inhomogeneous boundray conditions

International Nuclear Information System (INIS)

Yoo, K.J.

1982-01-01

The albedo boundary conditions are incorporated into the finite element method using bicubic Hermite element functions in order to reduce the computer memory and computation time in two-group diffusion calculations by excluding the reflector regions in computation space. The basis functions at the core-reflector interfaces are newly established to satisfy the albedo boundary conditions, and then the ''weak'' form of two-group diffusion equations is discretized using the principle of the weighted residual method in combination with the Galerkin approximation. The discretized two-group diffusion equation is then solved by the Gaussian elimination method with the scaled column pivoting algorithm in one-dimensional problem and Gauss-Seidel method in two-dimensional problem. Prior to the application of the method to two-group diffusion problems, the same method is applied to the one-speed neutron transport equation in a bare slab reactor with the vacuum boundary condition to confirm its usefulness in the diffusion calculations. To investigate the applicability of our diffusion method, several numerical calculations are performed: two-dimensional IAEA benchmark problem and two-dimensional ZION problem. The results are compared with the available results from the conventional finite difference and other finite element methods. If the albedo values are appropriately adjusted, our results of the two-dimensional IAEA benchmark problem are agreed within 0.002% of ksub(eff) with the fine mesh PDQ results. Comparing with CITATION results, one-eighth of core memory and one-fifteenth of computing time are required to obtain the same accuracy even though no acceleration technique is used in the present case. Also, it is found that the results are comparable with the other finite element results. However, no significant saving is obtained in computation time comparing with the other finite element results, where the reflector regions are explicity included. This mainly comes from

A discontinuous galerkin time domain-boundary integral method for analyzing transient electromagnetic scattering

KAUST Repository

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.

Finite element method for computational fluid dynamics with any type of elements; Finite Element Methode zur numerischen Stroemungsberechnung mit beliebigen Elementen

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

Mixed Generalized Multiscale Finite Element Methods and Applications

KAUST Repository

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.

A proposal for a determination method of element division on an analytical model for finite element elastic waves propagation analysis

International Nuclear Information System (INIS)

Ishida, Hitoshi; Meshii, Toshiyuki

2010-01-01

This study proposes an element size selection method named the 'Impact-Meshing (IM) method' for a finite element waves propagation analysis model, which is characterized by (1) determination of element division of the model with strain energy in the whole model, (2) static analysis (dynamic analysis in a single time step) with boundary conditions which gives a maximum change of displacement in the time increment and inertial (impact) force caused by the displacement change. In this paper, an example of application of the IM method to 3D ultrasonic wave propagation problem in an elastic solid is described. These examples showed an analysis result with a model determined by the IM method was convergence and calculation time for determination of element subdivision was reduced to about 1/6 by the IM Method which did not need determination of element subdivision by a dynamic transient analysis with 100 time steps. (author)

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

Science.gov (United States)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Mathematical aspects of finite element methods for incompressible viscous flows

Science.gov (United States)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Application of the finite element method to the neutron transport equation

International Nuclear Information System (INIS)

Martin, W.R.

1976-01-01

This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions

Natural element method for radiative heat transfer in a semitransparent medium with irregular geometries

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yong [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001 (China); Yi, Hong-Liang, E-mail: yihongliang@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001 (China); Tan, He-Ping, E-mail: tanheping@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001 (China)

2013-05-15

This paper develops a numerical solution to the radiative heat transfer problem coupled with conduction in an absorbing, emitting and isotropically scattering medium with the irregular geometries using the natural element method (NEM). The walls of the enclosures, having temperature and mixed boundary conditions, are considered to be opaque, diffuse as well as gray. The NEM as a meshless method is a new numerical scheme in the field of computational mechanics. Different from most of other meshless methods such as element-free Galerkin method or those based on radial basis functions, the shape functions used in NEM are constructed by the natural neighbor interpolations, which are strictly interpolant and the essential boundary conditions can be imposed directly. The natural element solutions in dealing with the coupled heat transfer problem for the mixed boundary conditions have been validated by comparison with those from Monte Carlo method (MCM) generated by the authors. For the validation of the NEM solution to radiative heat transfer in the semicircular medium with an inner circle, the results by NEM have been compared with those reported in the literatures. For pure radiative transfer, the upwind scheme is employed to overcome the oscillatory behavior of the solutions in some conditions. The steady state and transient heat transfer problem combined with radiation and conduction in the semicircular enclosure with an inner circle are studied. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction–radiation parameter and the boundary emissivity are analyzed on the radiative and conductive heat fluxes and transient temperature distributions.

SSI 2D/3D soil structure interaction: A program system for the calculation of structure-soil interactions using the boundary element method. Project C1

International Nuclear Information System (INIS)

Schmid, G.; Willms, G.; Huh, Y.; Gibhardt, M.

1988-12-01

SSI 2D/3D is a computer programm to calculate dynamic stiffness matrices for soil-structure-interaction problems in frequency domain. It is applicable to two- or three-dimensional situations. The present report is a detailed manual for the use of the computer code written in FORTRAN 77. In addition it gives a survey of the possibilities of the Boundary Element Method applied to dynamic problems in infinite domains. (orig.) [de

A finite element method for calculating the 3-dimensional magnetic fields of cyclotron

International Nuclear Information System (INIS)

Zhao Xiaofeng

1986-01-01

A series of formula of the finite element method (scalar potential) for calculating the three-dimensional magnetic field of the main magnet of a sector focused cyclotron, and the realization method of the periodic boundary conditions in the code are given

Efficient parallel iterative solvers for the solution of large dense linear systems arising from the boundary element method in electromagnetism

International Nuclear Information System (INIS)

Alleon, G.; Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E.

2003-01-01

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)

Efficient parallel iterative solvers for the solution of large dense linear systems arising from the boundary element method in electromagnetism

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)

Possibilities of Particle Finite Element Methods in Industrial Forming Processes

Science.gov (United States)

Oliver, J.; Cante, J. C.; Weyler, R.; Hernandez, J.

2007-04-01

The work investigates the possibilities offered by the particle finite element method (PFEM) in the simulation of forming problems involving large deformations, multiple contacts, and new boundaries generation. The description of the most distinguishing aspects of the PFEM, and its application to simulation of representative forming processes, illustrate the proposed methodology.

Implementation of a boundary element method to solve for the near field effects of an array of WECs

Science.gov (United States)

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.

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.

Direct displacement-based design of special composite RC shear walls with steel boundary elements

Directory of Open Access Journals (Sweden)

H. Kazemi

2016-06-01

Full Text Available Special composite RC shear wall (CRCSW with steel boundary elements is a kind of lateral force resisting structural system which is used in earthquake-prone regions. Due to their high ductility and energy dissipation, CRCSWs have been widely used in recent years by structural engineers. However, there are few studies in the literature on the seismic design of such walls. Although there are many studies in the literature on the Direct Displacement-Based Design (DDBD of RC structures, however, no study can be found on DDBD of CRCSWs. Therefore, the aim of present study is to evaluate the ability of DDBD method for designing CRCSWs. In this study, four special composite reinforced concrete shear walls with steel boundary elements of 4, 8, 12 and 16 story numbers were designed using the DDBD method for target drift of 2%. The seismic behavior of the four CRCSWs was studied using nonlinear time-history dynamic analyses. Dynamic analyses were performed for the mentioned walls using 7 selected earthquake records. The seismic design parameters considered in this study includes: lateral displacement profile, inelastic dynamic inter-story drift demand, failure pattern and the composite RC shear walls overstrength factor. For each shear wall, the overall overstrength factor was calculated by dividing the ultimate dynamic base shear demand (Vu by the base shear demand (Vd as per the Direct Displacement Based-Design (DDBD method. The results show that the DDBD method can be used to design CRCSWs safely in seismic regions with predicted behavior.

On the trial functions in nested element method

International Nuclear Information System (INIS)

Altiparmakov, D.V.

1985-01-01

The R-function method is applied to the multidimensional steady-state neutron diffusion equation. Using a variational principle the nested element approximation is formulated. Trial functions taking into account the geometrical shape of material regions are constructed. The influence of both the surrounding regions and the corner singularities at the external boundary is incorporated into the approximate solution. Benchmark calculations show that such an approximation can yield satisfactory results. Moreover, in the case of complex geometry, the presented approach would result in a significant reduction of the number of unknowns compared to other methods

Three-dimensional local ALE-FEM method for fluid flow in domains containing moving boundaries/objects interfaces

Energy Technology Data Exchange (ETDEWEB)

Carrington, David Bradley [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Monayem, A. K. M. [Univ. of New Mexico, Albuquerque, NM (United States); Mazumder, H. [Univ. of New Mexico, Albuquerque, NM (United States); Heinrich, Juan C. [Univ. of New Mexico, Albuquerque, NM (United States)

2015-03-05

A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is a fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

The Boundary Element Method Applied to the Two Dimensional Stefan Moving Boundary Problem

Science.gov (United States)

1991-03-15

Unc), - ( UGt )t - (UG,,),,] - (UG), If we integrate this equation with respect to r from 0 to t - c and with respect to and ij on the region 11(r...and others. "Moving Boundary Problems in Phase Change Mod- els," SIGNUM Newsletter, 20: 8-12 (1985). 21. Stefan, J. "Ober einige Probleme der Theorie ...ier Wirmelcitung," S.-B. \\Vein. Akad. Mat. Natur., 98: 173-484 (1889). 22.-. "flber (lie Theorie der Eisbildung insbesondere fiber die lisbildung im

Material equations for rock salt under mechanical and thermal load including treatment of boundary value problems by the finite element method

International Nuclear Information System (INIS)

Olschewski, J.; Stein, E.; Wagner, W.; Wetjen, D.

1981-01-01

This paper is a first step in the development of thermodynamically consistent material equations for inelastic materials, such as polycrystalline rock salt. In this context it is of particular importance to reduce the number and the structure of the internal variables, in order to allow for a fit with available experimental data. As an example this is demonstrated in detail in the case of the so-called dislocation model. As physical non-linearities and in addition also geometrical non-linearities lead to an inhomogeneous deformation - and stress state even in the case of simple samples, boundary value problems have to be studied, in order to test the material equations. For this purpose the finite element method has been used. (orig./HP) [de

A simple boundary element formulation for shape optimization of 2D continuous structures

International Nuclear Information System (INIS)

Luciano Mendes Bezerra; Jarbas de Carvalho Santos Junior; Arlindo Pires Lopes; Andre Luiz; Souza, A.C.

2005-01-01

For the design of nuclear equipment like pressure vessels, steam generators, and pipelines, among others, it is very important to optimize the shape of the structural systems to withstand prescribed loads such as internal pressures and prescribed or limiting referential values such as stress or strain. In the literature, shape optimization of frame structural systems is commonly found but the same is not true for continuous structural systems. In this work, the Boundary Element Method (BEM) is applied to simple problems of shape optimization of 2D continuous structural systems. The proposed formulation is based on the BEM and on deterministic optimization methods of zero and first order such as Powell's, Conjugate Gradient, and BFGS methods. Optimal characterization for the geometric configuration of 2D structure is obtained with the minimization of an objective function. Such function is written in terms of referential values (such as loads, stresses, strains or deformations) prescribed at few points inside or at the boundary of the structure. The use of the BEM for shape optimization of continuous structures is attractive compared to other methods that discretized the whole continuous. Several numerical examples of the application of the proposed formulation to simple engineering problems are presented. (authors)

Modeling grain boundaries in polycrystals using cohesive elements: Qualitative and quantitative analysis

Energy Technology Data Exchange (ETDEWEB)

El Shawish, Samir, E-mail: Samir.ElShawish@ijs.si [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Cizelj, Leon [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Simonovski, Igor [European Commission, DG-JRC, Institute for Energy and Transport, P.O. Box 2, NL-1755 ZG Petten (Netherlands)

2013-08-15

Highlights: ► We estimate the performance of cohesive elements for modeling grain boundaries. ► We compare the computed stresses in ABAQUS finite element solver. ► Tests are performed in analytical and realistic models of polycrystals. ► Most severe issue is found within the plastic grain response. ► Other identified issues are related to topological constraints in modeling space. -- Abstract: We propose and demonstrate several tests to estimate the performance of the cohesive elements in ABAQUS for modeling grain boundaries in complex spatial structures such as polycrystalline aggregates. The performance of the cohesive elements is checked by comparing the computed stresses with the theoretically predicted values for a homogeneous material under uniaxial tensile loading. Statistical analyses are performed under different loading conditions for two elasto-plastic models of the grains: isotropic elasticity with isotropic hardening plasticity and anisotropic elasticity with crystal plasticity. Tests are conducted on an analytical finite element model generated from Voronoi tessellation as well as on a realistic finite element model of a stainless steel wire. The results of the analyses highlight several issues related to the computation of normal and shear stresses. The most severe issue is found within the plastic grain response where the computed normal stresses on a particularly oriented cohesive elements are significantly underestimated. Other issues are found to be related to topological constraints in the modeling space and result in the increased scatter of the computed stresses.

