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Infinite Elements (infinite + element)

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Selected Abstracts

Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2003
Rie Sugimoto
Abstract The theory for coupling of mapped wave infinite elements and special wave finite elements for the solution of the Helmholtz equation in unbounded domains is presented. Mapped wave infinite elements can be applied to boundaries of arbitrary shape for exterior wave problems without truncation of the domain. Special wave finite elements allow an element to contain many wavelengths rather than having many finite elements per wavelength like conventional finite elements. Both types of elements include trigonometric functions to describe wave behaviour in their shape functions. However the wave directions between nodes on the finite element/infinite element interface can be incompatible. This is because the directions are normally globally constant within a special finite element but are usually radial from the ,pole' within a mapped wave infinite element. Therefore forcing the waves associated with nodes on the interface to be strictly radial is necessary to eliminate this internode incompatibility. The coupling of these elements was tested for a Hankel source problem and plane wave scattering by a cylinder and good accuracy was achieved. This paper deals with unconjugated infinite elements and is restricted to two-dimensional problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Mapped infinite elements for three-dimensional multi-region boundary element analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004
W. Moser
Abstract A formulation for an infinite boundary element (BE) is presented, which allows the modelling of infinite surfaces. The concept is that the finite surface is mapped to an infinite surface using special mapping functions. Using such mapping functions together with linear and quadratic interpolation for the displacements and the tractions, respectively, the desired decay behaviour can be modelled. The implementation of the proposed infinite elements becomes straightforward, since the Cauchy principal value, as well as the free term, are evaluated for the finite and infinite BEs with exactly the same techniques. The element developed can be used in a multi-region BE analysis of piecewise homogeneous domains, or for domains with joints and faults. The accuracy of the element is tested on some benchmark problems. Finally, a practical application in tunnelling is shown. Copyright © 2004 John Wiley & Sons, Ltd. [source]

The performance of spheroidal infinite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001
R. J. Astley
Abstract A number of spheroidal and ellipsoidal infinite elements have been proposed for the solution of unbounded wave problems in the frequency domain, i.e solutions of the Helmholtz equation. These elements are widely believed to be more effective than conventional spherical infinite elements in cases where the radiating or scattering object is slender or flat and can therefore be closely enclosed by a spheroidal or an ellipsoidal surface. The validity of this statement is investigated in the current article. The radial order which is required for an accurate solution is shown to depend strongly not only upon the type of element that is used, but also on the aspect ratio of the bounding spheroid and the non-dimensional wave number. The nature of this dependence can partially be explained by comparing the non-oscillatory component of simple source solutions to the terms available in the trial solution of spheroidal elements. Numerical studies are also presented to demonstrate the rates at which convergence can be achieved, in practice, by unconjugated-(,Burnett') and conjugated (,Astley-Leis')-type elements. It will be shown that neither formulation is entirely satisfactory at high frequencies and high aspect ratios. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Boundary elements for half-space problems via fundamental solutions: A three-dimensional analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001
J. Liang
Abstract An efficient solution technique is proposed for the three-dimensional boundary element modelling of half-space problems. The proposed technique uses alternative fundamental solutions of the half-space (Mindlin's solutions for isotropic case) and full-space (Kelvin's solutions) problems. Three-dimensional infinite boundary elements are frequently employed when the stresses at the internal points are required to be evaluated. In contrast to the published works, the strongly singular line integrals are avoided in the proposed solution technique, while the discretization of infinite elements is independent of the finite boundary elements. This algorithm also leads to a better numerical accuracy while the computational time is reduced. Illustrative numerical examples for typical isotropic and transversely isotropichalf-space problems demonstrate the potential applications of the proposed formulations. Incidentally, the results of the illustrative examples also provide a parametric study for the imperfect contact problem. Copyright © 2001 John Wiley & Sons, Ltd. [source]

An elastodynamic Galerkin Boundary Element Formulation for semi-infinite domains in time-domain

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
Lars Kielhorn
The present work focuses on the problem of modelling wave propagation phenomena within a 3,d elastodynamic halfspace by use of a symmetric Galerkin Boundary Element formulation. Unfortunately, this formulation requires the evaluation of hypersingular integral kernels which are regularized by integration by parts. In Boundary Element Methods semi,infinite domains are commonly approximated in space by considering just a sufficiently large enough region. Applying this simple discretization to the symmetric formulation implies the evaluation of the hypersingular bilinear form on a truncated mesh which will fail due to the regularization approach. To overcome this drawback a methodology based on infinite elements is presented. The numerical tests show that this approach is promising for treating semi,infinite domains with a symmetric Galerkin scheme. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]