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NUMERICAL STABILITY AND ACCURACY OF THE SCALED BOUNDARY FINITE ELEMENT METHOD IN ENGINEERING APPLICATIONS

Part of: General and miscellaneous specific topics Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 December 2015

MIAO LI ,
YONG ZHANG ,
HONG ZHANG  and
HONG GUAN
MIAO LI
Affiliation:
Griffith School of Engineering, Griffith University, Queensland 4222, Australia email hong.zhang@griffith.edu.au Engineering, Faculty of Business, Charles Sturt University, Bathurst, NSW 2795, Australia
YONG ZHANG
Affiliation:
Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui 230031, China
HONG ZHANG*
Affiliation:
Griffith School of Engineering, Griffith University, Queensland 4222, Australia email hong.zhang@griffith.edu.au
HONG GUAN
Affiliation:
Griffith School of Engineering, Griffith University, Queensland 4222, Australia email hong.zhang@griffith.edu.au
*
✉hong.zhang@griffith.edu.au
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Abstract

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The scaled boundary finite element method (SBFEM) is a semi-analytical computational method initially developed in the 1990s. It has been widely applied in the fields of solid mechanics, oceanic, geotechnical, hydraulic, electromagnetic and acoustic engineering problems. Most of the published work on SBFEM has focused on its theoretical development and practical applications, but, so far, no explicit discussion on the numerical stability and accuracy of its solution has been systematically documented. However, for a reliable engineering application, the inherent numerical problems associated with SBFEM solution procedures require thorough analysis in terms of its causes and the corresponding remedies. This study investigates the numerical performance of SBFEM with respect to matrix manipulation techniques and their properties. Some illustrative examples are given to identify reasons for possible numerical difficulties, and corresponding solution schemes are proposed to overcome these problems.

Keywords

SBFEMnumerical stability and accuracymatrix decompositionnondimensionalizationengineering application

MSC classification

Primary: 65M12: Stability and convergence of numerical methods
Secondary: 65M38: Boundary element methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 00A73: Dimensional analysis
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 2 , October 2015 , pp. 114 - 137
Copyright
© 2015 Australian Mathematical Society 

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