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Jacqueline A. Bettess

Bio: Jacqueline A. Bettess is an academic researcher from Durham University. The author has contributed to research in topics: Symbolic computation & Finite element method. The author has an hindex of 3, co-authored 3 publications receiving 25 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the theory for an improved wave element for wave diffraction is presented, which is based on the original wave element presented by Bettess, Zienkiewicz and others.

20 citations

Journal ArticleDOI
TL;DR: The method and how REDUCE is used to easily produce numerical code for C 0 continuous basis functions for use in the finite element method when the elements extend to infinity in one or more directions are described.

3 citations

Book ChapterDOI
01 Jan 1987
TL;DR: This paper shows how the use of an automatic symbolic algebraic manipulation system can greatly reduce the work involved in the generation of shape functions and their derivatives for finite element analyses.
Abstract: In this paper we show how the use of an automatic symbolic algebraic manipulation system can greatly reduce the work involved in the generation of shape functions and their derivatives for finite element analyses. The system used is called REDUCE and is available for most IBM and VAX machines. REDUCE can carry out algebraic operations on rational functions accurately, no matter how complicated the expression becomes and also produce the output in the form of a FORTRAN program. The power of the system is demonstrated by giving the code required to generate most of the one and two dimensional families of C0 continuoxis shape functions. The resulting FORTRAN code for the shape function and shape function derivatives are given for the 6 node triangular element. The advantages and disadvantages of using such a system are also considered.

3 citations


Cited by
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Journal ArticleDOI
TL;DR: In this article, a general computational scheme is implemented in which orthogonal functions are used for the transverse interpolation within the infinite element region, and a procedure is presented for assessing their performance.
Abstract: Infinite element schemes for unbounded wave problems are reviewed and a procedure is presented forassessing their performance. A general computational scheme is implemented in which orthogonal functions are used for the transverse interpolation within the infinite element region. This is used as a basis for numerical studies of the effectiveness of various combinations of the radial test and trial functions which give rise to different conjugated and unconjugated formulations. Results are presented for the test case of a spherical radiator to which infinite elements are directly attached. Accuracy of the various schemes is assessed for pure multipole solutions of arbitrary order. Previous studies which have indicated that the conjugated and unconjugated schemes are more effective in the far and near fields, respectively, are confirmed by the current results. All of the schemes tested converge to the exact solution as radial order increases. All are however susceptible to ill conditioning. This places practical restrictions on their effectiveness at high radial orders. A close relationship is demonstrated between the discrete equations which arise from first-order infiniteelement schemes and those derived from the application of more traditional, local non-reflecting boundary conditions. Copyright © 2000 John Wiley & Sons, Ltd.

244 citations

Journal ArticleDOI
TL;DR: In this article, a finite element model for the solution of Helmholtz problems at higher frequencies is described, which offers the possibility of computing many wavelengths in a single finite element.
Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

131 citations

Book
01 Jan 2003
TL;DR: Transliteration of Russian names has essentially followed the system adopted by the Library of Congress, but with no distinction between e and e or between Η and fi, and with yu used for κ> and ya for H .
Abstract: Editors' note: In the references cited we have used, as far as possible, the abbreviations for journals and reports used by Chemical Abstracts. A list of these abbrevi­ ations may be found in the List of Periodicals of the Chemical Abstracts Service published by the American Chemical Society. Transliteration of Russian names has essentially followed the system adopted by the Library of Congress, but with no distinction between e and e or between Η and fi, and with yu used for κ> and ya for H . In the case of books translated from Russian into English the transliterated author names are those appearing on the translation. Russian titles have been translated into English, but where a translation is indicated the title given is that appearing on the translated version. A source of an English translation for all cited Russian references has been given whenever known to the editors.

61 citations

Journal ArticleDOI
TL;DR: In this article, the authors used the computer algebra system MATHEMATICA for the SAN (semi-analytical/numerical) solution of two simple elasticity problems, having been reduced to systems of linear algebraic equations by the finite element method.
Abstract: The computer algebra system MATHEMATICA is used for the SAN (semi-analytical/numerical) solution of two simple elasticity problems, having been reduced to systems of linear algebraic equations by the finite element method. In both cases, one parameter was left in symbolic form and Taylor series expansions with respect to this parameter (either a material constant or a geometric parameter) were used in the SAN results. The Gauss-Seidel iterative method for systems of linear equations and its SOR variant were used for the solution of the systems of linear equations always in the SAN environment offered by MATHEMATICA. The SAN results were compared with the corresponding numerical results and they were found to be equally acceptable. The present approach, which can be generalized in a variety of ways, offers the advantage (over purely numerical techniques) that it permits the incorporation of symbolic parameters into the results of the finite element method.

29 citations

Journal ArticleDOI
TL;DR: A semi-analytical solution method, the scaled boundary finite element method (SBFEM), was developed for the two-dimensional Helmholtz equation in this article, which is applicable to 2D computational domains of any shape including unbounded domains.

26 citations