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.

Fictitious domain methods for elliptic problems with general boundary conditions with an application to the numerical simulation of two phase flows

International Nuclear Information System (INIS)

Ramiere, I.

2006-09-01

This work is dedicated to the introduction of two original fictitious domain methods for the resolution of elliptic problems (mainly convection-diffusion problems) with general and eventually mixed boundary conditions: Dirichlet, Robin or Neumann. The originality lies in the approximation of the immersed boundary by an approximate interface derived from the fictitious domain Cartesian mesh, which is generally not boundary-fitted to the physical domain. The same generic numerical scheme is used to impose the embedded boundary conditions. Hence, these methods require neither a surface mesh of the immersed boundary nor the local modification of the numerical scheme. We study two modelling of the immersed boundary. In the first one, called spread interface, the approximate immersed boundary is the union of the cells crossed by the physical immersed boundary. In the second one, called thin interface, the approximate immersed boundary lies on sides of mesh cells. Additional algebraic transmission conditions linking both flux and solution jumps through the thin approximate interface are introduced. The fictitious problem to solve as well as the treatment of the embedded boundary conditions are detailed for the two methods. A Q1 finite element scheme is implemented for the numerical validation of the spread interface approach while a new cell-centered finite volume scheme is derived for the thin interface approach with immersed jumps. Each method is then combined to multilevel local mesh refinement algorithms (with solution or flux residual) to increase the precision of the solution in the vicinity of the immersed interface. A convergence analysis of a Q1 finite element method with non-boundary fitted meshes is also presented. This study proves the convergence rates of the present methods. Among the various industrial applications, the simulation on a model of heat exchanger in french nuclear power plants enables us to appreciate the performances of the fictitious domain

A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

KAUST Repository

Bao, Kai

2012-10-01

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

KAUST Repository

Bao, Kai; Shi, Yi; Sun, Shuyu; Wang, Xiaoping

2012-01-01

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

Straight velocity boundaries in the lattice Boltzmann method

Science.gov (United States)

Latt, Jonas; Chopard, Bastien; Malaspinas, Orestis; Deville, Michel; Michler, Andreas

2008-05-01

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

A Finite Element Removal Method for 3D Topology Optimization

Directory of Open Access Journals (Sweden)

M. Akif Kütük

2013-01-01

Full Text Available Topology optimization provides great convenience to designers during the designing stage in many industrial applications. With this method, designers can obtain a rough model of any part at the beginning of a designing stage by defining loading and boundary conditions. At the same time the optimization can be used for the modification of a product which is being used. Lengthy solution time is a disadvantage of this method. Therefore, the method cannot be widespread. In order to eliminate this disadvantage, an element removal algorithm has been developed for topology optimization. In this study, the element removal algorithm is applied on 3-dimensional parts, and the results are compared with the ones available in the related literature. In addition, the effects of the method on solution times are investigated.

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 ...... it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies....

Simulation of the deformation of a fluid domain in motion in another fluid by the boundary element method

International Nuclear Information System (INIS)

Rocchi-Tavares, Miriam

1992-01-01

The objective of this research thesis is to model the sustentation (or aerodynamic levitation) of a drop by a fluid flowing through a porous plate. More precisely, the author developed a general calculation tool to solve the Stokes problem by using the boundary element method. The author reports the calculation of stresses at the surface of a solid body moving in an infinite medium, in order to validate the calculation tool before its extension to more complex problems. Then, the model is developed to describe the deformation of a fluid mass moving in another fluid. The surrounding environment is either infinite or limited by a plane wall which can be impervious or crossed by an ambient fluid. Then, the author addresses the study of the evolution of the surface of a drop moving in an infinite medium, analyses the behaviour of a fluid mass at the vicinity of a plane, infinite and impervious wall. The last part addresses the sustentation of a deformable fluid body above a porous plane wall crossed by another fluid [fr

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.

A time-domain finite element boundary integral approach for elastic wave scattering

Science.gov (United States)

Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.

2018-04-01

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Adaptive finite element method for shape optimization

KAUST Repository

Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco

2012-01-01

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.

Adaptive finite element method for shape optimization

KAUST Repository

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.

A resolution study for electrostatic force microscopy on bimetallic samples using the boundary element method

International Nuclear Information System (INIS)

Shen Yongxing; Lee, Minhwan; Lee, Wonyoung; Barnett, David M; Pinsky, Peter M; Prinz, Friedrich B

2008-01-01

Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip- and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM- and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities

Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

CERN Document Server

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...

Numerical analysis of melting/solidification phenomena using a moving boundary problem analysis method X-FEM

International Nuclear Information System (INIS)

Uchibori, Akihiro; Ohshima, Hiroyuki

2008-01-01

A numerical analysis method for melting/solidification phenomena has been developed to evaluate a feasibility of several candidate techniques in the nuclear fuel cycle. Our method is based on the eXtended Finite Element Method (X-FEM) which has been used for moving boundary problems. Key technique of the X-FEM is to incorporate signed distance function into finite element interpolation to represent a discontinuous gradient of the temperature at a moving solid-liquid interface. Construction of the finite element equation, the technique of quadrature and the method to solve the equation are reported here. The numerical solutions of the one-dimensional Stefan problem, solidification in a two-dimensional square corner and melting of pure gallium are compared to the exact solutions or to the experimental data. Through these analyses, validity of the newly developed numerical analysis method has been demonstrated. (author)

A mixed finite element domain decomposition method for nearly elastic wave equations in the frequency domain

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.

SAFE-3D, Stress Analysis of 3-D Composite Structure by Finite Elements Method

International Nuclear Information System (INIS)

Cornell, D.C.; Jadhav, K.; Crowell, J.S.

1969-01-01

1 - Description of problem or function: SAFE-3D is a finite-element program for the three-dimensional elastic analysis of heterogeneous composite structures. The program uses the following types of finite elements - (1) tetrahedral elements to represent the continuum, (2) triangular plane stress membrane elements to represent inner liner or outer case, and (3) uniaxial tension-compression elements to represent internal reinforcement. The structure can be of arbitrary geometry and have any distribution of material properties, temperatures, surface loadings, and boundary conditions. 2 - Method of solution: The finite-element variational method is used. Equilibrium equations are solved by the alternating component iterative method. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 nodes; 16000 elements. The program cannot be applied to incompressible solids and is not recommended for Poisson's ratio in the range of nu between 0.495 and 0.5

The numerical study and comparison of radial basis functions in applications of the dual reciprocity boundary element method to convection-diffusion problems

Science.gov (United States)

Chanthawara, Krittidej; Kaennakham, Sayan; Toutip, Wattana

2016-02-01

The methodology of Dual Reciprocity Boundary Element Method (DRBEM) is applied to the convection-diffusion problems and investigating its performance is our first objective of the work. Seven types of Radial Basis Functions (RBF); Linear, Thin-plate Spline, Cubic, Compactly Supported, Inverse Multiquadric, Quadratic, and that proposed by [12], were closely investigated in order to numerically compare their effectiveness drawbacks etc. and this is taken as our second objective. A sufficient number of simulations were performed covering as many aspects as possible. Varidated against both exacts and other numerical works, the final results imply strongly that the Thin-Plate Spline and Linear type of RBF are superior to others in terms of both solutions' quality and CPU-time spent while the Inverse Multiquadric seems to poorly yield the results. It is also found that DRBEM can perform relatively well at moderate level of convective force and as anticipated becomes unstable when the problem becomes more convective-dominated, as normally found in all classical mesh-dependence methods.

Analysis of a discrete element method and coupling with a compressible fluid flow method

International Nuclear Information System (INIS)

Monasse, L.

2011-01-01

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an un-deformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method. (author) [fr

Spectral element method for elastic and acoustic waves in frequency domain

Energy Technology Data Exchange (ETDEWEB)

Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)

2016-12-15

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

Design of a Double Anode Magnetron Injection Gun for Q-band Gyro-TWT Using Boundary Element Method

Science.gov (United States)

Li, Zhiliang; Feng, Jinjun; Liu, Bentian

2018-04-01

This paper presents a novel design code for double anode magnetron injection guns (MIGs) in gyro-devices based on boundary element method (BEM). The physical and mathematical models were constructed, and then the code using BEM for MIG's calculation was developed. Using the code, a double anode MIG for a Q-band gyrotron traveling-wave tube (gyro-TWT) amplifier operating in the circular TE01 mode at the fundamental cyclotron harmonic was designed. In order to verify the reliability of this code, velocity spread and guiding center radius of the MIG simulated by the BEM code were compared with these from the commonly used EGUN code, showing a reasonable agreement. Then, a Q-band gyro-TWT was fabricated and tested. The testing results show that the device has achieved an average power of 5kW and peak power ≥ 150 kW at a 3% duty cycle within bandwidth of 2 GHz, and maximum output peak power of 220 kW, with a corresponding saturated gain of 50.9 dB and efficiency of 39.8%. This paper demonstrates that the BEM code can be used as an effective approach for analysis of electron optics system in gyro-devices.

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT. [Conjugate Gradient Fast Fourier Transformation

Science.gov (United States)

Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming

1990-01-01

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Calculation of two-dimensional thermal transients by the finite element method

International Nuclear Information System (INIS)

Fontoura Rodrigues, J.L.A. da; Barcellos, C.S. de

1981-01-01

The linear heat conduction through anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is analysed. It only accepts time-independent boundary conditions and it is possible to have internal heat generation. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. (Author) [pt

Lattice Boltzmann methods for moving boundary flows

International Nuclear Information System (INIS)

Inamuro, Takaji

2012-01-01

The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)

Lattice Boltzmann methods for moving boundary flows

Energy Technology Data Exchange (ETDEWEB)

Inamuro, Takaji, E-mail: inamuro@kuaero.kyoto-u.ac.jp [Department of Aeronautics and Astronautics, and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 (Japan)

2012-04-01

The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)

Extended finite element method and its application in heterogeneous materials with inclusions

International Nuclear Information System (INIS)

Du Chengbin; Jiang Shouyan; Ying Zongquan

2010-01-01

To simplify the technology of finite element mesh generation for particle reinforced material, enrichment techniques is used to account for the material interfaces in the framework of extended finite element method (XFEM). The geometry of material distribution is described by level set function, which allows one to model the internal boundaries of the microstructure without the adaptation of the mesh. The enrichment function is used to improve the shape function of classical finite element method (FEM) for the nodes supporting the elements cut by the interface. The key issue of XFEM including constructing displacement pattern, establishment of the governing equation and scheme of numerical integration is also presented. It is not necessarily matching the internal features of the inclusions using XFEM, so the generation of finite element mesh can be performed easily. Finally, a plate with multi-circular inclusions under uniaxial tension is simulated by XFEM and FEM, respectively. The results show that XFEM is highly effective and efficient.

Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problems

Science.gov (United States)

Zhang, Shuhai; Oskay, Caglar

2015-04-01

This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global-local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson-Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.

Segregation of solute elements at grain boundaries in an ultrafine grained Al-Zn-Mg-Cu alloy

International Nuclear Information System (INIS)

Sha, Gang; Yao, Lan; Liao, Xiaozhou; Ringer, Simon P.; Chao Duan, Zhi; Langdon, Terence G.

