Isogeometric Boundary Element Method for the Simulation in Tunneling

2014 ◽  
Vol 553 ◽  
pp. 495-500 ◽  
Author(s):  
Benjamin Marussig ◽  
Gernot Beer ◽  
Christian Duenser
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Mechanical Engineering ◽  
Boundary Element Methods ◽  
Infinite Domain ◽  
Research Software ◽  
Element Method

Isogeometric finite element methods and more recently boundary element methods have been successfully applied to problems in mechanical engineering and have led to an increased accuracy and a reduction in simulation effort. Isogeometric boundary element methods have great potential for the simulation of problems in geomechanics, especially tunneling because an infinite domain can be considered without truncation. In this paper we discuss the implementation of the method in the research software BEFE++. Based on an example of a spherical excavation we show that a significant reduction in the number of parameters for describing the excavation boundary as well as an improved quality of the results can be obtained.

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

OPTIMAL SOURCE LOCATIONS FOR VARIOUS GEOMETRIES FOR ACOUSTIC REFLECTORS BY BOUNDARY ELEMENT METHODS

1994 ◽  
Vol 02 (04) ◽  
pp. 423-439
Author(s):  
RICHARD PAUL SHAW ◽  
PAUL VAN SLOOTEN ◽  
MATTHEW NOBILE
Keyword(s):  
Boundary Element Method ◽  
Point Source ◽  
Boundary Element ◽  
Boundary Element Methods ◽  
Center Line ◽  
Rectangular Enclosure ◽  
Acoustic Problem ◽  
Large Opening ◽  
Acoustic Space ◽  
Element Method

A boundary element method (BEM) approach is used to solve the acoustic problem of a point source within an enclosure with a large opening to an infinite (without a baffle) or semi-infinite (with a baffle) acoustic space. Emphasis is placed on 2D models with the source located along the center line of three types of geometries: a wedge, a parabola, and a rectangular enclosure.

A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions

2012 ◽  
Vol 11 (2) ◽  
pp. 573-593 ◽  
Author(s):  
S. N. Chandler-Wilde ◽  
S. Langdon ◽  
M. Mokgolele
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Incident Wave ◽  
Degrees Of Freedom ◽  
Boundary Element Methods ◽  
Convex Polygons ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Element Method

AbstractWe consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

scholarly journals Boundary element methods for particles and microswimmers in a linear viscoelastic fluid

2017 ◽  
Vol 831 ◽  
pp. 228-251 ◽  
Author(s):  
Kenta Ishimoto ◽  
Eamonn A. Gaffney
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Maxwell Fluid ◽  
Finite Amplitude ◽  
Deborah Number ◽  
Boundary Element Methods ◽  
Reciprocal Relation ◽  
Surface Boundary ◽  
Linear Viscoelastic ◽  
Element Method

The consideration of viscoelasticity within fluid dynamical boundary element methods has traditionally required meshing over the whole flow domain. In turn, a major advantage of the boundary element method is lost, namely the need to consider only surface boundary integrals. Here, using a generalised reciprocal relation and viscoelastic force singularities, a boundary element method is developed for linear viscoelastic flows. We proceed to explore finite-deformation microswimming in a linear Maxwell fluid. We firstly deduce a finite-amplitude generalisation of a previously reported result that the flow field is unchanged between a Newtonian and linear Maxwell fluid for prescribed small-amplitude deformations. Hence Purcell’s theorem holds for a linear Maxwell fluid. We proceed to consider deformation swimming in a linear Maxwell fluid given an external forcing. Boundary scattering trajectories for an exemplar squirmer approaching a surface are observed to exhibit a weak dependence on the Deborah number, while the trajectories of a sperm and monotrichous bacterium near a surface are predicted to be essentially unaffected at moderate Deborah number. In turn, the latter supports the common simplification of using Newtonian Stokes flows for studying flagellate swimming in linear Maxwell media. In addition, the motion of a magnetic helix under the influence of an external magnetic field is considered, and highlights that linear viscoelasticity can significantly impact the propagation of the helix, in turn demonstrating that even linear rheology is important to consider for forced swimmers. Finally, the presented framework requires minimalistic adjustments to Newtonian boundary element codes, enabling rapid implementation, and is more generally applicable, for instance to studies of particle interactions in active linear rheology on the microscale.

