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Journal ArticleDOI

A new mapped infinite wave element for general wave diffraction problems and its validation on the ellipse diffraction problem

02 Oct 1998-Computer Methods in Applied Mechanics and Engineering (North-Holland)-Vol. 164, pp 17-48
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.
About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1998-10-02. It has received 20 citations till now. The article focuses on the topics: Diffraction & Surface wave.
Citations
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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

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

Journal ArticleDOI
Yuan Yuan1, Jianke Qiang1, Jingtian Tang1, Zhengyong Ren1, Xiao Xiao1 
TL;DR: In this article, a finite-element-infinite-element coupled method was proposed to reduce the computation time and memory cost in the 2.5D direct-current resistivity inversion.
Abstract: To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite-element–infinite-element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct-current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite-element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi-pole potentials can be swiftly obtained by simple back-substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.

9 citations

Journal ArticleDOI
Isaac Harari1
TL;DR: A novel approach to infinite element formulations is presented, leading to various approximations for two-dimensional configurations with circular interfaces, and numerical results demonstrate the good performance of these schemes.

9 citations

References
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Book
01 Jan 1989
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08

17,327 citations

Book
01 Jan 1964

2,100 citations

Book
01 Jan 1983
TL;DR: In this article, the authors present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from a deterministic point of view, and the bulk of the material deals with the linearized theory.
Abstract: The aim of this book is to present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from the deterministic point of view. The bulk of the material deals with the linearized theory.

2,003 citations

Book
01 Jan 1949

1,445 citations

Journal ArticleDOI
TL;DR: In this article, a sequence of radiating boundary conditions is constructed for wave-like equations, and it is proved that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r exp -m-1/2) for the m-th boundary condition.
Abstract: In the numerical computation of hyperbolic equations it is not practical to use infinite domains; instead, the domain is truncated with an artificial boundary. In the present study, a sequence of radiating boundary conditions is constructed for wave-like equations. It is proved that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r exp -m-1/2) for the m-th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature of the boundary conditions.

999 citations