2011-01-01

The solute segregation at grain boundaries (GBs) of an ultrafine grained (UFG) Al-Zn-Mg-Cu alloy processed by equal-channel angular pressing (ECAP) at 200 o C was characterised using three-dimensional atom probe. Mg and Cu segregate strongly to the grain boundaries. In contrast, Zn does not always show clear segregation and may even show depletion near the grain boundaries. Trace element Si selectively segregates at some GBs. An increase in the number of ECAP passes leads to a decrease in the grain size but an increase in solute segregation at the boundaries. The significant segregation of alloying elements at the boundaries of ultrafine-grained alloys implies that less solutes will be available in the matrix for precipitation with a decrease in the average grain size. -- Research Highlights: → Atom probe tomography has been employed successfully to reveal unique segregation of solutes at ultrafine grained material. → Mg and Cu elements segregated strongly at the grain boundary of an ultrafine grained Al-Zn-Mg-Cu alloy processed by 4-pass and 8-pass ECAP at 200 o C. Zn frequently depleted at GBs with a Zn depletion region of 7-15 nm in width on one or both sides of the GBs. Only a small fraction (3/13) of GBs were observed with a low level of Zn segregation where the combined Mg and Cu excess is over 3.1 atom/nm 2 . Si appeared selectively segregated at some of the GBs. → The increase in number of ECAP passes from 4 to 8 correlated with the increase in mean level segregation of Mg and Cu for both solute excess and peak concentration. → The change of plane normal of a grain boundary within 30 o only leads to a slight change in the solute segregation level.

Effects of Heat Input and Bead Generation Methods on Finite Element Analysis of Multi-Pass Welding Process

Energy Technology Data Exchange (ETDEWEB)

Park, Won Dong; Kim, Ji Hoon; Bahn, Chi Bum [Pusan National University, Busan (Korea, Republic of)

2016-10-15

Welding residual stresses are determined by various factors such as heat input, initial temperature of molten bead, heating time, cooling time, cooling conditions, and boundary conditions. In this study, a sensitivity analysis was performed to find the major factors and reasonable assumptions for simulation. Two-dimensional axisymmetric simulation was conducted by using commercial finite element analysis program ABAQUS, for multi-pass Alloy 82 welds in a 304 Stainless Steel and SA-105 Carbon Steel. The major object is to evaluate effects of the heat input methods and weld bead generation methods on the welding residual stress distribution. Totally four kinds of methods were compared. From the previous results, we could make the following conclusions. 1. Although there are non-negligible differences in HAZ depending on heat input method, welding residual stress distributions have roughly similar trends. However, it is needed to perform the more exact analysis to apply heat energy more carefully into the individual bead. 2. Residual stress distribution were similar for the two weld bead generation technique. However, overlapping was happened when element birth technique was applied. Effects of overlapping could not ignore as deformation increases. However, overlapping problem was avoided when quiet element technique was used. 3. Since existence of inactive bead elements, inaccurate weld residual stresses could be occurred in boundaries of previous and next weld elements in case of quiet element technique.

Node-based finite element method for large-scale adaptive fluid analysis in parallel environments

International Nuclear Information System (INIS)

Toshimitsu, Fujisawa; Genki, Yagawa

2003-01-01

In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)

Node-based finite element method for large-scale adaptive fluid analysis in parallel environments

Energy Technology Data Exchange (ETDEWEB)

Toshimitsu, Fujisawa [Tokyo Univ., Collaborative Research Center of Frontier Simulation Software for Industrial Science, Institute of Industrial Science (Japan); Genki, Yagawa [Tokyo Univ., Department of Quantum Engineering and Systems Science (Japan)

2003-07-01

In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

Science.gov (United States)

Chen, Z.; Shu, C.; Tan, D.

2018-05-01

An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

Determination of stable shapes of a thin liquid metal layer using a boundary integral method

Energy Technology Data Exchange (ETDEWEB)

Hinaje, M [Groupe de Recherche en Electrotechnique et Electronique de Nancy, 2 avenue de la Foret de Haye, 54516 Vandoeuvre-les-Nancy (France); Vinsard, G [Laboratoire d' Energetique et de Mecanique Theorique et Appliquee, 2 avenue de la Foret de Haye, 54516 Vandoeuvre-les-Nancy (France); Dufour, S [Groupe de Recherche en Electrotechnique et Electronique de Nancy, 2 avenue de la Foret de Haye, 54516 Vandoeuvre-les-Nancy (France)

2006-03-21

This paper deals with a thin liquid metal layer submitted to an ac magnetic field. Experimentally, we have noticed that even if the system (inductor+liquid metal) is axisymmetric, when an ac magnetic field is applied the symmetry is broken. The observed deformations of the liquid metal are in three dimensions. Therefore, our aim is to investigate this deformation using a numerical method as boundary element method in three dimensions.

Determination of stable shapes of a thin liquid metal layer using a boundary integral method

International Nuclear Information System (INIS)

Hinaje, M; Vinsard, G; Dufour, S

2006-01-01

This paper deals with a thin liquid metal layer submitted to an ac magnetic field. Experimentally, we have noticed that even if the system (inductor+liquid metal) is axisymmetric, when an ac magnetic field is applied the symmetry is broken. The observed deformations of the liquid metal are in three dimensions. Therefore, our aim is to investigate this deformation using a numerical method as boundary element method in three dimensions

A 2.5D finite element and boundary element model for the ground vibration from trains in tunnels and validation using measurement data

Science.gov (United States)

Jin, Qiyun; Thompson, David J.; Lurcock, Daniel E. J.; Toward, Martin G. R.; Ntotsios, Evangelos

2018-05-01

A numerical model is presented for the ground-borne vibration produced by trains running in tunnels. The model makes use of the assumption that the geometry and material properties are invariant in the axial direction. It is based on the so-called two-and-a-half dimensional (2.5D) coupled Finite Element and Boundary Element methodology, in which a two-dimensional cross-section is discretised into finite elements and boundary elements and the third dimension is represented by a Fourier transform over wavenumbers. The model is applied to a particular case of a metro line built with a cast-iron tunnel lining. An equivalent continuous model of the tunnel is developed to allow it to be readily implemented in the 2.5D framework. The tunnel structure and the track are modelled using solid and beam finite elements while the ground is modelled using boundary elements. The 2.5D track-tunnel-ground model is coupled with a train consisting of several vehicles, which are represented by multi-body models. The response caused by the passage of a train is calculated as the sum of the dynamic component, excited by the combined rail and wheel roughness, and the quasi-static component, induced by the constant moving axle loads. Field measurements have been carried out to provide experimental validation of the model. These include measurements of the vibration of the rail, the tunnel invert and the tunnel wall. In addition, simultaneous measurements were made on the ground surface above the tunnel. Rail roughness and track characterisation measurements were also made. The prediction results are compared with measured vibration obtained during train passages, with good agreement.

Local deformation method for measuring element tension in space deployable structures

Directory of Open Access Journals (Sweden)

Belov Sergey

2017-01-01

Full Text Available The article describes the local deformation method to determine the tension of cord and thin membrane elements in space deployable structure as antenna reflector. Possible measuring instrument model, analytical and numerical solutions and experimental results are presented. The boundary effects on measurement results of metallic mesh reflector surface tension are estimated. The study case depicting non-uniform reflector surface tension is considered.

Semianalytical analysis of shear walls with the use of discrete-continual finite element method. Part 1: Mathematical foundations

Directory of Open Access Journals (Sweden)

Akimov Pavel

2016-01-01

Full Text Available The distinctive paper is devoted to the two-dimensional semi-analytical solution of boundary problems of analysis of shear walls with the use of discrete-continual finite element method (DCFEM. This approach allows obtaining the exact analytical solution in one direction (so-called “basic” direction, also decrease the size of the problem to one-dimensional common finite element analysis. The resulting multipoint boundary problem for the first-order system of ordinary differential equations with piecewise constant coefficients is solved analytically. The proposed method is rather efficient for evaluation of the boundary effect (such as the stress field near the concentrated force. DCFEM also has a completely computer-oriented algorithm, computational stability, optimal conditionality of resultant system and it is applicable for the various loads at an arbitrary point or a region of the wall.

Calculation of two-dimensional thermal transients by the method of finite elements

International Nuclear Information System (INIS)

Fontoura Rodrigues, J.L.A. da.

1980-08-01

The unsteady linear heat conduction analysis throught anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is presented. The boundary conditions and the internal heat generation are supposed time - independent. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. Optionally, it can be used with a reduced resolution method called Stoker Economizing Method wich allows a decrease on the program processing costs. (Author) [pt

Variational Multiscale Finite Element Method for Flows in Highly Porous Media

KAUST Repository

Iliev, O.; Lazarov, R.; Willems, J.

2011-01-01

We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

Variational Multiscale Finite Element Method for Flows in Highly Porous Media

KAUST Repository

Iliev, O.

2011-10-01

We present a two-scale finite element method (FEM) for solving Brinkman\\'s and Darcy\\'s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes\\' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy\\'s equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

KAUST Repository

Jin, B.; Lazarov, R.; Pasciak, J.; Zhou, Z.

2014-01-01

© 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.

Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

KAUST Repository

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.

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

International Nuclear Information System (INIS)

Kılıç, Emre; Eibert, Thomas F.

2015-01-01

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

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

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.

[Stress analysis on the acetabular side of bipolar hemiarthroplasty by the two-dimensional finite element method incorporating the boundary friction layer].

Science.gov (United States)

Ichihashi, K; Imura, S; Oomori, H; Gesso, H

1994-11-01

We compared the biomechanical characteristics of bipolar and unipolar hemiarthroplasty on the proximal migration of the outer head by determining the von Mises stress distribution and acetabular (outer head) displacement with clinical assessment of hemiarthroplasty in 75 patients. This analysis used the two-dimensional finite element method, which incorporated boundary friction layers on both the inner and outer bearings of the prosthesis. Acetabular reaming increased stress within the pelvic bone and migration of the outer head. A combination of the acetabular reaming and bone transplantation increased the stress within the pelvic bone and grafted bone, and caused outer head migration. These findings were supported by clinical results. Although the bipolar endoprosthesis was biomechanically superior to the unipolar endoprosthesis, migration of the outer head still occurred. The bipolar endoprosthesis appeared to be indicated in cases of a femoral neck fracture or of avascular necrosis in the femoral head, but its use in cases of osteoarthritis in the hip required caution.

Self-adaptive treatment of time dependent nonlinear nonhomogeneous radial heat flow in reactor components with boundary element method; Samoadaptivno obravnanje spemenljivega nelinearnega nehomogenoga radialnega topltnega toka v reaktorskih komponentah z metodo robnih elementov

Energy Technology Data Exchange (ETDEWEB)

Sarler, B; Alujevic, A [Univerza B. Kardelja, Institut ' Jozef Stefan' , Ljubljana (Yugoslavia)

1988-07-01

The basic principles of self-adaptive algorithm for treatment of transient nonlinear nonhomogeneous radial heat flow, based on direct Boundary Element method formulation, are presented. The indicators of discretization error are developed, together with binary-tree strategy for manipulation with time domain mesh, assuring automatic optimisation of calculation procedure with respect to predetermined error. The developed method is particularly suitable for use in a spectrum of extremely nonlinear cases, occurring in thermal analyses of reactor components.(author)

Basic Finite Element Method

International Nuclear Information System (INIS)

Lee, Byeong Hae

1992-02-01

This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.

Finite element flow analysis; Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, Chuo University, Tokyo, Japan, July 26-29, 1982

Science.gov (United States)

Kawai, T.

Among the topics discussed are the application of FEM to nonlinear free surface flow, Navier-Stokes shallow water wave equations, incompressible viscous flows and weather prediction, the mathematical analysis and characteristics of FEM, penalty function FEM, convective, viscous, and high Reynolds number FEM analyses, the solution of time-dependent, three-dimensional and incompressible Navier-Stokes equations, turbulent boundary layer flow, FEM modeling of environmental problems over complex terrain, and FEM's application to thermal convection problems and to the flow of polymeric materials in injection molding processes. Also covered are FEMs for compressible flows, including boundary layer flows and transonic flows, hybrid element approaches for wave hydrodynamic loadings, FEM acoustic field analyses, and FEM treatment of free surface flow, shallow water flow, seepage flow, and sediment transport. Boundary element methods and FEM computational technique topics are also discussed. For individual items see A84-25834 to A84-25896

A spectral element-FCT method for the compressible Euler equations

International Nuclear Information System (INIS)

Giannakouros, J.; Karniadakis, G.E.

