Schur decomposition in the scaled boundary finite element method in elastostatics

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Title Schur decomposition in the scaled boundary finite element method in elastostatics
Author Li, Miao; Song, Hao; Guan, Hong; Zhang, Hong
Publication Title 9th World Congress on Computational Mechanics and 4th Asian Pacific Congress on Computational Mechanics
Editor Nasser Khalili
Year Published 2010
Place of publication United Kingdom
Publisher IOP Publishing
Abstract The scaled boundary finite element method (SBFEM) was originally proposed for modelling elastodynamics in bounded and unbounded media. The method has demonstrated its superiority to the finite element method and the boundary element method when dealing with problems involving unbounded computational domains, or with difficulties of irregular frequencies and sharp corners. The SBFEM transforms the governing equations from partial differential equations to ordinary differential equations (ODEs). In addition, only the boundary of the study domain needs to be discretised which significantly reduces the computational cost. In the existing solution procedure, an eigenvalue problem of the Hamiltonian matrix, formulated from the coefficient matrices of ODEs, needs to be solved. Subsequently, the eigenvectors of the Hamiltonian matrix are arranged in a matrix form for the stiffness matrix in the nodal force-displacement relationship. However, the matrix formulated by the eigenvectors is close to singular when multiple eigenvalues with parallel eigenvectors exist, which leads to an inaccurate solution. In the present study, this problem is eliminated by using the Schur decomposition instead of the eigenvalue decomposition. A three-dimensional study of a cylindrical pile subjected to uniformly distributed load, is carried out. The performance and efficiency of the Schur decomposition are discussed in some detail for achieving more accurate solutions in using the SBFEM.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1088/1757-899X/10/1/012243
Copyright Statement Copyright 2010 IOP Publishing Ltd. The attached file is reproduced here in accordance with the copyright policy of the publisher. For information about this conference please refer to the conference's website or contact the authors.
ISBN 1757-899X
Conference name 9th World Congress on Computational Mechanics & 4th Asian Pacific Congress on Computational Mechanic
Location Sydney, Australia
Date From 2010-07-19
Date To 2010-07-23
URI http://hdl.handle.net/10072/35569
Date Accessioned 2010-06-22
Date Available 2011-06-07T06:55:58Z
Language en_AU
Research Centre Centre for Infrastructure Engineering and Management
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Numerical and Computational Mathematics; Ship and Platform Hydrodynamics
Publication Type Conference Publications (Full Written Paper - Refereed)
Publication Type Code e1

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