THE VARIATIONAL INDIRECT BOUNDARY ELEMENT METHOD: A STRATEGY TOWARD THE SOLUTION OF VERY LARGE PROBLEMS OF SITE RESPONSE

2001 ◽  
Vol 09 (02) ◽  
pp. 531-541 ◽  
Author(s):  
FRANCISCO J. SÁNCHEZ-SESMA ◽  
ROSSANA VAI ◽  
ELINA DRETTA
Keyword(s):  
Boundary Element Method ◽  
Dimension Reduction ◽  
Boundary Element ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Force Density ◽  
Indirect Boundary Element Method ◽  
Starting Point ◽  
Complete Set ◽  
Element Method

Boundary integral equation approaches and their discretization into boundary element methods (BEM) have been useful to obtain solutions for numerous problems in dynamic elasticity. Well documented advantages over domain approaches are dimension reduction, relatively easy fulfillment of radiation conditions at infinity, and high accuracy of results. In spite of dimension reduction, the computational cost at high frequencies may easily exceed the capacity of computing facilities. To overcome this problem, Galerkin's ideas may be used. The Indirect Boundary Element Method (IBEM) equations are the starting point of the proposed methodology. The boundary force density is expanded in terms of a complete set of functions. Weighting functions from the same complete set are used to minimize the error of this approximation. Once a significant subset is selected, the size of the resulting linear system is much smaller than that of the IBEM method as currently applied. Moreover, with appropriate trial functions, some matrix operations can be reduced to Fourier transformations. In what follows, the formulation and some examples for scalar problems are presented. Simple 2-D topographies are studied, but the extension to 3-D realistic configurations may well be treated on the same basis.

Least Squares – Boundary Element Method of Calculating Minimum Anisotropic Stress and Displacement

2014 ◽  
Vol 900 ◽  
pp. 703-706
Author(s):  
Wei Zhang
Keyword(s):  
Boundary Element Method ◽  
Least Squares ◽  
Boundary Element ◽  
Laurent Series ◽  
Least Squares Method ◽  
Elastic Plane ◽  
Infinite Domain ◽  
Calculation Results ◽  
Anisotropic Elastic ◽  
Element Method

The boundary element method , combined with the least squares method is proposed to determine the anisotropic elastic plane Laurent series of coefficients a boundary element method of least squares . This method sets the boundary element method and Laurent series method is a long one, not only high accuracy, while access to the plane problem abundance analytical solutions to the infinite domain oval hole of stress concentration problems as an example, the results of the calculation results with the analytical solution compared to illustrate the method is to solve the proble of elastic plane an effective way .

A Meshless Boundary Element Method for Simulating Slamming in Context of Generalized Wagner

2013 ◽  
Author(s):  
Jens B. Helmers ◽  
Geir Skeie
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Boundary Element ◽  
The Body ◽  
Boundary Element Methods ◽  
Body Contour ◽  
Smooth Body ◽  
Body Velocity ◽  
Body Location ◽  
Element Method

A boundary element method designed for solving the symmetric Generalized Wagner formulation is presented. The flow field is parameterized with analytical functions and can describe the kinematics at any free surface or body location using a small set of parameters obtained from a collocation scheme. The method is fast and robust for all deadrise angles, even for flat plate impacts where classical boundary element methods usually fails. The method is easy to implement and is easy to apply. Given a smooth body contour the only additional input is the requested accuracy. There is no mesh involved. When solving the temporal problem we exploit the analytical distribution of free surface velocities and apply an integral equation formalism consistent with the Wagner formulation. The output of the spatial and temporal scheme is a set of functions and parameters suitable for fast computation of the complete kinematics for any impact trajectory given the position of the keel and the body velocity. The method is developed to be combined with seakeeping programs for statistical impact and whipping assessment.

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

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150216 ◽  
Author(s):  
Elena Atroshchenko ◽  
Stéphane P. A. Bordas
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Couple Stress ◽  
Edge Crack ◽  
Fundamental Solutions ◽  
Boundary Element Methods ◽  
Griffith Crack ◽  
Cosserat Elasticity ◽  
Crack Problems ◽  
Element Method

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.

scholarly journals The Boundary Element Method in Acoustics: A Survey

2019 ◽  
Vol 9 (8) ◽  
pp. 1642 ◽  
Author(s):  
Kirkup
Keyword(s):  
Integral Equation ◽  
Computational Complexity ◽  
Boundary Element Method ◽  
Inverse Problems ◽  
Boundary Element ◽  
Integral Operators ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Software Library ◽  
Element Method

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

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