1994-01-01

A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements

Accurate characterization of 3D diffraction gratings using time domain discontinuous Galerkin method with exact absorbing boundary conditions

KAUST Repository

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.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

Science.gov (United States)

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems

Survey of the status of finite element methods for partial differential equations

Science.gov (United States)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Performance improvement of extended boundary node method for solving elliptic boundary-value problems

International Nuclear Information System (INIS)

Saitoh, Ayumu; Kamitani, Atsushi; Takayama, Teruou; Nakamura, Hiroaki

2016-01-01

The extended boundary-node method (X-BNM) with the hierarchical-matrix (H-matrix) method has been developed and its performance has been investigated numerically. The results of computations show that the solver speed of the X-BNM with the H-matrix method is much faster than that of the standard X-BNM for the case where the number of boundary nodes exceeds a certain limit. Furthermore, the accuracy of the X-BNM with the H-matrix method is almost equal to that of the standard X-BNM. From these results, it is found that the H-matrix method is useful as the acceleration technique of the X-BNM. (author)

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

Science.gov (United States)

Jokhio, G. A.; Izzuddin, B. A.

2015-05-01

This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

Immersed boundary methods for high-resolution simulation of atmospheric boundary-layer flow over complex terrain

Science.gov (United States)

Lundquist, Katherine Ann

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

Immersed Boundary Methods for High-Resolution Simulation of Atmospheric Boundary-Layer Flow Over Complex Terrain

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

Formulation of natural convection around repository for dual reciprocity boundary element solution

International Nuclear Information System (INIS)

Vrankar, L.; Sarler, B.

1998-01-01

The disposal of high-level radioactive wastes in deep geological formations is of pronounced technological importance for nuclear safety. The understanding of related fluid flow, heat and mass transport in geological systems is of great interest. This article prepares necessary physical, mathematical and numerical fundamentals for computational modeling of related phenomena. The porous media is described by the simple Darcy law and momentum-energy coupling is due to Boussinesq approximation. The Dual Reciprocity of Boundary Element Method (DRBEM) is used for solving coupled mass, momentum and energy equations in two-dimensions for the steady buoyancy induced convection problem in an semi-infinite porous media. It is structured by weighting with the fundamental solution of the Laplace equation. The inverse multi quadrics are used in the DRBEM transformation. The solution is obtained in an iterative way.(author)

SOLUTION OF TRANSIENT HEAT CONDUCTION PROBLEM BY THE FINITE ELEMENT METHOD

Directory of Open Access Journals (Sweden)

Süleyman TAŞGETİREN

1995-01-01

Full Text Available Determination of temperature distribution is generally the first step in the design of machine elements subjected to ubnormal temperatures in their service life and for selection of materials. During this heat transfer analysis, the boundary and enviromental conditions must be modeled realistically and the geometry must be well represented. A variety of materials deviating from simple constant property isotropic material to composit materials having different properties according to direction of reinforcements are to be analysed. Then, the finite element method finds a large application area due to its use of same notation in heat transfer analysis and mechanical analysis of elements. In this study, the general formulation of two dimensional transient heat conduction is developed and a sample solution is given for arectangular bar subjected to convection baundary condition.

The analytical solution to the problem on the temperature field in a structural element of rectangular profile for third kind boundary conditions

International Nuclear Information System (INIS)

Kulich, N.V.; Nemtsev, V.A.

1986-01-01

The analytical solution to the problem on the stationary temperature field in an infinite structural element of rectangular profile characteristic of the conjugation points of a vessel and a tube sheet of a heat exchanger (or of a finned surface) at the third-kind boundary conditions has been obtained by the methods of the complex variable function theory. With the help of the obtained analytical dependences the calculations of the given element of the design and the comparison with the known data have been conducted. The proposed analytical solution can be effectively used in calculations of temperature fields in finned surfaces and structural elements of the power equipment of the considered profile and the method is applied for solution of the like problems

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)

Efficient evaluation of influence coefficients in three-dimensional extended boundary-node method for potential problems

International Nuclear Information System (INIS)

Itoh, Taku; Saitoh, Ayumu; Kamitani, Atsushi; Nakamura, Hiroaki

2011-01-01

For the purpose of speed-up of the three-dimensional eXtended Boundary-Node Method (X-BNM), an efficient algorithm for evaluating influence coefficients has been developed. The algorithm can be easily implemented into the X-BNM without using any integration cells. By applying the resulting X-BNM to the Laplace problem, the performance of the algorithm is numerically investigated. The numerical experiments show that, by using the algorithm, computational costs for evaluating influence coefficients in the X-BNM are reduced considerably. Especially for a large-sized problem, the algorithm is efficiently performed, and the computational costs of the X-BNM are close to those of the Boundary-Element Method (BEM). In addition, for the problem, the X-BNM shows almost the same accuracy as that of the BEM. (author)

Conforming discretizations of boundary element solutions to the electroencephalography forward problem

Science.gov (United States)

Rahmouni, Lyes; Adrian, Simon B.; Cools, Kristof; Andriulli, Francesco P.

2018-01-01

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, in terms of numerical stability and effectiveness when compared with other differential equation based techniques. Unfortunately, however, it is widely reported in literature that the accuracy of standard BEM schemes for the forward EEG problem is often 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 and classically discretized EEG forward problem operators, 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 standardly used discretizations of these formulations are consistent only with an L2-framework, requiring the expansion term to be a square integrable function (i.e., in a Petrov-Galerkin scheme with expansion and testing functions). Instead, those techniques are not consistent when a more appropriate mapping in terms of fractional-order Sobolev spaces is considered. Such a mapping allows the expansion function term to be a less regular function, thus sensibly reducing the need for mesh refinements and low-precisions handling strategies that are currently required. These more favorable mappings, however, require a different and conforming discretization, which must be suitably adapted to them. In order to appropriately fulfill this requirement, we adopt a mixed

Non-equilibrium grain boundary segregation of boron in austenitic stainless steel - IV. Precipitation behaviour and distribution of elements at grain boundaries

International Nuclear Information System (INIS)

Karlsson, L.; Norden, H.

1988-01-01

The distribution of elements and the precipitation behaviour at grain boundaries have been studied in boron containing AISI 316L and ''Mo-free AISI 316L'' type austenitic stainless steels. A combination of microanalytical techniques was used to study the boundary regions after cooling at 0.29-530 0 C/s from 800, 1075 or 1250 0 C. Tetragonal M/sub 2/B, M/sub 5/B/sub 3/ and M/sub 3/B/sub 2/, all rich in Fe, Cr and Mo, precipitated in the ''high B'' (40 ppm) AISI 316L steel whereas orthorhombic M/sub 2/B, rich in Cr and Fe was found in the ''Mo-free steel'' with 23 ppm B. In the ''high B steel'' a thin (<2nm), continuous layer, containing B, Cr, Mo and Fe and having a stoichiometry of typically M/sub 9/B, formed at boundaries after cooling at intermediate cooling rates. For both types of steels a boundary zone was found, after all heat treatments, with a composition differing significantly from the bulk composition. The differences were most marked after cooling at intermediate cooling rates. In both types of steel boundary depletion of Cr and enrichment of B and C occurred. It was found that non-equilibrium grain boundary segregation of boron can affect the precipitation behaviour by making the boundary composition enter a new phase field ''Non-equilibrium phases'' might also form. The synergistic effect of B and Mo on the boundary composition and precipitation behaviour, and the observed indications of C non-equilibrium segregation are discussed

3D modeling of the total electric field induced by transcranial magnetic stimulation using the boundary element method

Energy Technology Data Exchange (ETDEWEB)

Salinas, F S; Lancaster, J L; Fox, P T [Research Imaging Center, University of Texas Health Science Center at San Antonio, San Antonio, TX 78229 (United States)

2009-06-21

Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.

3D modeling of the total electric field induced by transcranial magnetic stimulation using the boundary element method

International Nuclear Information System (INIS)

Salinas, F S; Lancaster, J L; Fox, P T

2009-01-01

Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.

3D modeling of the total electric field induced by transcranial magnetic stimulation using the boundary element method

Science.gov (United States)

Salinas, F. S.; Lancaster, J. L.; Fox, P. T.

2009-06-01

Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.

Randomized Oversampling for Generalized Multiscale Finite Element Methods

KAUST Repository

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.

Modeling of asphalt by means of discrete element method – an initial study

DEFF Research Database (Denmark)

Feng, Huan; Hededal, Ole; Stang, Henrik

of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples....... Results from initial tests will be presented and the future development of the model towards characterising asphalt from its composition will be outlined....

Heat Conduction Analysis Using Semi Analytical Finite Element Method

International Nuclear Information System (INIS)

Wargadipura, A. H. S.

1997-01-01

Heat conduction problems are very often found in science and engineering fields. It is of accrual importance to determine quantitative descriptions of this important physical phenomena. This paper discusses the development and application of a numerical formulation and computation that can be used to analyze heat conduction problems. The mathematical equation which governs the physical behaviour of heat conduction is in the form of second order partial differential equations. The numerical resolution used in this paper is performed using the finite element method and Fourier series, which is known as semi-analytical finite element methods. The numerical solution results in simultaneous algebraic equations which is solved using the Gauss elimination methodology. The computer implementation is carried out using FORTRAN language. In the final part of the paper, a heat conduction problem in a rectangular plate domain with isothermal boundary conditions in its edge is solved to show the application of the computer program developed and also a comparison with analytical solution is discussed to assess the accuracy of the numerical solution obtained

A Finite Element Method for Simulation of Compressible Cavitating Flows

Science.gov (United States)

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.

Coarse mesh finite element method for boiling water reactor physics analysis

International Nuclear Information System (INIS)

Ellison, P.G.

1983-01-01

A coarse mesh method is formulated for the solution of Boiling Water Reactor physics problems using two group diffusion theory. No fuel assembly cross-section homogenization is required; water gaps, control blades and fuel pins of varying enrichments are treated explicitly. The method combines constrained finite element discretization with infinite lattice super cell trial functions to obtain coarse mesh solutions for which the only approximations are along the boundaries between fuel assemblies. The method is applied to bench mark Boiling Water Reactor problems to obtain both the eigenvalue and detailed flux distributions. The solutions to these problems indicate the method is useful in predicting detailed power distributions and eigenvalues for Boiling Water Reactor physics problems

Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation

KAUST Repository

Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi

2014-01-01

© 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.

Vortex sheet approximation of boundary layers

International Nuclear Information System (INIS)

Chorin, A.J.

1978-01-01

a grid free method for approximating incomprssible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier voartex method. The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder- piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms

A finite element method for neutron transport

International Nuclear Information System (INIS)

Ackroyd, R.T.

1978-01-01

A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)

Steam generator tube rupture simulation using extended finite element method

Energy Technology Data Exchange (ETDEWEB)

Mohanty, Subhasish, E-mail: smohanty@anl.gov; Majumdar, Saurin; Natesan, Ken

2016-08-15

Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.

Steam generator tube rupture simulation using extended finite element method

International Nuclear Information System (INIS)

Mohanty, Subhasish; Majumdar, Saurin; Natesan, Ken

2016-01-01

Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

Energy Technology Data Exchange (ETDEWEB)

Gao, Kai, E-mail: kaigao87@gmail.com [Department of Geology and Geophysics, Texas A& M University, College Station, TX 77843 (United States); Fu, Shubin, E-mail: shubinfu89@gmail.com [Department of Mathematics, Texas A& M University, College Station, TX 77843 (United States); Gibson, Richard L., E-mail: gibson@tamu.edu [Department of Geology and Geophysics, Texas A& M University, College Station, TX 77843 (United States); Chung, Eric T., E-mail: tschung@math.cuhk.edu.hk [Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT (Hong Kong); Efendiev, Yalchin, E-mail: efendiev@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, TX 77843 (United States); Numerical Porous Media SRI Center (NumPor), King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

2015-08-15

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

International Nuclear Information System (INIS)

Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin

2015-01-01

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

KAUST Repository

Gao, Kai

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both boundaries and the interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.

