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The general boundary element method and its further generalizations
Author(s) -
Liao ShiJun
Publication year - 1999
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19991015)31:3<627::aid-fld894>3.0.co;2-9
Subject(s) - boundary element method , mathematics , boundary (topology) , calculus (dental) , numerical analysis , element (criminal law) , boundary value problem , finite element method , mathematical analysis , physics , medicine , dentistry , political science , law , thermodynamics
In this paper, the basic ideas of the general boundary element method (BEM) proposed by Liao [in Boundary Elements XVII , Computational Mechanics Publications, Southampton, MA, 1995, pp. 67–74; Int. J. Numer. Methods Fluids , 23 , 739–751 (1996), 24 , 863–873 (1997); Comput. Mech. , 20 , 397–406 (1997)] and Liao and Chwang [ Int. J. Numer. Methods Fluids , 23 , 467–483 (1996)] are further generalized by introducing a non‐zero parameter $\hbar$ . Some related mathematical theorems are proposed. This general BEM contains the traditional BEM in logic, but is valid for non‐linear problems, including those whose governing equations and boundary conditions have no linear terms. Furthermore, the general BEM can solve non‐linear differential equations by means of no iterations. This disturbs the absolutely governing place of iterative methodology of the BEM for non‐linear problems. The general BEM can greatly enlarge application areas of the BEM as a kind of numerical technique. Two non‐linear problems are used to illustrate the validity and potential of the further generalized BEM. Copyright © 1999 John Wiley & Sons, Ltd.