Science.gov (United States)

Suk, Heejun

2016-07-01

MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.

Coupling of modal and finite elements methods for the diffraction of guided elastics waves: application to non destructive testing

International Nuclear Information System (INIS)

Baronian, V.

2009-11-01

A typical nondestructive examination based on guided elastic waves can be simulated by considering an elastic 2D (a plate) or 3D (a rod) guide that contains a defect (a crack, a local heterogeneity due to a weld etc.). Our aim is to solve numerically the problem of the scattering by a defect of a mode propagating in a guide. This has been achieved by developing a method that couples i) finite elements in the smallest possible region of the guide that contains the defect, with ii) the modal decomposition of waves outside this region. The main challenge consists in finding the right linking condition of both representations. A decisive tool is the obtaining of an orthogonality relation which makes it possible to project the finite element solution onto guided modes. For this, the problem is formulated in terms of hybrid vectors (displacement/stress) for which a bi-orthogonality relation exists, namely, the Fraser's relation. It is then possible to derive an exact (transparent) condition on the artificial boundaries of the finite element domain; the modal series taken into account being necessarily truncated, transparency is achieved only approximately. Eventually, this boundary condition is integrated in a variational approach (in terms of displacement) in order to develop a finite element method. The transparent boundary condition being expressed in terms of the hybrid vectors, the stress normal to the artificial boundary is introduced as a supplementary unknown, together with a mixed formulation. Both 2D and 3D isotropic guides with free boundary conditions have been considered numerically. Guided modes are computed thanks to an original modeling approach also based on the hybrid (displacement/stress) vectors; interestingly, bi-orthogonality relation expressed in a discrete form is preserved. The code implementing these methods leads to fast computations of the scattering matrix of a defect; once this matrix has been computed at various frequencies, the defect

Grain boundary segregation and intergranular failure

International Nuclear Information System (INIS)

White, C.L.

1980-01-01

Trace elements and impurities often segregate strongly to grain boundaries in metals and alloys. Concentrations of these elements at grain boundaries are often 10 3 to 10 5 times as great as their overall concentration in the alloy. Because of such segregation, certain trace elements can exert a disproportionate influence on material properties. One frequently observed consequence of trace element segregation to grain boundaries is the occurrence of grain boundary failure and low ductility. Less well known are incidences of improved ductility and inhibition of grain boundary fracture resulting from trace element segregation to grain boundaries in certain systems. An overview of trace element segregation and intergranular failure in a variety of alloy systems as well as preliminary results from studies on Al 3% Li will be presented

An h-p Taylor-Galerkin finite element method for compressible Euler equations

Science.gov (United States)

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.

Electrical machine analysis using finite elements

CERN Document Server

Bianchi, Nicola

2005-01-01

OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I

GASEOUS ELEMENTAL MERCURY IN THE MARINE BOUNDARY LAYER: EVIDENCE FOR RAPID REMOVAL IN ANTHROPOGENIC POLLUTION

Science.gov (United States)

In this study, gas-phase elemental mercury (Hg0) and related species (including inorganic reactive gaseous mercury (RGM) and particulate mercury (PHg)) were measured at Cheeka Peak Observatory (CPO), Washington State, in the marine boundary layer (MBL) during 2001-2002. Air of...

Analysis and Modeling of Boundary Layer Separation Method (BLSM).

Science.gov (United States)

Pethő, Dóra; Horváth, Géza; Liszi, János; Tóth, Imre; Paor, Dávid

2010-09-01

Nowadays rules of environmental protection strictly regulate pollution material emission into environment. To keep the environmental protection laws recycling is one of the useful methods of waste material treatment. We have developed a new method for the treatment of industrial waste water and named it boundary layer separation method (BLSM). We apply the phenomena that ions can be enriched in the boundary layer of the electrically charged electrode surface compared to the bulk liquid phase. The main point of the method is that the boundary layer at correctly chosen movement velocity can be taken out of the waste water without being damaged, and the ion-enriched boundary layer can be recycled. Electrosorption is a surface phenomenon. It can be used with high efficiency in case of large electrochemically active surface of electrodes. During our research work two high surface area nickel electrodes have been prepared. The value of electrochemically active surface area of electrodes has been estimated. The existence of diffusion part of the double layer has been experimentally approved. The electrical double layer capacity has been determined. Ion transport by boundary layer separation has been introduced. Finally we have tried to estimate the relative significance of physical adsorption and electrosorption.

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

An adaptive finite element method for steady and transient problems

International Nuclear Information System (INIS)

Benner, R.E. Jr.; Davis, H.T.; Scriven, L.E.

1987-01-01

Distributing integral error uniformly over variable subdomains, or finite elements, is an attractive criterion by which to subdivide a domain for the Galerkin/finite element method when localized steep gradients and high curvatures are to be resolved. Examples are fluid interfaces, shock fronts and other internal layers, as well as fluid mechanical and other boundary layers, e.g. thin-film states at solid walls. The uniform distribution criterion is developed into an adaptive technique for one-dimensional problems. Nodal positions can be updated simultaneously with nodal values during Newton iteration, but it is usually better to adopt nearly optimal nodal positions during Newton iteration upon nodal values. Three illustrative problems are solved: steady convection with diffusion, gradient theory of fluid wetting on a solid surface and Buckley-Leverett theory of two phase Darcy flow in porous media

Invariant TAD Boundaries Constrain Cell-Type-Specific Looping Interactions between Promoters and Distal Elements around the CFTR Locus.

Science.gov (United States)

Smith, Emily M; Lajoie, Bryan R; Jain, Gaurav; Dekker, Job

2016-01-07

Three-dimensional genome structure plays an important role in gene regulation. Globally, chromosomes are organized into active and inactive compartments while, at the gene level, looping interactions connect promoters to regulatory elements. Topologically associating domains (TADs), typically several hundred kilobases in size, form an intermediate level of organization. Major questions include how TADs are formed and how they are related to looping interactions between genes and regulatory elements. Here we performed a focused 5C analysis of a 2.8 Mb chromosome 7 region surrounding CFTR in a panel of cell types. We find that the same TAD boundaries are present in all cell types, indicating that TADs represent a universal chromosome architecture. Furthermore, we find that these TAD boundaries are present irrespective of the expression and looping of genes located between them. In contrast, looping interactions between promoters and regulatory elements are cell-type specific and occur mostly within TADs. This is exemplified by the CFTR promoter that in different cell types interacts with distinct sets of distal cell-type-specific regulatory elements that are all located within the same TAD. Finally, we find that long-range associations between loci located in different TADs are also detected, but these display much lower interaction frequencies than looping interactions within TADs. Interestingly, interactions between TADs are also highly cell-type-specific and often involve loci clustered around TAD boundaries. These data point to key roles of invariant TAD boundaries in constraining as well as mediating cell-type-specific long-range interactions and gene regulation. Copyright © 2016 The American Society of Human Genetics. Published by Elsevier Inc. All rights reserved.

Generalized multiscale finite element methods (GMsFEM)

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao

2013-01-01

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.

Generalized multiscale finite element methods (GMsFEM)

KAUST Repository

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.

Stratification of TAD boundaries reveals preferential insulation of super-enhancers by strong boundaries.

Science.gov (United States)

Gong, Yixiao; Lazaris, Charalampos; Sakellaropoulos, Theodore; Lozano, Aurelie; Kambadur, Prabhanjan; Ntziachristos, Panagiotis; Aifantis, Iannis; Tsirigos, Aristotelis

2018-02-07

The metazoan genome is compartmentalized in areas of highly interacting chromatin known as topologically associating domains (TADs). TADs are demarcated by boundaries mostly conserved across cell types and even across species. However, a genome-wide characterization of TAD boundary strength in mammals is still lacking. In this study, we first use fused two-dimensional lasso as a machine learning method to improve Hi-C contact matrix reproducibility, and, subsequently, we categorize TAD boundaries based on their insulation score. We demonstrate that higher TAD boundary insulation scores are associated with elevated CTCF levels and that they may differ across cell types. Intriguingly, we observe that super-enhancers are preferentially insulated by strong boundaries. Furthermore, we demonstrate that strong TAD boundaries and super-enhancer elements are frequently co-duplicated in cancer patients. Taken together, our findings suggest that super-enhancers insulated by strong TAD boundaries may be exploited, as a functional unit, by cancer cells to promote oncogenesis.

Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions

Directory of Open Access Journals (Sweden)

Yuan Li

2013-01-01

Full Text Available This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.

Crack nucleation in solid materials under external load - simulations with the Discrete Element Method

Directory of Open Access Journals (Sweden)

Klejment Piotr

2018-01-01

Full Text Available Numerical analysis of cracking processes require an appropriate numerical technique. Classical engineering approach to the problem has its roots in the continuum mechanics and is based mainly on the Finite Element Method. This technique allows simulations of both elastic and large deformation processes, so it is very popular in the engineering applications. However, a final effect of cracking - fragmentation of an object at hand can hardly be described by this approach in a numerically efficient way since it requires a solution of a problem of nontrivial evolving in time boundary conditions. We focused our attention on the Discrete Element Method (DEM, which by definition implies “molecular” construction of the matter. The basic idea behind DEM is to represent an investigated body as an assemblage of discrete particles interacting with each other. Breaking interaction bonds between particles induced by external forces imeditelly implies creation/evolution of boundary conditions. In this study we used the DEM approach to simulate cracking process in the three dimensional solid material under external tension. The used numerical model, although higly simplified, can be used to describe behaviour of such materials like thin films, biological tissues, metal coatings, to name a few.

Development of a three-dimensional neutron transport code DFEM based on the double finite element method

International Nuclear Information System (INIS)

Fujimura, Toichiro

1996-01-01

A three-dimensional neutron transport code DFEM has been developed by the double finite element method to analyze reactor cores with complex geometry as large fast reactors. Solution algorithm is based on the double finite element method in which the space and angle finite elements are employed. A reactor core system can be divided into some triangular and/or quadrangular prism elements, and the spatial distribution of neutron flux in each element is approximated with linear basis functions. As for the angular variables, various basis functions are applied, and their characteristics were clarified by comparison. In order to enhance the accuracy, a general method is derived to remedy the truncation errors at reflective boundaries, which are inherent in the conventional FEM. An adaptive acceleration method and the source extrapolation method were applied to accelerate the convergence of the iterations. The code structure is outlined and explanations are given on how to prepare input data. A sample input list is shown for reference. The eigenvalue and flux distribution for real scale fast reactors and the NEA benchmark problems were presented and discussed in comparison with the results of other transport codes. (author)

A ghost-cell immersed boundary method for flow in complex geometry

International Nuclear Information System (INIS)

Tseng, Y.-H.; Ferziger, Joel H.

2003-01-01

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes

System and method for free-boundary surface extraction

KAUST Repository

Algarni, Marei

2017-10-26

A method of extracting surfaces in three-dimensional data includes receiving as inputs three-dimensional data and a seed point p located on a surface to be extracted. The method further includes propagating a front outwardly from the seed point p and extracting a plurality of ridge curves based on the propagated front. A surface boundary is detected based on a comparison of distances between adjacent ridge curves and the desired surface is extracted based on the detected surface boundary.

Selecting boundary conditions in physiological strain analysis of the femur: Balanced loads, inertia relief method and follower load.

Science.gov (United States)

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. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

Discretization of the induced-charge boundary integral equation.

Science.gov (United States)

Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Discretization of the induced-charge boundary integral equation.

Energy Technology Data Exchange (ETDEWEB)

Bardhan, J. P.; Eisenberg, R. S.; Gillespie, D.; Rush Univ. Medical Center

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch et al. [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Explicitly represented polygon wall boundary model for the explicit MPS method

Science.gov (United States)

Mitsume, Naoto; Yoshimura, Shinobu; Murotani, Kohei; Yamada, Tomonori

2015-05-01

This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.

The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

OpenAIRE

Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi

2014-01-01

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite...

A system boundary identification method for life cycle assessment

DEFF Research Database (Denmark)

Li, Tao; Zhang, Hongchao; Liu, Zhichao

2014-01-01

, 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...... as processes are added. The two threshold rules and identification methods presented can be used to identify system boundary of LCA. The case study demonstrated that the methodology presented in this paper is an effective tool for the boundary identification....

Method of interior boundaries in a mixed problem of acoustic scattering

Directory of Open Access Journals (Sweden)

P. A. Krutitskii

1999-01-01

Full Text Available The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.

Computational method for estimating boundary of abdominal subcutaneous fat for absolute electrical impedance tomography.

Science.gov (United States)

Yamaguchi, Tohru F; Okamoto, Yoshiwo

2018-01-01

Abdominal fat accumulation is considered an essential indicator of human health. Electrical impedance tomography has considerable potential for abdominal fat imaging because of the low specific conductivity of human body fat. In this paper, we propose a robust reconstruction method for high-fidelity conductivity imaging by abstraction of the abdominal cross section using a relatively small number of parameters. Toward this end, we assume homogeneous conductivity in the abdominal subcutaneous fat area and characterize its geometrical shape by parameters defined as the ratio of the distance from the center to boundary of subcutaneous fat to the distance from the center to outer boundary in 64 equiangular directions. To estimate the shape parameters, the sensitivity of the noninvasively measured voltages with respect to the shape parameters is formulated for numerical optimization. Numerical simulations are conducted to demonstrate the validity of the proposed method. A 3-dimensional finite element method is used to construct a computer model of the human abdomen. The inverse problems of shape parameters and conductivities are solved concurrently by iterative forward and inverse calculations. As a result, conductivity images are reconstructed with a small systemic error of less than 1% for the estimation of the subcutaneous fat area. A novel method is devised for estimating the boundary of the abdominal subcutaneous fat. The fidelity of the overall reconstructed image to the reference image is significantly improved. The results demonstrate the possibility of realization of an abdominal fat scanner as a low-cost, radiation-free medical device. Copyright © 2017 John Wiley & Sons, Ltd.

Boundary element analysis of stress singularity in dissimilar metals by friction welding

International Nuclear Information System (INIS)

Chung, N. Y.; Park, C. H.

2012-01-01

Friction welded dissimilar metals are widely applied in automobiles, rolling stocks, machine tools, and various engineering fields. Dissimilar metals have several advantages over homogeneous metals, including high strength, material property, fatigue endurance, impact absorption, high reliability, and vibration reduction. Due to the increased use of these metals, understanding their behavior under stress conditions is necessary, especially the analysis of stress singularity on the interface of friction-welded dissimilar metals. To establish a strength evaluation method and a fracture criterion, it is necessary to analyze stress singularity on the interface of dissimilar metals with welded flashes by friction welding under various loads and temperature conditions. In this paper, a method analyzing stress singularity for the specimens with and without flashes set in friction welded dissimilar metals is introduced using the boundary element method. The stress singularity index (λ) and the stress singularity factor (Γ) at the interface edge are computed from the stress analysis results. The shape and flash thickness, interface length, residual stress, and load are considered in the computation. Based on these results, the variations of interface length (c) and the ratio of flash thickness (t2 t1) greatly influence the stress singularity factors at the interface edge of friction welded dissimilar metals. The stress singularity factors will be a useful fracture parameter that considers stress singularity on the interface of dissimilar metals

Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

Directory of Open Access Journals (Sweden)

Kosuke Hayashi

2012-06-01

Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

Short climatology of the atmospheric boundary layer using acoustic methods

International Nuclear Information System (INIS)

Schubert, J.F.

1975-06-01

A climatology of the boundary layer of the atmosphere at the Savannah River Laboratory is being compiled using acoustic methods. The atmospheric phenomenon as depicted on the facsimile recorder is classified and then placed into one of sixteen categories. After classification, the height of the boundary layer is measured. From this information, frequency tables of boundary layer height and category are created and then analyzed for the percentage of time that each category was detected by the acoustic sounder. The sounder also accurately depicts the diurnal cycle of the boundary layer and, depending on the sensitivity of the system, shows microstructure that is normally unavailable using other methods of profiling. The acoustic sounder provides a means for continuous, real time measurements of the time rate of change of the depth of the boundary layer. This continuous record of the boundary layer with its convective cells, gravity waves, inversions, and frontal system passages permits the synoptic and complex climatology of the local area to be compiled. (U.S.)

Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems

Directory of Open Access Journals (Sweden)

Neng Wan

2014-01-01

Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

Science.gov (United States)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

Effects of Heat Input and Bead Generation Methods on Finite Element Analysis of Cylindrical Multi-Pass Welding Process of Metals

International Nuclear Information System (INIS)

Park, Won Dong; Bahn, Chi Bum; Kim, Ji Hoon

2017-01-01

In this study, a finite element analysis of a cylindrical multi-pass weldment for dissimilar metals was performed. The effects of the heat input method and weld bead generation method were considered. We compared two heat input methods: the heat flux method and the temperature method. We also compared two weld bead generation methods: the element birth method and the quiet element method. Although the results of the thermal analysis show deviations between the two heat input methods, the welding residual stresses were similar. Because the areas exposed to high temperature were similar and the strength of the material was very low in high temperature (above the 1000 ℃), the effects of the weld bead temperature were insignificant. The distributions of the welding residual stress were similar to each other. However, gaps and overlaps occurred on the welding boundary surfaces when the element birth method was applied. The quiet element method is more suitable for a large deformation model in order to simulate a more accurate weld shape.

Effects of Heat Input and Bead Generation Methods on Finite Element Analysis of Cylindrical Multi-Pass Welding Process of Metals

Energy Technology Data Exchange (ETDEWEB)

Park, Won Dong; Bahn, Chi Bum; Kim, Ji Hoon [Pusan Nat’l Univ., Busan (Korea, Republic of)

2017-06-15

In this study, a finite element analysis of a cylindrical multi-pass weldment for dissimilar metals was performed. The effects of the heat input method and weld bead generation method were considered. We compared two heat input methods: the heat flux method and the temperature method. We also compared two weld bead generation methods: the element birth method and the quiet element method. Although the results of the thermal analysis show deviations between the two heat input methods, the welding residual stresses were similar. Because the areas exposed to high temperature were similar and the strength of the material was very low in high temperature (above the 1000 ℃), the effects of the weld bead temperature were insignificant. The distributions of the welding residual stress were similar to each other. However, gaps and overlaps occurred on the welding boundary surfaces when the element birth method was applied. The quiet element method is more suitable for a large deformation model in order to simulate a more accurate weld shape.

Fictitious domain methods for elliptic problems with general boundary conditions with an application to the numerical simulation of two phase flows; Methodes de domaine fictif pour des problemes elliptiques avec conditions aux limites generales en vue de la simulation numerique d'ecoulements diphasiques

Energy Technology Data Exchange (ETDEWEB)

Ramiere, I

2006-09-15

This work is dedicated to the introduction of two original fictitious domain methods for the resolution of elliptic problems (mainly convection-diffusion problems) with general and eventually mixed boundary conditions: Dirichlet, Robin or Neumann. The originality lies in the approximation of the immersed boundary by an approximate interface derived from the fictitious domain Cartesian mesh, which is generally not boundary-fitted to the physical domain. The same generic numerical scheme is used to impose the embedded boundary conditions. Hence, these methods require neither a surface mesh of the immersed boundary nor the local modification of the numerical scheme. We study two modelling of the immersed boundary. In the first one, called spread interface, the approximate immersed boundary is the union of the cells crossed by the physical immersed boundary. In the second one, called thin interface, the approximate immersed boundary lies on sides of mesh cells. Additional algebraic transmission conditions linking both flux and solution jumps through the thin approximate interface are introduced. The fictitious problem to solve as well as the treatment of the embedded boundary conditions are detailed for the two methods. A Q1 finite element scheme is implemented for the numerical validation of the spread interface approach while a new cell-centered finite volume scheme is derived for the thin interface approach with immersed jumps. Each method is then combined to multilevel local mesh refinement algorithms (with solution or flux residual) to increase the precision of the solution in the vicinity of the immersed interface. A convergence analysis of a Q1 finite element method with non-boundary fitted meshes is also presented. This study proves the convergence rates of the present methods. Among the various industrial applications, the simulation on a model of heat exchanger in french nuclear power plants enables us to appreciate the performances of the fictitious domain

Analysis of the optimized H type grid spring by a characterization test and the finite element method under the in-grid boundary

International Nuclear Information System (INIS)

Yoon, Kyung Ho; Lee, Kang Hee; Kang, Heung Seok; Song, Kee Nam

2006-01-01

Characterization tests (load vs. displacement curve) are conducted for the springs of Zirconium alloy spacer grids for an advanced LWR fuel assembly. Twofold testing is employed: strap-based and assembly-based tests. The assembly-based test satisfies the in situ boundary conditions of the spring within the grid assembly. The aim of the characterization test via the aforementioned two methods is to establish an appropriate assembly-based test method that fulfills the actual boundary conditions. A characterization test under the spacer grid assembly boundary condition is also conducted to investigate the actual behavior of the spring in the core. The stiffness of the characteristic curve is smaller than that of the strap-wised boundary condition. This phenomenon may cause the strap slit condition. A spacer grid consists of horizontal and vertical straps. The strap slit positions are differentiated from each other. They affords examination of the variation of the external load distribution in the grid spring. Localized regions of high stress and their values are analyzed, as they may be affected by the spring shape. Through a comparison of the results of the test and FE analysis, it is concluded that the present assembly-based analysis model and procedure are reasonably well conducted and can be used for spring characterization in the core. Guidelines for improving the mechanical integrity of the spring are also discussed

A Method for Extracting Road Boundary Information from Crowdsourcing Vehicle GPS Trajectories.

Science.gov (United States)

Yang, Wei; Ai, Tinghua; Lu, Wei

2018-04-19

Crowdsourcing trajectory data is an important approach for accessing and updating road information. In this paper, we present a novel approach for extracting road boundary information from crowdsourcing vehicle traces based on Delaunay triangulation (DT). First, an optimization and interpolation method is proposed to filter abnormal trace segments from raw global positioning system (GPS) traces and interpolate the optimization segments adaptively to ensure there are enough tracking points. Second, constructing the DT and the Voronoi diagram within interpolated tracking lines to calculate road boundary descriptors using the area of Voronoi cell and the length of triangle edge. Then, the road boundary detection model is established integrating the boundary descriptors and trajectory movement features (e.g., direction) by DT. Third, using the boundary detection model to detect road boundary from the DT constructed by trajectory lines, and a regional growing method based on seed polygons is proposed to extract the road boundary. Experiments were conducted using the GPS traces of taxis in Beijing, China, and the results show that the proposed method is suitable for extracting the road boundary from low-frequency GPS traces, multi-type road structures, and different time intervals. Compared with two existing methods, the automatically extracted boundary information was proved to be of higher quality.

A Method for Extracting Road Boundary Information from Crowdsourcing Vehicle GPS Trajectories

Directory of Open Access Journals (Sweden)

Wei Yang

2018-04-01

Full Text Available Crowdsourcing trajectory data is an important approach for accessing and updating road information. In this paper, we present a novel approach for extracting road boundary information from crowdsourcing vehicle traces based on Delaunay triangulation (DT. First, an optimization and interpolation method is proposed to filter abnormal trace segments from raw global positioning system (GPS traces and interpolate the optimization segments adaptively to ensure there are enough tracking points. Second, constructing the DT and the Voronoi diagram within interpolated tracking lines to calculate road boundary descriptors using the area of Voronoi cell and the length of triangle edge. Then, the road boundary detection model is established integrating the boundary descriptors and trajectory movement features (e.g., direction by DT. Third, using the boundary detection model to detect road boundary from the DT constructed by trajectory lines, and a regional growing method based on seed polygons is proposed to extract the road boundary. Experiments were conducted using the GPS traces of taxis in Beijing, China, and the results show that the proposed method is suitable for extracting the road boundary from low-frequency GPS traces, multi-type road structures, and different time intervals. Compared with two existing methods, the automatically extracted boundary information was proved to be of higher quality.

Hybrid immersed boundary method for airfoils with a trailing-edge flap

DEFF Research Database (Denmark)

Zhu, Wei Jun; Behrens, Tim; Shen, Wen Zhong

2013-01-01

In this paper, a hybrid immersed boundary technique has been developed for simulating turbulent flows past airfoils with moving trailing-edge flaps. Over the main fixed part of the airfoil, the equations are solved using a standard body-fitted finite volume technique, whereas the moving trailing......-edge flap is simulated using the immersed boundary method on a curvilinear mesh. An existing in-house-developed flow solver is employed to solve the incompressible Reynolds-Averaged Navier-Stokes equations together with the k-ω turbulence model. To achieve consistent wall boundary conditions at the immersed...... boundaries the k-ωturbulence model is modified and adapted to the local conditions associated with the immersed boundary method. The obtained results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing-edge flap and that flow control...

Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

KAUST Repository

Jin, Bangti

2013-01-01

We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.

A solution of the dispersion-convection equation of radial tracer transportation by the finite element variational method

International Nuclear Information System (INIS)

Hubert, J.

1979-01-01

The variational finite element method (of the Rayleigh-Ritz type) has been applied to solve the standard diffusion-convection equation of radial flow in a dispersive medium. It was shown that the imposing of the boundary condition ΔC/Δx = 0 (=null concentration gradient) introduced great errors in computation results. To remedy it this condition was imposed at the free end of the artifical domain. Its other end joined to the downstream boundary of the investigated domain. The results of calculations compared with the known analytical solutions of the parallel flow show their good accuracy. The method was used to discuss the applicability of the approximate analytical solutions of the radial flow. (author)

Subgroup report on grain boundary and interphase boundary structure and properties

International Nuclear Information System (INIS)

Balluffi, R.W.; Cannon, R.M.; Clarke, D.R.; Heuer, A.H.; Ho, P.S.; Kear, B.H.; Vitek, V.; Weertman, J.R.; White, C.L.

1979-01-01

In many high temperature structural applications, the performance characteristics of a materials system are largely controlled by the properties of its grain and interphase boundaries. Failure in creep and fatigue frequently occurs by cavitation, or cracking along grain boundaries. In a few special cases, this failure problem has been overcome by directional alignment of grain and interphase boundaries by various types of metallurgical processing such as directional solidification and directional recrystallization. A good example is to be found in the application of directionally aligned structures in high performance gas-turbine airfoils. However, where fine, equiaxed grain structures are desirable, other methods of controlling grain boundary properties have been developed. Important among these has been the introduction of improvements in primary melting practices, designed to control important impurities. This is of decisive importance because even traces of certain impurity elements present in grain boundaries in high temperature materials can seriously affect properties. Impurities are deleterious and need to be removed. However, in certain cases, (e.g., creep fracture) controlled impurity additions can be beneficial and result in improved properties

Three Dimensional Plenoptic PIV Measurements of a Turbulent Boundary Layer Overlying a Hemispherical Roughness Element

Science.gov (United States)

Johnson, Kyle; Thurow, Brian; Kim, Taehoon; Blois, Gianluca; Christensen, Kenneth

2016-11-01

Three-dimensional, three-component (3D-3C) measurements were made using a plenoptic camera on the flow around a roughness element immersed in a turbulent boundary layer. A refractive index matched approach allowed whole-field optical access from a single camera to a measurement volume that includes transparent solid geometries. In particular, this experiment measures the flow over a single hemispherical roughness element made of acrylic and immersed in a working fluid consisting of Sodium Iodide solution. Our results demonstrate that plenoptic particle image velocimetry (PIV) is a viable technique to obtaining statistically-significant volumetric velocity measurements even in a complex separated flow. The boundary layer to roughness height-ratio of the flow was 4.97 and the Reynolds number (based on roughness height) was 4.57×103. Our measurements reveal key flow features such as spiraling legs of the shear layer, a recirculation region, and shed arch vortices. Proper orthogonal decomposition (POD) analysis was applied to the instantaneous velocity and vorticity data to extract these features. Supported by the National Science Foundation Grant No. 1235726.

Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Javier A. Dottori

2015-01-01

Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.

Discrete elements method of neutron transport

International Nuclear Information System (INIS)

Mathews, K.A.

1988-01-01

In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

A Novel Polygonal Finite Element Method: Virtual Node Method

Science.gov (United States)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

Science.gov (United States)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

Hole-expansion formability of dual-phase steels using representative volume element approach with boundary-smoothing technique

International Nuclear Information System (INIS)

Kim, Ji Hoon; Lee, M.G.; Kim, D.; Matlock, D.K.; Wagoner, R.H.

2010-01-01

Research highlights: → Robust microstructure-based FE mesh generation technique was developed. → Local deformation behavior near phase boundaries could be quantitatively understood. → Macroscopic failure could be connected to microscopic deformation behavior of multi-phase steel. - Abstract: A qualitative analysis was carried out on the formability of dual-phase (DP) steels by introducing a realistic microstructure-based finite element approach. The present microstructure-based model was constructed using a mesh generation process with a boundary-smoothing algorithm after proper image processing. The developed model was applied to hole-expansion formability tests for DP steel sheets having different volume fractions and morphological features. On the basis of the microstructural inhomogeneity observed in the scanning electron micrographs of the DP steel sheets, it was inferred that the localized plastic deformation in the ferritic phase might be closely related to the macroscopic formability of DP steel. The experimentally observed difference between the hole-expansion formability of two different microstructures was reasonably explained by using the present finite element model.

An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)

International Nuclear Information System (INIS)

Shi Ting-Yu; Ge Hong-Xia; Cheng Rong-Jun

2013-01-01

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The exact mathematical result of the GFE has been widely used in population dynamics and genetics, where it originated. Many researchers have studied the numerical solutions of the GFE, up to now. In this paper, we introduce an element-free Galerkin (EFG) method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics. Compared with other numerical methods, the EFG method for the GFE needs only scattered nodes instead of meshing the domain of the problem. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. In comparison with the traditional method, numerical solutions show that the new method has higher accuracy and better convergence. Several numerical examples are presented to demonstrate the effectiveness of the method

Numerical Methods for Free Boundary Problems

CERN Document Server

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...

New mixed finite-element methods

International Nuclear Information System (INIS)

Franca, L.P.

1987-01-01

New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates

An efficient implicit direct forcing immersed boundary method for incompressible flows

International Nuclear Information System (INIS)

Cai, S-G; Ouahsine, A; Smaoui, H; Favier, J; Hoarau, Y

2015-01-01

A novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature

An approximate moving boundary method for American option pricing

NARCIS (Netherlands)

Chockalingam, A.; Muthuraman, K.

2015-01-01

We present a method to solve the free-boundary problem that arises in the pricing of classical American options. Such free-boundary problems arise when one attempts to solve optimal-stopping problems set in continuous time. American option pricing is one of the most popular optimal-stopping problems

Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

KAUST Repository

Iliev, Oleg P.

2010-01-01

We present a two-scale finite element method for solving Brinkman\\'s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy\\'s equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.

A boundary element model for investigating the effects of eye tumor on the temperature distribution inside the human eye.

Science.gov (United States)

Ooi, E H; Ang, W T; Ng, E Y K

2009-08-01

A three-dimensional boundary element model of the human eye is developed to investigate the thermal effects of eye tumor on the ocular temperature distribution. The human eye is modeled as comprising several regions which have different thermal properties. The tumor is one of these regions. The thermal effects of the tumor are simulated by taking it to have a very high metabolic heat generation and blood perfusion rate. Inside the tumor, the steady state temperature is governed by the Pennes bioheat equation. Elsewhere, in normal tissues of the eye, the temperature satisfies the Laplace's equation. To compute the temperature on the corneal surface, the surface boundary of each region is divided into triangular elements.

2.5-D frequency-domain viscoelastic wave modelling using finite-element method

Science.gov (United States)

Zhao, Jian-guo; Huang, Xing-xing; Liu, Wei-fang; Zhao, Wei-jun; Song, Jian-yong; Xiong, Bin; Wang, Shang-xu

2017-10-01

2-D seismic modelling has notable dynamic information discrepancies with field data because of the implicit line-source assumption, whereas 3-D modelling suffers from a huge computational burden. The 2.5-D approach is able to overcome both of the aforementioned limitations. In general, the earth model is treated as an elastic material, but the real media is viscous. In this study, we develop an accurate and efficient frequency-domain finite-element method (FEM) for modelling 2.5-D viscoelastic wave propagation. To perform the 2.5-D approach, we assume that the 2-D viscoelastic media are based on the Kelvin-Voigt rheological model and a 3-D point source. The viscoelastic wave equation is temporally and spatially Fourier transformed into the frequency-wavenumber domain. Then, we systematically derive the weak form and its spatial discretization of 2.5-D viscoelastic wave equations in the frequency-wavenumber domain through the Galerkin weighted residual method for FEM. Fixing a frequency, the 2-D problem for each wavenumber is solved by FEM. Subsequently, a composite Simpson formula is adopted to estimate the inverse Fourier integration to obtain the 3-D wavefield. We implement the stiffness reduction method (SRM) to suppress artificial boundary reflections. The results show that this absorbing boundary condition is valid and efficient in the frequency-wavenumber domain. Finally, three numerical models, an unbounded homogeneous medium, a half-space layered medium and an undulating topography medium, are established. Numerical results validate the accuracy and stability of 2.5-D solutions and present the adaptability of finite-element method to complicated geographic conditions. The proposed 2.5-D modelling strategy has the potential to address modelling studies on wave propagation in real earth media in an accurate and efficient way.

Modeling of a fluid-loaded smart shell structure for active noise and vibration control using a coupled finite element–boundary element approach

International Nuclear Information System (INIS)

Ringwelski, S; Gabbert, U

2010-01-01

A recently developed approach for the simulation and design of a fluid-loaded lightweight structure with surface-mounted piezoelectric actuators and sensors capable of actively reducing the sound radiation and the vibration is presented. The objective of this paper is to describe the theoretical background of the approach in which the FEM is applied to model the actively controlled shell structure. The FEM is also employed to model finite fluid domains around the shell structure as well as fluid domains that are partially or totally bounded by the structure. Boundary elements are used to characterize the unbounded acoustic pressure fields. The approach presented is based on the coupling of piezoelectric and acoustic finite elements with boundary elements. A coupled finite element–boundary element model is derived by introducing coupling conditions at the fluid–fluid and fluid–structure interfaces. Because of the possibility of using piezoelectric patches as actuators and sensors, feedback control algorithms can be implemented directly into the multi-coupled structural–acoustic approach to provide a closed-loop model for the design of active noise and vibration control. In order to demonstrate the applicability of the approach developed, a number of test simulations are carried out and the results are compared with experimental data. As a test case, a box-shaped shell structure with surface-mounted piezoelectric actuators and four sensors and an open rearward end is considered. A comparison between the measured values and those predicted by the coupled finite element–boundary element model shows a good agreement

Shooting method for solution of boundary-layer flows with massive blowing

Science.gov (United States)

Liu, T.-M.; Nachtsheim, P. R.

1973-01-01

A modified, bidirectional shooting method is presented for solving boundary-layer equations under conditions of massive blowing. Unlike the conventional shooting method, which is unstable when the blowing rate increases, the proposed method avoids the unstable direction and is capable of solving complex boundary-layer problems involving mass and energy balance on the surface.

A finite-volume method for convection problems with embedded moving boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2009-01-01

htmlabstractAn 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

Automatic classification of singular elements for the electrostatic analysis of microelectromechanical systems

Science.gov (United States)

Su, Y.; Ong, E. T.; Lee, K. H.

2002-05-01

The past decade has seen an accelerated growth of technology in the field of microelectromechanical systems (MEMS). The development of MEMS products has generated the need for efficient analytical and simulation methods for minimizing the requirement for actual prototyping. The boundary element method is widely used in the electrostatic analysis for MEMS devices. However, singular elements are needed to accurately capture the behavior at singular regions, such as sharp corners and edges, where standard elements fail to give an accurate result. The manual classification of boundary elements based on their singularity conditions is an immensely laborious task, especially when the boundary element model is large. This process can be automated by querying the geometric model of the MEMS device for convex edges based on geometric information of the model. The associated nodes of the boundary elements on these edges can then be retrieved. The whole process is implemented in the MSC/PATRAN platform using the Patran Command Language (the source code is available as supplementary data in the electronic version of this journal issue).

Carbon and oxygen stable isotope and trace element studies in speleothems and across the J-K boundary, Central Italy

International Nuclear Information System (INIS)

Kudielka, G.

2001-07-01

Frasassi Cave have always been lower in d18O and higher in d13C compared to Soreq Cave. This indicates lower temperatures and a higher portion of C4 type vegetation in the Frasassi area compared to Israel. The agreement of the two records demonstrates that calcite deposits in caves are ideal recorders to global climatic changes. Investigation of the Jurassic/Cretaceous Boundary in Central Italy, the Jurassic/Cretaceous (J-K) boundary has not been satisfactory defined yet. Among others, various boundary definitions have been proposed at the Bosso River Gorge in the Marche region of Northern Italy: by calcareous nanofossils (at 329 m), calpionellids (at 334.1 m) and magnetostratigraphy (at 318 m). A large impact structure near Morokweng in South Africa was recently radiometrically dated to 144.7±1.9 Ma, which is indistinguishable from the stratigraphic age of the J-K boundary (144.2±2.6 Ma). A possible link between the impact event and the J-K boundary might be manifested in form of stratigraphic and geochemical features across the boundary, such as sudden stable-isotope shifts and spheroidal element anomalies. A set of 110 samples spanning about 40 m across the boundary was investigated for stable isotope ratios, and trace element content was determined in the corresponding decarbonated samples. d13C and d18O hardly vary but show a significant decrease at 333.5 m, which is close to the boundary-definition based upon calpionellids (at 334.1 m). Trace element abundances of Fe, Co, Ni, and Cr show remarkable enrichments very close to the boundary as defined by calcareous nanofossils (at 329 m). Another minor anomaly is noticeable at 333.5 m for Ir and Cr. Thus, the present data might be interpreted to hint - not to confirm - the presence of an impactoclastic layer at the Bosso River Gorge. (author)

Finite elements and approximation

CERN Document Server

Zienkiewicz, O C

2006-01-01

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

Science.gov (United States)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2012-09-20

The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered

The Finite Element Numerical Modelling of 3D Magnetotelluric

Directory of Open Access Journals (Sweden)

Ligang Cao

2014-01-01

Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.

Static and Vibrational Analysis of Partially Composite Beams Using the Weak-Form Quadrature Element Method

Directory of Open Access Journals (Sweden)

Zhiqiang Shen

2012-01-01

Full Text Available Deformation of partially composite beams under distributed loading and free vibrations of partially composite beams under various boundary conditions are examined in this paper. The weak-form quadrature element method, which is characterized by direct evaluation of the integrals involved in the variational description of a problem, is used. One quadrature element is normally sufficient for a partially composite beam regardless of the magnitude of the shear connection stiffness. The number of integration points in a quadrature element is adjustable in accordance with convergence requirement. Results are compared with those of various finite element formulations. It is shown that the weak form quadrature element solution for partially composite beams is free of slip locking, and high computational accuracy is achieved with smaller number of degrees of freedom. Besides, it is found that longitudinal inertia of motion cannot be simply neglected in assessment of dynamic behavior of partially composite beams.

A new approach to implement absorbing boundary condition in biomolecular electrostatics.

Science.gov (United States)

Goni, Md Osman

2013-01-01

This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.

Modified Differential Transform Method for Two Singular Boundary Values Problems

Directory of Open Access Journals (Sweden)

Yinwei Lin

2014-01-01

Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

A general mixed boundary model reduction method for component mode synthesis

NARCIS (Netherlands)

Voormeeren, S.N.; Van der Valk, P.L.C.; Rixen, D.J.

2010-01-01

A classic issue in component mode synthesis (CMS) methods is the choice for fixed or free boundary conditions at the interface degrees of freedom (DoF) and the associated vibration modes in the components reduction base. In this paper, a novel mixed boundary CMS method called the “Mixed

Transonic shock wave. Boundary layer interaction at a convex wall

NARCIS (Netherlands)

Koren, B.; Bannink, W.J.

1984-01-01

A standard finite element procedure has been applied to the problem of transonic shock wave – boundary layer interaction at a convex wall. The method is based on the analytical Bohning-Zierep model, where the boundary layer is perturbed by a weak normal shock wave which shows a singular pressure

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method

International Nuclear Information System (INIS)

Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke

2012-01-01

Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.

Platinum group element enrichments and possible chondritic Ru:Ir across the Frasnian-Famennian boundary, western New York State.

Science.gov (United States)

Over, D J; Conaway, C A; Katz, D J; Goodfellow, W D; Gregoire, D C

1997-08-01

The Frasnian-Famennian boundary is recognized as the culmination of a global mass extinction in the Late Devonian. In western New York State the boundary is a distinct horizon within a pyritic black shale bed of the upper Hanover Shale defined by the first occurrence of Palmatolepis triangularis in the absence of Frasnian conodonts. The boundary is characterized by a minor disconformity marked by a lag concentration of conodonts. Iridium at the boundary is 0.11-0.24 ng/g, two to five times background levels of <0.05 ng/g; other Ir enrichments of 0.38 ng/g and 0.49 ng/g occur within 50 cm of the conodont-constrained boundary. Numerous Ir enrichments in the boundary interval suggest extraterrestrial accretion and platinum group element (PGE) concentration at disconformities, or mobilization and concentration in organic-rich/pyritic-rich laminations from cosmic or terrestrial sources. PGE ratios of Pt/Pd and Ku/Ir at the boundary horizon approximate chondritic ratios and are suggestive of an unaltered extraterrestrial source. These values do not conclusively establish a single extraterrestrial impact as the ultimate cause of the Frasnian-Famennian mass extinction, especially given the presence of similar Ir enrichments elsewhere in the section and the absence at the boundary of microtektites and shocked mineral grains.

The dimension split element-free Galerkin method for three-dimensional potential problems

Science.gov (United States)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-02-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Stability Analysis of Algebraic Reconstruction for Immersed Boundary Methods with Application in Flow and Transport in Porous Media

Science.gov (United States)

Yousefzadeh, M.; Battiato, I.

2017-12-01

Flow and reactive transport problems in porous media often involve complex geometries with stationary or evolving boundaries due to absorption and dissolution processes. Grid based methods (e.g. finite volume, finite element, etc.) are a vital tool for studying these problems. Yet, implementing these methods requires one to answer a very first question of what type of grid is to be used. Among different possible answers, Cartesian grids are one of the most attractive options as they possess simple discretization stencil and are usually straightforward to generate at roughly no computational cost. The Immersed Boundary Method, a Cartesian based methodology, maintains most of the useful features of the structured grids while exhibiting a high-level resilience in dealing with complex geometries. These features make it increasingly more attractive to model transport in evolving porous media as the cost of grid generation reduces greatly. Yet, stability issues and severe time-step restriction due to explicit-time implementation combined with limited studies on the implementation of Neumann (constant flux) and linear and non-linear Robin (e.g. reaction) boundary conditions (BCs) have significantly limited the applicability of IBMs to transport in porous media. We have developed an implicit IBM capable of handling all types of BCs and addressed some numerical issues, including unconditional stability criteria, compactness and reduction of spurious oscillations near the immersed boundary. We tested the method for several transport and flow scenarios, including dissolution processes in porous media, and demonstrate its capabilities. Successful validation against both experimental and numerical data has been carried out.

The application of finite element method for mhd viscous flow over a porous stretching sheet

International Nuclear Information System (INIS)

Mahmood, R.; Sajid, M.

2007-01-01

This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a porous stretching sheet. The similarity solution of the problem is obtained using finite element method. The physical quantities of interest like the fluid velocity and skin friction coefficient is obtained and discussed under the influence of suction parameter and Hartman number. It is evident from the results that MHD can be used to control the boundary layer thickness. (author)

User's Manual for FEM-BEM Method. 1.0

Science.gov (United States)

Butler, Theresa; Deshpande, M. D. (Technical Monitor)

2002-01-01

A user's manual for using FORTRAN code to perform electromagnetic analysis of arbitrarily shaped material cylinders using a hybrid method that combines the finite element method (FEM) and the boundary element method (BEM). In this method, the material cylinder is enclosed by a fictitious boundary and the Maxwell's equations are solved by FEM inside the boundary and by BEM outside the boundary. The electromagnetic scattering on several arbitrarily shaped material cylinders using this FORTRAN code is computed to as examples.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik [Pusan National University, Busan (Korea, Republic of); Jeong, Hae Kwon [POSCO, Pohang (Korea, Republic of); Balachandar, S. [University of Florida, Florida (United States)

2013-02-15

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

International Nuclear Information System (INIS)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik; Jeong, Hae Kwon; Balachandar, S.

2013-01-01

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

Directory of Open Access Journals (Sweden)

S. S. Motsa

2013-01-01

Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

KAUST Repository

Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.

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.

hp Spectral element methods for three dimensional elliptic problems

Indian Academy of Sciences (India)

elliptic boundary value problems on non-smooth domains in R3. For Dirichlet problems, ... of variable degree bounded by W. Let N denote the number of layers in the geomet- ric mesh ... We prove a stability theorem for mixed problems when the spectral element functions vanish ..... Applying Theorem 3.1,. ∫ r l. |Mu|2dx −.

Productivity of a coral reef using boundary layer and enclosure methods

Science.gov (United States)

McGillis, W.R.; Langdon, C.; Loose, B.; Yates, K.K.; Corredor, Jorge

2011-01-01

The metabolism of Cayo Enrique Reef, Puerto Rico, was studied using in situ methods during March 2009. Benthic O2 fluxes were used to calculate net community production using both the boundary layer gradient and enclosure techniques. The boundary layer O2 gradient and the drag coefficients were used to calculate productivity ranging from -12.3 to 13.7 mmol O2 m-2 h-1. Productivity measurements from the enclosure method ranged from -11.0 to 12.9 mmol O2 m-2 h-1. During the study, the mean hourly difference between the methods was 0.65 mmol O2 m-2 h-1 (r2 = 0.92), resulting in well-reconciled estimates of net community production between the boundary layer (-33.1 mmol m-2 d-1) and enclosure (-46.3 mmol m-2 d-1) techniques. The results of these independent approaches corroborate quantified rates of metabolism at Cayo Enrique Reef. Close agreement between methods demonstrates that boundary layer measurements can provide near real-time assessments of coral reef health.

Application of Monte Carlo method to solving boundary value problem of differential equations

International Nuclear Information System (INIS)

Zuo Yinghong; Wang Jianguo

2012-01-01

This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

Variational boundary conditions based on the Nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled Cahn-Hilliard equation

Science.gov (United States)

Zhao, Ying; Schillinger, Dominik; Xu, Bai-Xiang

2017-07-01

The primal variational formulation of the fourth-order Cahn-Hilliard equation requires C1-continuous finite element discretizations, e.g., in the context of isogeometric analysis. In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn-Hilliard equation in primal variables. Our formulation is based on the symmetric variant of Nitsche's method, does not introduce additional degrees of freedom and is shown to be variationally consistent. In contrast to strong enforcement, the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree. In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions. Unfitted Cartesian B-spline meshes constitute an effective alternative to boundary-fitted isogeometric parametrizations for constructing C1-continuous discretizations, in particular for complex geometries. We combine our variational boundary condition formulation with unfitted Cartesian B-spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode. This example, involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces, demonstrates the flexibility of variational boundary conditions in the context of higher-order unfitted isogeometric discretizations.

A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

International Nuclear Information System (INIS)

Ackroyd, R.T.

1987-01-01

A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)